Conference submissions

Darboux transformation and soliton solutions for the two-dimensional complex modif ied Korteweg-de Vries equations
Kuralay Yesmakhanova, Eurasian National University, Department of Higher Mathematics, Kazakhstan
Gaukhar Shaikhova, Eurasian National University, General and Theoretical physics, Kazakhstan
Guldana Bekova, Eurasian National University, , Kazakhstan
Ratbay Myrzakulov, Eurasian National University, , Kazakhstan
Abstract: In this paper, we consider the two-dimensional complex modi fied Korteweg-de Vries equations (CMKdVE). Using the Lax pair, we construct the Darboux transformation. The soliton solutions are obtained from the di erent "seeds" by using the Darboux transformation.
Evaluation of the implementation of entrepreneurial potential (on the example of the Republic of Tatarstan)
Diana Rakhmatullina, Kazan (Volga region) Federal University, Department of Economic Methodology and History, Russian Federation
Gulshat Guzelbaeva, Kazan (Volga region) Federal University, Department of financial management, Russian Federation
Elvira Akhmetshina, Kazan (Volga region) Federal University, Department of Economic Methodology and History, Russian Federation
Abstract: Increase in the number of small businesses and the lack of effectiveness of existing support at local and regional level have led to curb the development of entrepreneurial activity. The article presents the methodological tools for assessing the effectiveness, which allows to identify existing municipalities in the advantages and disadvantages for the implementation of entrepreneurial potential, including the effectiveness of state and municipal support measures, as well as calculate the degree of progress in the implementation of entrepreneurial potential In order to evaluate the implementation of the business potential of the Republic of Tatarstan and the impact of their public support at the regional level was calculated indexes of business activity in the municipal districts (MD) of the republic. Business activity is estimated using relative indicators such as the number of SMEs in the 10 th. Residents output by 1 company, and others., To achieve comparability of data and evaluate the business activity of all MP, regardless of their size. Results of calculation are grouped by six economic zones, which allowed to identify the most developed areas of the country. It should be noted that a major breakthrough in share of small and medium-sized businesses is important to the whole ecosystem. The method of evaluation of the implementation of entrepreneurial potential which is presented in this paper can be used by every competent organizations to analyze and form the effective programs of the economic and finance development.
Dynamics of LRS Bianchi type-I cosmological model in $f(R,T)$ gravity
Pradyumn Sahoo, BITS-Pilani, Hyderabad Campus, Mathematics, India
Abstract: A spatially homogeneous anisotropic LRS Bianchi type-I cosmological model is studied in $f(R,T)$ gravity with a special form of Hubble's parameter, which leads to constant deceleration parameter. The parameters involved in the considered form of Hubble parameter can be tuned to match, our models with the $\Lambda $CDM model. With the present observed value of the deceleration parameter, we have discussed physical and kinematical properties of a specific model. Moreover, we have discussed the cosmological distances for our model.
Modeling of multidimensional light bullets in Fermi liquid and ADS/CFT correspondence
Natalia Konobeeva, Volgograd State University, Information systems and computer modeling, Russian Federation
Abstract: In this work we investigate the propagation of two-dimensional and three-dimensional solitary electromagnetic waves in a Fermi liquid with taking into account the ADS/CFT correspondence approach. Electromagnetic field is considered in the basis of Maxwell’s equations. We obtain an effective equation, which is numerically analysed. And the state of the electromagnetic field which is localized in two/three spatial dimensions is revealed. Also the stability of the obtained solutions with respect to perturbations that depend on the angle is analyzed.
Acknowledgements: This This work was supported by the Russian Ministry for Education and Science (under the Project No. MK-4562.2016.2) and by the Russian Foundation for Fundamental Research (Grant No.16-07-01265 A). Numerical modeling was carried out in the framework of the state assignment of the Ministry of Education and Science (project no. 2.852.2017/PCh).
MODELING OF TERMONIKETIC OSCILLATIONS AT PARTIAL OXIDATION OF METHANE
Artem Arutyunov, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics (CMC), Russian Federation
Andrey Belyaev, Semenov Institute of Chemical Physics of Russian Academy of Sciences, Kinetic and catalysis, Russian Federation
Igor Inovenkov, Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics (CMC), Russian Federation
Vladimir Nefedov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Abstract: Partial oxidation of natural gas at moderate temperatures below 1500 K has significant interest for a number of industrial applications. But such processes can proceed at different unstable regimes including oscillating modes. Non-linear phenomena at partial oxidation of methane were observed at different conditions. The investigation of the complex non-linear system of equations that describes this process is a real method to insure its stability at industrial conditions and, at the same time, is an effective tool for its further enhancement. Numerical analysis of methane oxidation kinetics in the continuous stirred-tank reactor, with the use of detailed kinetic model has shown the possibility of the appearance of oscillating modes in the appropriate range of reaction parameters, that characterize the composition, pressure, reagents flow, thermalphysic features of the system, and geometry of the reactor. The appearance of oscillating modes is connected both with the reaction kinetics, heat release and sink and reagents introduction and removing. At that, oscillations appear only at a limited range of parameters, but can be accompanied by significant change in the yield if products. We have determined the range of initial temperature and pressure at which oscillations can be observed, if all other parameters remained fixed. The boundaries of existence of oscillations on the phase plane were calculated. It was shown that depending on the position inside the oscillation region the oscillations have different frequency and amplitude. It was reviled the role of heat exchange with the environment: at the absence of heat exchange the oscillating modes are impossible. In the vicinity of the boundary of phase range, where oscillations exist, the very strong change of concentration of some products were observed, for example, that of CO2, which in this case is one of the principal products. At that, insignificant increase in pressure not only change the character of CO2 behaving with time, but as well lead to significant increase of its mole fraction simultaneously twice decreasing mole fraction of CO.
Restoration of valence density of states from XPS spectra
Andrey Krasavin, National Research Nuclear University MEPhI, Physics of Metrology, Russian Federation
Vladimir Kashurnikov, National Research Nuclear University MEPhI, , Russian Federation
Yaroslav Zhumagulov, National Research Nuclear University MEPhI, Solid state physics, Russian Federation
Abstract: Low-dimensional structures such as thin films, nanotubes, and nanoclusters, being in an intermediate position between single atoms and bulk materials, possess unique physical properties that can separate them in a special area of condensed matter physics. The practical use of low-dimensional structures and those consisting of transition metals in particular, is based on the features of their electronic properties due to crystal structure. The necessity of the accounting of electron correlations leads to considerable complexity of the theoretical description of such systems; in the case of transition metal structures of reduced dimensionality, the description of the electronic properties is an even more difficult task. For this reason, the development of experimental and numerical methods for the study of the electronic properties of nanoscale structures is an urgent task. We propose the technique of restoring the valence density of states from X-ray photoelectron spectra for such low-dimensional structures. The technique uses a stochastic optimization method, which accurately takes into account the broadening of a XPS-spectrometer. XPS spectra of a sample in the region of valence states allowed us to obtain the instrument function of the spectrometer. Further, the stochastic procedure was applied to restore the density of states by solving an integral equation. This technique was applied to calculate the valence density of states of various metal nanoclusters. The key feature of the method, distinguishing it from first-principles calculations, is that it is not necessary to take into account the crystal structure of nanoclusters. This advantage allows one to use the method for determining the dependence of the properties of low-dimensional structures on their characteristic size.
Magnetic reconnection in terms of catastrophe theory
Igor Inovenkov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Evgenia Echkina, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Vladimir Nefedov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Abstract: Magnetic field line reconnection (magnetic reconnection) is a phenomenon that occurs in space and laboratory plasma. Magnetic reconnection allows both the change the magnetic topology and the conversion of the magnetic energy into energy of fast particles. The critical point (critical line or plane in higher dimensional cases) of the magnetic field play an important role in process of magnetic reconnection, as in its neighborhood occurs a change of its topology of a magnetic field and redistribution of magnetic field energy. A lot of literature is devoted to the analytical and numerical investigation of the reconnection process. The main result of these investigations as the result of magnetic reconnection the current sheet is formed and the magnetic topology is changed. While the studies of magnetic reconnection in 2D and 3D configurations have a led to several important results, many questions remain open, including the behavior of a magnetic field in the neighborhood of a critical point of high order. The magnetic reconnection problem is closely related to the problem of the structural stability of vector fields. Since the magnetic field topology changes during both spontaneous and induced magnetic reconnection, it is natural to expect that the magnetic field should evolve from a structurally unstable into a structurally stable configuration. Note that, in this case, the phenomenon under analysis is more complicated since, during magnetic reconnection in a highly conducting plasma, we deal with the non-linear interaction between two vector fields: the magnetic field and the field of the plasma velocities. The aim of our article is to consider the process of magnetic reconnection and transformation of the magnetic topology from the viewpoint of catastrophe theory. Bifurcations in similar configurations (2D magnetic configuration with null high order point) with varying parameters were thoroughly discussed in a monograph by Poston and Stewart.
Application of the multicriterion optimization techniques and hierarchy of computational models to the research of ion acceleration due to laser-plasma interaction
Evgenia Echkina, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Igor Inovenkov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Vladimir Nefedov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Liubov Ponomarenko, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Abstract: In this paper we discuss how a particles-in-cell computation code can be combined with methods of multicriterion optimization (in particular the Pareto optimal solutions of the multicriterion optimization problem) and a hierarchy of computational models approach to create an efficient tool for solving a wide array of problems related to the laser-plasma interaction. In case of the computational experiment the multicriterion optimization can be applied as follows: the researcher defines the objectives of the experiment - some computable scalar values (i.e. high kinetic energy of the ions leaving the domain, least possible number of electrons leaving domain in the given direction, etc). After that the parameters of the experiment which can be varied to achieve these objectives and the constrains on these parameters are chosen (e.g. amplitude and wave-length of the laser radiation, dimensions of the plasma slab(s)). The Pareto optimality of the vector of the parameters can be seen as this: x(0) is Pareto optimal if there exists no vector which would improve some criterion without causing a simultaneous degradation in at least one other criterion. These efficient set of parameter and constrains can be selected based on the preliminary calculations in the simplified models (one or two-dimensional) either analytical or numerical. The multistage computation of the Pareto set radically reduces the number of variants which are to be evaluated to achieve the given accuracy. During the final stage we further improve the results by recomputing some of the optimal variants on the finer grids, with more particles and/or in the frame of a more detailed model. As an example we have considered the ion acceleration caused by interaction of very intense and ultra-short laser pulses with plasmas and have calculated the optimal set of experiment parameters for optimizing number and average energy of high energy ions leaving the domain in the given direction and minimizing the expulsion of electrons.
Computer simulation of population dynamics inside the urban environment
Alex Andreev, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Evgenia Echkina, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Igor Inovenkov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Vladimir Nefedov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Liubov Ponomarenko, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Vasilij Tikhomirov, Moscow State University, Computational Mathematics & Cybernatics, Russian Federation
Abstract: In this paper using a mathematical model of the so-called “space-dynamic” approach we investigate the problem of development and temporal dynamics of different urban population groups. For simplicity we consider an interaction of only two population groups inside a single urban area with axial symmetry. This problem can be described qualitatively by a system of two non-stationary nonlinear differential equations of the diffusion type with boundary conditions of the third type. The results of numerical simulations show that with a suitable choice of the diffusion coefficients and interaction functions between different population groups we can receive different scenarios of population dynamics: from complete displacement of one population group by another (originally more “aggressive”) to the “peaceful” situation of co-existence of them together.
Calculation of electron density of states for ensemble of gold nanoclusters
Yaroslav Zhumagulov, National Research Nuclear University MEPhI, Solid state physics, Russian Federation
Vladimir Kashurnikov, National Research Nuclear University MEPhI, , Russian Federation
Andrey Krasavin, National Research Nuclear University MEPhI, Physics of Metrology, Russian Federation
Abstract: Ensembles of metal nanoclusters are characterized by unique physical and chemical properties. These properties differ from the properties of both bulk metals and individual atoms, and currently are studied with particular intensity due to numerous potential applications in physics, chemistry, and engineering. There is a wide choice of well-established techniques designed by now of obtaining ensembles of metal nanoclusters, but a significant gap exists in explaining the properties of ensembles of nanoclusters, such as thermal emf, conductivity, thermal conductivity, and other thermodynamic parameters, and their dependence on the size of nanoclusters. This is primarily due to difficulty in taking account of electron correlations in such systems. Existing universally accepted methods of studying the electronic structure of many-body systems, such as density functional theory and quantum Monte Carlo algorithms, encounter serious difficulties associated with the need to take into account a large number of elements of a system. Such calculations are extremely resource and time consuming. In this work, we develop a method, which is much less resource consuming, and is able effectively to take into account the heterogeneity of the ensemble of nanoclusters, reducing the problem to the one of a single isolated nanocluster. According to the cluster perturbation theory, we have calculated the density of states of an isolated nanocluster and constructed its bonds with other nanoclusters with the use of the strong coupling perturbation theory. The method was applied to calculate the properties of ensemble of gold nanoclusters: density of single-particle electron states, the Seebeck coefficient, specific heat, and conductivity.
Dissipative gravitational bouncer on a vibrating surface
Julio S Espinoza-Ortiz, Universidade Federal de Goiás, Physics, Brazil
Roberto E Lagos, Instituto de Geociências e Ciências Exats, UNESP, Physics, Brazil
Abstract: We study the dynamical behavior of a particle flying under the influence of a gravitational field, with dissipation constant {$\lambda$} (Stokes-like), and colliding successive times against a rigid surface vibrating harmonically with restitution coefficient {$\alpha$}. We define re-scaled dimensionless dynamical variables, such as the relative particle velocity {$\Omega$} with respect to the surface's velocity; and the real parameter {$\tau$} accounting for the temporal evolution of the system. At the particle-surface contact point and for the {$k'th$} collision, we construct the mapping described by {$\left(\tau_{k}\,,\Omega_{k}\right)$} in order to analyze the system's nonlinear dynamical behavior. From the dynamical mapping, the fixed point trajectory is computed and its stability is analyzed. We find the dynamical behavior of the fixed point trajectory to be stable or unstable, depending on the values of the re-scaled vibrating surface amplitude {$\Gamma$}, the restitution coefficient {$\alpha$} and the damping constant {$\lambda$}. Other important dynamical aspects such as the phase space volume and the one cycle vibrating surface (decomposed into absorbing and transmitting regions) are also discussed. Furthermore, the model rescues well known results in the limit {$\lambda\,=\,0$}\,.
Acknowledgements: The authors would like to thank the support of the Goi\'as Research Foundation - FAPEG.
Mathematical modelling of elementary trapping-modification processes in positron-electron annihilation lifetime spectroscopy
Yaroslav Shpotyuk, University of Rzeszow, Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge , Poland
Jozef Cebulski, University of Rzeszow, , Poland
Adam Ingram, Opole University of Technology, , Poland
Oleh Shpotyuk, Institute of Physics of Jan Dlugosz University of Czestochowa, Department of Structural Study and Medical Physics, Poland
Abstract: Methodological possibilities of positron annihilation lifetime spectroscopy applied to characterize different types of nanostructured materials treated within three-term fitting procedure are critically reconsidered in order to parameterize their atomic-deficient structure. In contrast to conventional three-term analysis based on admixed positron- and positronium-trapping modes, the process of nanostructurization due to guest inserted within the same host matrix is considered as modified trapping, which involves (i) reduction, (ii) enhancement or (iii) conversion between positron- and positronium-decaying channels. The developed formalism referred to as x3-x2-CDA (coupling decomposition algorithm) allows estimation the volumes of interfacial voids (holes) responsible for positron trapping and characteristic bulk lifetimes in nanoparticle-affected media.
Simulation of the process of thermalization of a weakly interacting Bose gas by kinetic equations
Iliya Kuznetsov, National Research Nuclear University MEPhI, Department of Physics of Solid State and Nanosystems, Russian Federation
Abstract: In this paper we investigate the influence of the interparticle interaction on the process of thermalization of a weakly interacting Bose gas. We give a numerical solution with a system of kinetic equations based on the application of the "Fermi golden rule" and consider the distribution function of particles in the system as a function of various types of interactions, including taking into account the energy exchange with the thermostat, i.e. the interaction with the phonon subsystem. The possibility of establishing a Bose-Einstein condensate in a system with optimal parameters is also discussed.
A new algorithm to sovle nonlocal nonlinear Schrodinger equation
QI GUO, South China Normal University, School of Information and Photoelectronic Science and Engineering, China
Abstract: The propagation of the optical beam in the nonlocal nonlinear media is modeled by the nonlocal nonlinear Schrodinger equation, and the Hermit-Gaussian- like soliton solution (multi-peak soliton solution, MPSS) exists for the strongly nonlocal case. However, it has some limitations to obtain the numerical solutions of the MPSS by the algorithms used, such as the Newton iteration algorithm and the imaginary-time method. We find a new easy and convenient algorithm based on perturbation method for the Schrodinger equation in quantum mechanics to find the numerical MPSS fastly. We can use the algorithm to obtain the numerical MPSS for any response function and in any degree of nonlocality as long as the soliton solution exists. Moreover, the precision of the solutions can be improved by adding higher order perturbation.
Kinetics models describing degradation-relaxation effects in nanoinhomogeneous substances
Oleh Shpotyuk, Institute of Physics of Jan Dlugosz University of Czestochowa, Department of Structural Study and Medical Physics, Poland
Valentina Balitska, Lviv State University of Life Safety, , Ukraine
Michael Brunner, TH Koln, , Germany
Abstract: Disordered solids prepared by rapid cooling from high-temperature fluid state compose a class of practically-important materials known as jammed systems, their functionality being realized due to structural nanoinhomogeneities frozen at atomic and/or sub-atomic length scales. With tending towards equilibrium in the controlled parameter, such systems obey compressed-exponential relaxation kinetics (super-exponential), which is faster than simple exponential decay. In this report, the mathematical models of degradation-relaxation kinetics are considered for jammed systems composed of screen-printed spinel Cu0.1Ni0.1Co1.6Mn1.2O4 and conductive Ag or Ag-Pd alloys. Structurally-intrinsic nanoinhomogeneous due to Ag and Ag-Pd diffusing agents embedded in spinel phase environment are shown to define governing kinetics of thermally-induced degradation obeying an obvious non-exponential behavior in resistance drift. The stretched-to-compressed exponential crossover is detected for degradation-relaxation kinetics in these systems with conductive contacts made of Ag Pd and Ag alloys. Under essential migration of conductive phase, the resulting kinetics is though to be considerable two-step diffusing process originated from Ag penetration deep into spinel ceramics.
Causal detectability for linear descriptor systems
Mahendra Kumar Gupta, Indian Institute of Technology Madras, Department of Chemical Engineering, India
Nutan Tomar, Indian Institute of Technology Patna, Department of Mathematics, India
Raghunathan Rangaswamy, Indian Institute of Technology Madras, Department of Chemical Engineering, India
Abstract: Observer design for descriptor systems has received a large attention of researchers in the last few decades. Various types of observers have been introduced to fulfill the purpose of state estimation. The difference among various types of observers lies in either required conditions on the system operators or methodologies to find the coefficient matrices of the proposed observers. Most of the work in the literature has been done on the design of Luenberger observer. It has already been proved in the literature that the causal observability is the necessary and sufficient condition for the existence of Luenberger observer for linear descriptor systems. However, in earlier works, the causal observability has not been given in terms of system coefficient matrices. In this paper, the causal observability has been established in terms of system coefficient matrices. The proposed observer design theory is illustrated by one example.
Spiraling elliptic beams in nonlocal nonlinear media with linear anisotropy
Guo Liang, Shangqiu Normal University, School of Electrical & Electronic Engineering, China
Zhanmei Ren, South China Normal University, Laboratory of Nanophotonic Functional Materials and Devices, China
QI GUO, South China Normal University, School of Information and Photoelectronic Science and Engineering, China
Abstract: Analytically discussed is the nonlinear propagations of spiraling elliptic beams in nonlocal nonlinear media with linear anisotropy by using an approach of two dimensional asynchronous fractional Fourier transform. The spiraling elliptic beams exhibit a kind of molecule-like libration due to the combined effects of the linear anisotropy and the orbital angular momentum. Depending on the anisotropy parameter of the media, the molecule-like libration mode has two different kinds of dynamical behaviors. When the anisotropy parameter of the media is a rational number, the spiraling elliptic beams evolve as the breathers and can recover their initial shapes after one propagation period. However, when the anisotropy parameter of the media is an irrational number, all the related parameters of spiraling elliptic beams such as the optical intensity, the beam width, and the angular velocity cannot evolve in a periodic manner, and no spiraling elliptic breathers exist in this case.
Mathematical modeling of precipitation
Satoshi Yoshio, Sumitomo Metal Mining Co.,Ltd., Computer Aided Engineering and Development Dept., Japan
Kazuhiko Tsuchioka, Sumitomo Metal Mining.Co.,Ltd., , Japan
Motoaki Saruwatari, Sumitomo Metal Mining.,Co.Ltd., , Japan
Koichiro Maki, Sumitomo Metal Mining.Co.,Ltd., , Japan
Abstract: The reaction precipitation is industrially widely used as a method for obtaining desired fine particles at low cost and at high speed. The particle size distribution of the particles produced from these prepicitation steps is one of the most fundamental properties. Therefore, when planning the scale-up of the reaction precipitation tank, it is indispensable to design the main physical factors related to the particle size distribution and to understand the scale-up characteristics thereof in order to design the apparatus efficiently. However, when scaling up the apparatus based on the stirring tank, a method of scaling up the apparatus based on the power required for stirring is generally used, but with this method, the particle size distribution changes . Therefore, we constructed a mathematical model to predict the particle size distribution of particles produced from the precipitation stirred tank. This mathematical model was constructed by defining the coalescence efficiency of particles from the kinetic energy based on the relative velocity between particles and the binding energy based on the deposition rate, taking into account the process of particle growth due to surface precipitation and collision between particles. With this model, it was possible to reproduce the difference in the particle size distribution of the particles produced under the condition that the shape of the stirring blade, rotation speed and tank scale were changed in the actual precipitation reaction tank.
Local mean field approximation applied to the Ising-like model for 2D Spin Crossover nanoparticles
Salah ALLAL, University of Versailles St. Quentin en Yvelines, LATMOS, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Kamel Boukheddaden, University of Versailles St. Quentin en Yvelines, GEMAC, France
Pierre DAHOO, University of Versailles St. Quentin en Yvelines, LATMOS, France
Abstract: Iron (II) complexes coordinated to six Nitrogen in an octahedral symmetry may exhibit thermal-, optical-, electrical-, magnetic- or pressure-induced spin-crossover (SCO) between the diamagnetic low-spin (LS, with S=0) and the paramagnetic high-spin (HS; S=2) states [1]. This property may lead to potential applications of these compounds in molecular devices as, molecular switches, displays, temperature and/or pressure sensors [2]. Historically, a homogeneous Ising-like model has been proposed in order to reproduce the hysteresis thermal behaviour [3,4]. In this contribution, we extend the previous model to include the local mean field approach to describe the thermal-dependence of 2D nanoparticles embedded in a matrix. By solving the equations for 10000 molecules in the case of a rectangular- and square-shaped lattices, using the same model parameters , we have identified the existence of a shape effect on the thermal properties. Indeed, as shown in this contribution, the thermal hysteresis appears for a rectangular case 2x5000 while it disappears for a square lattice 100x100
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.
Edge Effect on Nanoparticles of an Interconnect Alloy from the ABV Model
Chems-eddine Saada, University of Versailles St. Quentin en Yvelines, LATMOS, France
Pierre DAHOO, University of Versailles St. Quentin en Yvelines, LATMOS, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
tarek merzouki, University of Versailles St. Quentin en Yvelines, lisv, France
philippe pougnet, valeo-siemens, , France
abdelkhalak el hami, insa-rouen, , France
Abstract: The physical phenomena underlying crack initiation and hence failures in interconnection alloy is investigated using the ABV model [1] (Metals A and B and void V) focusing on boundary effects at the interface with the device. The Hamiltonian which is expressed as the sum of the interaction energies between A, B and V with interaction parameters EAA, EBB, EAB , EAV and EBV is reformulated so as to obtain an expression in terms of fictitious 3 states spins (-1, 0, +1). New parameters K, J and U function of the interaction energy parameters between the metal atoms A, B and void V are defined and associated to the different spin combinations of the transformed Hamitonian. A Monte Carlo (MC) simulation of a 2D microscopic 3 states Ising model taking into account edge effects [2] at the boundary between an active chip in a photovoltaic device or a sensor and nanoparticles of an interconnect alloy is performed. The results are discussed in terms of realistic values of interaction parameters and different compositions of A,B and V.
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.
On the decomposition of modular multiplicative inverse operators via a new functional algorithm approach to Bachet's--Bezout's Lemma
Luis Cortés-Vega, Antofagasta University, Mathematics Department, Chile
Abstract: In this paper, the notion of modular multiplicative inverse operators (MMIO) is introduced and studied. A general method to decompose (MMIO)'s over the group of units is discussed through a new algorithmic functional version of Bachet's--Bezout's Lemma. As a result, interesting decomposition laws for (MMIO)'s are obtained. Some numerical examples confirming the theoretical results are also reported.
Acknowledgements: Work supported by ``Decanatura de la Facultad de Ciencias B\'{a}sicas", Antofagasta University, Chile. I am especially indebted to Professor Dr. Alvaro Restuccia, academic of Department of Physics of the Antofagasta University by their support, via fondecyt Grant #1161192, Chile.
Modelling of the densification of silver particles during sintering at low pressure and temperature
Nassim Khiat, University of Versailles St. Quentin en Yvelines, LISV, France
Xudong Wang, University of Versailles St. Quentin en Yvelines, LISV, France
Lahourai Benabou, University of Versailles St. Quentin en Yvelines, LISV, France
Luc Chassagne, University of Versailles St. Quentin en Yvelines, LISV, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Abstract: The control of the densification of a powder compact during the sintering process is of primary interest since this affects directly the obtained mechanical and physical properties. For example, silver sintering can be used to obtain joints for assembling optical or electronic components and, in such applications, an efficient thermal conductivity and a good material strength are requested. These properties are shown to be dependent on the density reached during compaction [1]. In our study, an analytical modelling is first employed to predict the main characteristics of the sintered material, such as the neck growth and the shrinkage during the different stages of densification [2]. Effects of the temperature and the applied pressure are accounted for in the calculations in order to find the optimal process parameters for some given objectives. The results are complemented with densification predictions obtained from finite element simulations. The constitutive laws, which are implemented in the commercial code COMSOL Multiphysics, are based on a continuum approach of the sintered material as developed in [3]. Comparisons between analytical and numerical results are performed and differences are discussed with respect to the underlying hypotheses of both methods. References [1] K.S. Siow, Are sintered silver joints ready for use as interconnect material in microelectronic packaging?, Journal of Electronic materials 43, 947-961, 2014. [2] R.L. Coble, Diffusion models for hot pressing with surface energy and pressure effects as driving forces, Journal of Applied Physics 41, 4798-4807, 1970. [3] M. Abaouf, Modélisation de la compaction de poudres métalliques frittés – Approche par la mécanique des milieux continus, Thèse de doctorat, Grenoble, 1985.
Acknowledgements: MATINNOV (Innovative Materials) and TALSO (Sintering for Optics) chairs are gratefully acknowledged.
Investigating CH4 Thermal Activation in Clathrate Nano-cages
Azzedine Lakhlifi, Institut UTINAM-UMR 6213 CNRS, Université de Franche-Comté, Observatoire de Besançon, France
Pierre DAHOO, University of Versailles St. Quentin en Yvelines, LATMOS, France
CONSTANTIN MEIS, CEA - Saclay, National Institute for Nuclear Science and Technology, France
Julian GALE, Curtin Institute for Computation, Department of Chemistry, Curtin University, Australia
Abstract: The energy levels of CH4 in the small (s) and large (l) nano-cages of cubic sI and sII types clathrates [1] are calculated in the Born-Oppenheimer approximation using the Extended Lakhlifi-Dahoo model [2][3] based on pairwise atom-atom effective charge interaction potentials and induction effects. Calculations show that the coupling between the CH4 molecule and the nano-cage is quite different for the low frequency translational, rotational or librational modes in the small (s) and large (l) nano-cages of the sI. The two methods used to calculate the encaged translational frequencies, namely the 3D harmonic approximation or the discrete variable 1D representation, give the same values, which are 133 cm-1, 108 cm-1 and 120 cm-1 for the small (s) and 63 cm-1, 52 cm-1 and 47 cm-1 for the large (l) nano-cages. The energy level schemes are different from those composed of discrete rotational energy levels characterizing the isolated gas phase molecule. In the small (s) nano-cage the quantum scheme is modified by the presence of numerous intermixed sublevels grouped in polyads, but in the large (l) nano-cage, the spacings between the levels are smaller and the intermixed polyads denser. In this case the relaxation channels for de-excitation of CH4 are different in the two types of cages. These results are quite different from those determined for CO2 [2][3] with expected radiative and non-radiative relaxation. In particular, thermal effects through transfer to the clathrate media by non-radiative relaxation channels should be more important.
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.
The Design of Single-Point Mooring System with Moored Buoy
Meijun Fu, Yunnan Minzu University, School of Mathematics and Computer Science, China
Abstract: The single-point mooring system is currently under a wide range of applications in marine engineering, marine observation, marine farming and other fields. Therefore, we intended to investigate into the single-point mooring system with moored buoy that was made of a buoy, four steel pipes, a steel drum, a compact ball, an anchor chain and an anchor. Our purpose is to design a single-point mooring system mentioned above, which can be utilized in the shallow sea. Namely, we must determine the following parameter values: the type and length of anchor chain, the weight of compact ball. Not only reached as small as possible both buoy draught and swimming range, but also the vertical angle of steel drum did. For these reasons, we firstly used the static force method to analyze various components. Secondly, we established a mathematical model to calculate under different wind speed all the important parameters, including the vertical tilt angle of the steel drum, the horizontal tilt angle of each steel pipe, the buoy draught, the buoy swimming range and the anchor chain shape. Thirdly, on the basis of the previous work, we established a multi-objective programming model to achieve our design scheme in diverse environmental conditions covering sea surface wind speed, seawater velocity and sea depth. Finally, by simulation experiments we validated and analyzed the parameters mentioned above. It turned out that the single-point mooring system with moored buoy in shallow sea, designed by us, is reasonable and applicable, so it has definite theoretical significance and practical values.
Finsler Geometry Modeling of Orientation Asymmetric Surface Model for Membranes
Hiroshi Koibuchi, National Institute of Technology, Ibaraki College, Department of Industrial Engineering , Japan
Abstract: A discrete surface model with non-Euclidean metric is studied in the context of Finsler geometry (FG) modeling. The FG modeling technique expands the range of application of the surface model of Helfrich and Polyakov for membranes (2014, Physica A {\bf 393}, 37-50). Indeed, the so-called soft elasticity and the elongation under the temperature change observed in the liquid crystal elastomers are analyzed by 3D FG modeling technique (2017, Polymer {\bf 114}, 335-369). It was also shown that the J-shaped stress-strain curve of biological materials such as human skin and muscle is calculated by 2D FG model (2017, Phys. Rev. E {\bf 95}, 042411(1-11)). Moreover, the origin of the line tension energy, which plays an important role in the model for two-component membranes, is explained by another 2D FG model (2016, Polymers {\bf 8}, 284(1-18)). This 2D FG model is extended to be asymmetric under the surface inversion (2017, Axioms {\bf 6}, 10 ). This FG model is independent of how the Finsler length of bond is defined, where the Finsler length of bond is in general essentially new and important ingredient in an FG model. In this presentation, we discuss the details of this interesting property, which was mentioned only simply in (2017, Axioms {\bf 6}, 10).
On the degeneracy of barrier options
J C Ndogmo, University of Venda, Department of Mathematics and Applied Mathematics, South Africa
Abstract: We consider the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option such as a vanilla or other possible types, and when it can be considered as a typical barrier option of the given type. The problem is reduced to finding certain critical values of the initial stock price, and this is achieved through a probability-based approach. Due to the approximate nature of a certain parameter in the formulas obtained, a numerical test is also implemented to confirm the validity of these formulas.
ASYMPTOTIC SYMMETRIES IN 3-DIM GENERAL RELATIVITY: THE B(2,1) CASE
Evangelos Melas, University of Athens, Economics Unit of Mathematics and Informatics Sofokleous 1 Athens 10559 Greece, Greece
Abstract: The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity (G.R.). Strongly continuous unitary irreducible representations (IRs) of B(2,1), the analogue of B in three space-time dimensions, are analysed in the Hilbert topology. It is proved that all IRs of B(2,1) are induced from IRs of compact `little groups', which are the closed subgroups of SO(2). It follows that some IRS of B(2,1) are controlled by the IRs of the finite symmetry groups of regular polygons in ordinary Euclidean 2-space. It is proved that all IRs of B(2,1) are obtained by Wigner-Mackey's inducing constructionsemi-direct product theory notwithstanding the fact that B(2,1) is not locally compact in the employed Hilbert topology.
The influence of the gas flow at the wave flow of a viscous liquid film
Liudmila Prokudina, South Ural State University, Higher school of electronics and computer science, Russian Federation
Abstract: A method for calculating the flow of a liquid film while blowing its free surface with a gas flow of arbitrary direction is presented. Mathematical model of the flow of a liquid film is adopted in the approximation of the boundary layer. Based on the assumption of parabolic velocity profile of the liquid film was found analytic expressions for the deviation of the free surface of the film and the perturbations of velocity. Analytical dependence for the spatial increment of instability of the developed wave flow of liquid films is obtained. The calculations for the stationary monochromatic perturbations of the maximum of the increment there are areas of stability are showed.
Dynamics of an Anisotropic Universe with Bulk Viscous Fluid in f(R,T) Theory
Bivudutta Mishra, BITS-Pilani, Hyderabad Campus, Mathematics, India
Abstract: In this paper, the dynamical behaviour of the anisotropic universe has been investigated in $f(R,T)$ theory of gravity. The functional $f(R,T)$ has been rescaled in the form $f(R,T)=\mu R+\mu T$, where $R$ is the Ricci scalar and $T$ is the trace of energy momentum tensor. Three cosmological models are constructed using the power law expansion in Bianchi type $VI_h$ ($BVI_h$) universe for three different values of $h=-1,0,1$, where the matter field is considered to be of bulk viscous fluid. It is found from the model that the anisotropic $BVI_h$ model in the modified theory of gravity is in agreement with a quintessence phase for the value of $h=-1$ and $0$. We could not obtain a viable cosmological model in accordance with the present day observations for $h=1$. The bulk viscous coefficient in both the cases are found to be positive and remain constant at late time. The physical behaviours of the models along with the energy conditions are also studied.
Object recognition of real targets using modelled SAR images
Denis Zherdev, Samara University, Supercomputers and General Informatics, Russian Federation
Abstract: The study is a continuation of works [1, 2]. In addition, we are developing technology of real target recognition using modeled SAR images. We using the 3D models of objects in SAR image construction. The is advantage that in real time recognition scenario it is not necessary store a big dataset of whole aspect angle SAR images of target. Moreover, if the parameters of target position is known it should leads to higher recognition quality. The process of SAR image formation is based on the use of coherent phase history that contained in a sequence of reflected signals which were received on a track of synthesis, which is larger than a real antenna length. The synthesis of antenna aperture is executed in the result of airborne radar movement on a specified trajectory. The received reflected signals are stored in a phase and amplitude and then processed to obtain an image. A high resolution in the slant range is achieved by using radiated wideband signals, and in the cross range because of a coherent sum of high number reflected impulses. Moreover, we perform the parallel algorithm using CUDA. The technology includes three stages. Firstly, we generate the dataset of SAR images of estimated objects in specified conditions and parameters of observation. Secondly, we construct the support subspaces as it described in works [1, 2]. Finally, we train the neural network with one hidden layer. The vectors that form the support subspace are set at input layer. To accelerate learning after each step of the training, weights that take large values are fixed. In work [1] was achieved 97% of correct recognition using support subspaces. With inclusion of neural network in the technology the result is increased to 99% that can be matched with a convolutional network. We emphasize that the proposed technology in difference with a convolutional network, does not require a large number of images at training stage and the training time is reduced by hundreds of times. [1] Fursov, V., Zherdev, D., Kazanskiy, N., “Support subspaces method for synthetic aperture radar automatic target recognition,” International Journal of Advanced Robotic Systems. V. 13(5). 2016. [2] Zherdev, D.A. Fursov, V.A. “Support plane method applied to ground objects recognition using modelled SAR images,” Proceedings of SPIE 9599, Applications of Digital Image Processing XXXVIII. P. 95992J-95992J-7. 2015. DOI: 10.1117/12.2188531.
Free fermion vertex operator algebras in the geometric Langlands correspondence
Alexander Zuevsky, Academy of Science of the Czech Republic, Mathematics, Czech Republic
Abstract: We review our recent results and point out further directions in understanding of the vertex algebra approach in the geometric Langlands correspondence.
The continuous-time quantum walk with transition moments of the Gaussian distribution as a mathematical model of rotational excitation in molecules by an optical pulse
Leo Matsuoka, Hiroshima University, Graduate School of Engineering, Japan
Hynek Lavička, KU Leuven, Institute for Theoretical Physics, Belgium
Abstract: The time-evolution of the density distribution on a network of the quantum states which are connected by the optical transitions can be modeled by the continuous-time quantum walk (CTQW). The interaction between diatomic molecules and a train of broadband optical pulses can be modeled as a class of the CTQW, and its asymptotic behavior and localization behavior have been discussed so far. The understanding of the localization is also important to the practical use of molecular excitation such as isotope separation. In this study, we focused on the "localization" induced by the asymptotic decrease of the transition moment. For an example of a simple case, we investigated a time-evolution of the density distribution on the half line with the transition moments of the Gaussian distribution peaked at the boundary. By the numerical simulation with the initial state of J=0, we observed a clear time-averaged distribution that is well fitted to the stretched exponential distribution with parameters close to Gaussian distribution, even though the time-evolution shows oscillatory motion inside a certain region repeatedly. The coefficients of the stretched exponential distribution were determined by regression varying the coefficients of the Gaussian distribution of the transition moment.
Simple model of optical diffuser using Mie scattering
Olesia Synooka, ams AG, Photonic devices, Austria
Abstract: Authors: Olesia Synooka, Ingrid Jonak- Auer, Anderson Singulani, ams AG, Graz, Austria Abstract: Optical diffusers are widely used in the backlight systems of liquid-crystal display (LCD) devices, such as TVs, overhead projectors, handheld game consoles, and mobile phones and getting important also in various semiconductor optical sensors. This work studies the scattering profile of optical diffuser based on TiO2 particles immersed in clear silicon used for semiconductor industry. Optical properties of the diffuser with various thicknesses and particle loadings were simulated by ASAP (Breault Research Organization, Inc.) Raytracing tool. The angular dependence of the light intensity on a diffuser at various incident angles were measured experimentally. We developed a simple and compact model which can be used to simulate the angular dependence of scattered light intensity by a diffuser with variable film thickness. The results are very useful in improving performance of a big variety of optical semiconductor sensors.
Fuzzy Logic Control Technique for Stability of Nonlinear plant
Dr N K Yadav, Arba Minch University, Electrical & Computer Engineering, Ethiopia
Abstract: This paper is concerned with the problems of stability analysis for nonlinear systems. The researchers are facing the difficulties for the mathematical modeling of the ill-defined system, which is very complex and tedious work. Practical control systems are existing of different kinds of delays such as communication delays, transporting delays, input-delays etc. These delays are prime cause for affecting the system’s performance indices. The development of the discrete-time domain microprocessor and microcontroller leads to enhance the system performances quicker and faster. For ill-modeled systems existence condition with the aid of Takagi-Sugeno fuzzy logic control methodology will solve the problem of stability and stabilization of the system. The application of the discrete domain fuzzy logic technique will aid for the speedy performances, which are being process very fast computation by application of computer, which leads to reduce the computation time and cost reduction due to advancement of microprocessor and micro-controller. This designed algorithm will be more effective with uniqueness by subsidizing the observation erroneous response. This algorithm will be more suitable for application of aerodynamic system to generate stability.
Methods of verification of compliance with an asymptotically power law
Inna Belashova , Kazan Federal University , Radio physic, Russian Federation
Vladimir Bochkarev, Kazan Federal University, Radiophysics, Russian Federation
Vladimir Tyurin, Kazan federal university, Instituts of Physics, department of Radiophysics , Russian Federation
Abstract: It was found out that the power law occurs in many practical cases relating to various fields of science and technology. However, the conclusion about power-law distribution in empirical data was not strictly verified in all cases in terms of statistics. In [A. Clauset, CR Shalizi, MEJ Newman Power-law distributions in empirical data SIAM Review 51, 661-703 (2009)], a large number of data sets from earlier works were analyzed, and it was shown that the conclusion about compliance with the power law is statistically verified only in 11 out of 24 cases. In [Clauset et al. 2009], the verification was performed assuming that the measured values precisely correspond to power distribution, at least in some relatively large range of values. At the same time, one can expect only an asymptotic approximation to the power law in many practical cases. This work describes two methods of the power law verification in different empirical data. We don’t analyze the value of deviations from the model but try to find out whether these deviations are systematic or random. The suggested approach is based on the idea of finding the local power approximation of the considered series for each range of ranks, after which one or another trend criterion is applied to the obtained series of local indicators. The possibility of applying this criterion to the problem under consideration is also discussed. The described criteria were tested using 10 sets of empirical data, which were considered in the above-mentioned work [Clauset et al. 2009] and are available for free. It is shown that satisfactory correspondence with the power law was found only in one of the cases.
Acknowledgements: This work was supported by the Russian Foundation for Basic Research, Grant no. 15-06-07402 and by the Russian Government Program of Competitive Growth of Kazan Federal University.
Modelling the dynamics of multipartite quantum systems created departing from two-level systems using general local and non-local interactions
Francisco Delgado, Instituto Tecnologico y de Estudios Superiores de Monterrey RFC: ITE430714KI0, Physics and Mathematics, Mexico
Abstract: Quantum information and quantum computation were born inheriting the binary nature of classical computation. As a result, settlement and manipulation of quantum information exploit two-level quantum systems to state their minimum information resource, the qubit. Evolution dynamics of this resource is universally based on SU(2). In addition, natural interactions in the systems are used as driven quantum operations on a group of qubits to manipulate the information stored on them, particularly providing outstanding quantum properties as superposition and entanglement, two key processing resources in these implementations. This work shows a modelling of a combined system of 2d qubits interacting through quantum general interactions (applicable for optical and magnetic systems) used to get an achievable binary description of complex quantum information settled on it, which is available for certain interactions, notably existing in nature. The dynamics of this system runs on SU(2d), but the procedure presented lets to decompose it into SU(2) operations on the quantum information stored. Thus, this approach shows the dynamics for the quantum information and not more for the circumstantial physical quantum systems being used, thus letting to achieve the scope of quantum operations, set up architectures, manipulation of quantum states and more.
Design of Oscillator Networks for Generating Signal with Prescribed Statistical Property
Tatsuo Yanagita, Osaka Electro-Communication University, Engineering Science, Japan
Abstract: We design network oscillators to generate a signal with a prescribed power spectrum. We consider a identical sin-wave oscillator as the element of the network and the Kuramoto order parameter as an output signal of the network oscillators. We use the Kullback-Leibler entropy as a measure of the distance between the power spectrum of the output signal and those of desired one. By optimizing of the connection network through the Markov chain Monte Carlo method, we found that even network oscillator with a small number of elements can be generate a variety of time signals. The outputs include periodic and quasi-periodic signals with prescribed periods, and chaotic signals with prescribed power spectrums.
Acknowledgements: This study has been partially supported by JSPS KAKENHI Grant No. 15K05221 and the Volkswagen Foundation (Germany).
COMSOL simulation of an attenuated magnetic field through a metallic plate
Amine Touazi, University of Versailles St. Quentin en Yvelines, LISV, France
Ibrahim Dergham, University of Versailles St. Quentin en Yvelines, LISV, France
Yasser Alayli, University of Versailles St. Quentin en Yvelines, LISV, France
Luc Chassagne, University of Versailles St. Quentin en Yvelines, LISV, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Abstract: This paper presents the evaluation, by COMSOL software simulations, of the magnetic fields due to a circular coil [1-3] when a 0.7 mm metallic plate (iron, iron 3% Si, steel) is placed near the coil. We have analysed the variation of this magnetic field Be as function of the frequency as well of z (perpendicular to the circular coil). We show that a clear evanescent magnetic field Be, near the metallic plate, appears due to the skin effect related to the "Plasmon current". We analyse also the particular effect near the metallic plate concerning the increasing value with the frequency The comparison of the results shows that the developed model and the experimental measurements conducted are accurate and effective. References [1] AO Anele, Y Hamam, L Chassagne, J Linares, Y Alayli, K. Djouani, Journal of Physics: Conference Series 633 (2015) 012012. [2] J. Ronald Moser, Low-frequency shielding of a Circular Loop Electromagnetic Field Source, IEE Transactions on Electromagnetic Compatibility Vol EMC-9, N°1 (1967), 6-18. [3] Wilson, P. F., & Ma, M. T. Techniques for measuring the electromagnetic shielding effectiveness of materials. II. Near-field source simulation. IEEE Transactions on Electromagnetic Compatibility, 30(3), 251-259 (1988).
Acknowledgements: MATINNOV chair (Innovative Materials) is gratefully acknowledged.
On damping of an edge dislocation vibrations in a dissipative crystal: limiting cases
Viktor Dezhin, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Abstract: The expression for the generalized susceptibility of the dislocation obtained earlier was used. The electronic drag mechanism of dislocations is considered. The study of small dislocation oscillations was limited. The contribution of the attenuation of low-frequency bending dislocation vibrations to the overall coefficient of dynamic dislocation drag in the long-wave and short-wave limits is calculated. The attenuation of long-wave bending dislocation vibrations caused by an external action of an arbitrary frequency has been investigated. Contribution short-wave bending dislocation vibrations damping in total drag coefficient at an arbitrary frequency is found.
Principal features of the atomic and electronic structure of the (111) surface reconstructions in ZnSe and CdSe crystals. S.M.Zubkova, V.L.Bekenev, I.N.Frantsevych Institute for Problems of Materials Science, National Academy of Sciences of Ukraine
Svetlana Zubkova, Frantsevich Institute for Problems of Materials Science NASU, Department of functional oxide materials, Ukraine
Abstract: Based on the data of [1-2], the theoretical investigation and ab initio calculations of the atomic and electronic structure were performed for four variants of the cation-terminated polar ZnSe and CdSe (111)A –(2 × 2) surfaces, namely, ideal, relaxed, reconstructed with a Zn (Cd) vacancy, and reconstructed with the subsequent relaxation. In the approximation of a layered superlattice, the surfaces were simulated by a film with a thickness of 12 atomic layers and a vacuum gap of ~16 Å. Dangling bonds of Se atoms were closed by adding, on the opposite side of the film, four fictive hydrogen atoms, each having a charge of 0.5 electrons. The ab initio calculations were performed with the QUANTUM ESPRESSO complex of programs based on the DFT–LDA approach. In each of the variants the optimized forces acting on atoms and the equilibrium coordinates of Zn(Cd) and Se atoms of the upper four freestanding layers were determined. The positions of the atoms in these layers were considered to be completely relaxed when the forces acting on the atoms became less than 0.017 eV/Å. It is shown that the reconstruction splits each of the 4 upper "freestanding" layers into 2 layers containing 3 and 1 atoms. Our previous results and experimental data have shown that such a splitting is inherent in the (111) surface terminating by a cation for the majority of A2B6 semiconductors. The band structures of the four variants of the slab have been calculated and the influence of the relaxation and reconstruction on the specific features in the behavior of the conduction band and the valence band was analyzed. In the case of a real (reconstruction / relaxation) surface the typical direct-gap semiconductor was obtained. The full and layered densites of states of the valence electrons have been calculated for the four upper layers 9, 10, 11, 12. Presented figures clearly show the gradual change in the magnitude and location of surface structures on the energy scale upon changing over from layer to layer and from one type to another type of surfaces.
Acknowledgements: All the calculations were performed on the Computing Grid Cluster at the Institute for Problems of Materials Science of the National Academy of Sciences of Ukraine.
Numerical Simulation of the thermal and pressure effects on 1D and 2D spin crossover nanoparticles
Camille Harlé, University of Versailles St. Quentin en Yvelines, LATMOS, France
Salah ALLAL, University of Versailles St. Quentin en Yvelines, LATMOS, France
Devan Sohier, University of Versailles St. Quentin en Yvelines, LI-PaRAD, France
Thomas Dufaud, University of Versailles St. Quentin en Yvelines, LI-PARAD, France
Rafael Caballero, Pontificia Universidad Católica del Perú, Departamento de Ciencias - Sección Física, Peru
Francisco De Zela, Pontificia Universidad Católica del Perú, Departamento de Ciencias - Sección Física, Peru
Pierre DAHOO, University of Versailles St. Quentin en Yvelines, LATMOS, France
Kamel Boukheddaden, University of Versailles St. Quentin en Yvelines, GEMAC, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Abstract: In the framework of the Ising-like model, the thermal and pressure effects on the spin crossover systems [1] are evaluated through fictitious spin operators σ with two eigenvalues σ =-1 for low-spin (LS) and σ=+1 for high-spin (HS) characterizing each molecule. Based on each configurational state, associated to +1 and -1, for a SCO system, described by m=Σ σi , s=Σ σi σj and c=Σ σk (molecules at the surface), the number of configurations with the same m, s and c values is given by the density of states d[m][s][c]. In this contribution we present two ways to calculate this value: by entropic sampling Monte Carlo simulations and using a specific dynamic programming. We calculate the average value of < σ> for 1D and 2D spin crossover nanoparticles[2] taking into account short-, long- range interactions as well as the interaction between molecules at the surface with the surroundings matrix. The results obtained show the effect of the pressure, temperature and size. In particular we analyse the role of different interactions parameters to find-out the re-entrance phase transitions References [1] A. Bousseksou, J. Nasser, J. Linares, K. Boukheddaden, F. Varret, J. Physique I, 2 (1992) 1381-1403 [2] S. Guerroudj, R. Caballero, F. de Zela, C. Jureschi, J. Linares, K. Boukheddaden "Monte Carlo - Metropolis investigations of Shape and Matrix Effects in 2D and 3D Spin Crossover Nanoparticles", Journal of Physics Conference Series, 738 (2016) 012068
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged
Cancer treatment optimization with hyperthermia using genetic algorithm
Gustavo Fatigate, Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais, Poços de Caldas, Brasil, Computação, Brazil
Eliezer Mafra, Instituto Federal de Educação, Ciência e Tecnologia do Sul de Minas Gerais, Poços de Caldas, Brasil, Computação, Brazil
Rafael Coelho Neves, Instituto Federal de Ciência e Tecnologia do Sul de Minas Gerais , PHYSICS, Brazil
Ruy Reis, Universidade Federal de Juiz de Fora, Modelagem Computacional, Brazil
Abstract: Cancer is the second biggest cause of death in the world, according to World Health Organization (2017). Globally, almost 1 in 6 deaths is due to cancer, in 2015. Among the known treatments include chemotherapy and radiotherapy. Nevertheless, an alternative therapy has been developed and might be used along with the standard techniques. This treatment is based on hyperthermia using magnetic nanoparticles fluid. When this fluid is submitted under an oscillating magnetic field it produces heat making possible to overheat the target area until the cell necrosis. So, it is possible to achieve the tumor destruction once when the cells reach $43^o$ C they necrosis. On the other hand, the surrounding healthy cells ends up to be destroyed as well. Then, this research article aims to propose a method to minimize the health cells death by choosing the bests locals to place the injections points. This method consists in apply genetic algorithm to optimize the cell death once the Pennes bioheat model are used to evaluate the temperature distribution. Finally, the numerical method used to approach the solution of Pennes bioheat model are the finite difference method. To ensure a second-order solution approach, a centered finite difference method was used for space discretization and forward difference for time evolution.
Acknowledgements: CAPES, CNPq, FAPEMIG
Modeling the assessment of the economic factors impact on the development of social entrepreneurship
Timur Absalyamov, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Rezeda Kundakchyan, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Liliya Zulfakarova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Zulfira Zapparova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Abstract: The article deals with the research of modern trends in the development of social entrepreneurship in Russia. The results of the research allow the authors to identify a system of factors that affect the development of entrepreneurship in the modern Russian economy. Moreover, the authors argue the regional specificity of the development of social entrepreneurship. The paper considers specific features and formulates the main limitations of the development of entrepreneurship and the competitive environment in the social sphere. The authors suggest an econometric model for assessing the influence of economic factors on the development of socially-oriented entrepreneurship and present an algorithm for calculating its components. The results of the econometric analysis identify the main factors of the change in the performance indicators of entrepreneurial activity and determine the degree of their impact on social entrepreneurship. The results and conclusions can serve as an estimation of the socioeconomic consequences of the sustainability disruption of the entrepreneurial potential realization in the social sphere.
Quasi-coherent structures and flows in turbulent transport
Madalina Vlad, National Institute of Laser Plasma and Radiation Physics, Plasma and Fusion, Romania
Florin Spineanu, National Institute of Laser Plasma and Radiation Physics, Plasma and Fusion, Romania
Abstract: The nonlinear effects that appear in test particle transport in two-dimensional incompressible turbulence are discussed. Test particle trajectories show both random and quasi-coherent aspects. The random motion leads to diffusive transport while the coherent motion is associated with trapping or eddying in the structure of the stochastic field. The strength of each of these aspects depends on the parameters of the turbulence. The trapping events appear when the trajectory arrives around the maxima or the minima of the stream function (potential). The process is quasi-coherent because it affects all the particles situated in these regions in the same way. The high degree of coherence of the trapped trajectories is evidenced by the statistical properties of the distance δx between neighbor trajectories. The time evolution of <δx²(t)> is very slow. The neighbor particles have a coherent motion that approximately keeps the initial distance for a long time. They are characterized by a strong clump effect. These trajectories form intermittent quasi-coherent structures similar to fluid vortices and represent eddying regions. The trapping events alternate with large displacements that correspond to large size contour lines of the potential. These large jumps are random. The transport is essentially determined by them, while the trapping events have negligible contributions. Trapping can be associated to a process of micro-confinement. At a given moment, the micro-confinement affects a fraction of the particles, and, in a large time interval, every particle is subjected to micro-confinement events during a fraction of this time. The micro-confinement determines the existence of transport reservoirs in the sense that diffusion can be strongly enhanced when these trapped particles are released by the increase of the perturbation strength determined by collisions. The quasi-coherent trajectory structures have more complex effects in the presence of an average velocity Vm or in a turbulence that drifts with a velocity Vm. Quasi-coherent flows are generated beside the vortical trajectory structures. The transport coefficients, the average size and life-time of the quasi-coherent structures are determined as function of the characteristics of the turbulence. Our instrument, the decorrelation trajectory method [1], [2], is essentially analytical. The transport process is completely different in the presence of structures in the sense that the dependence on the parameters is different. The quasi-coherent structures and flows also influence the evolution of turbulence [3]. 1. M. Vlad, F. Spineanu, J.H. Misguich, R. Balescu, Phys. Rev. E 58, 7359 (1998). 2. M. Vlad, F. Spineanu, Phys. Rev. E 70, 056304 (2004). 3. M. Vlad, F. Spineanu, New J. Phys. 19, 025014 (2017).
Acknowledgements: This work was supported by the Romanian Ministry of National Education under the contracts WPJET1_C and WPENR_C
Data re-arranging techniques leading to proper variable selections in high energy physics
Vaclav Kus, Czech Technical University in Prague, (Department of mathematics), Czech Republic
Petr Bour, Czech Technical University in Prague, Department of mathematics, Czech Republic
Abstract: We introduce a new data based approach to homogeneity testing and variable selection carried out in high energy physics experiments, where one of the basic tasks is to test the homogeneity of weighted samples, mainly the Monte Carlo simulations (weighted) and real data measurements (unweighted). This technique is called 'data re-arranging' and it enables variable selection performed by means of the classical statistical homogeneity tests such as Kolmogorov-Smirnov, Anderson-Darling, or divergence based tests (e.g. Pearson's chi-squared,...). All the tests cannot be used for weighted samples directly due to the apparent violation of their asymptotic distribution behaviour derived in classical statistics. Thus, the p-values of our variants of homogeneity tests are investigated by means of simulation experiments and, consequently, the empirical verifications through 46 dimensional high energy particle physics data sets are accomplished. Particularly, the procedure of homogeneity testing is applied to Monte Carlo samples and real DATA sets measured at the particle accelerator Tevatron in Fermilab at D0 experiment originating from top-antitop quark pair production in two decay channels (electron, muon) with 2, 3, or 4+ jets detected. Finally, the variable selections in the electron and muon channels induced by our re-arranging procedure for weighted homogeneity testing are provided for Tevatron top-antitop quark data sets.
Acknowledgements: This work was supported by the grants LG15047 (MYES), LM2015068 (MYES), SGS15/214/OHK4/3T/14 (CTU), all of the Ministry of Education of the Czech Republic, and GA16-09848S (GACR).
The Use of Modeling for Teaching Exponential Functions
Lincoln Ferreira Nunes, UFVJM, PROFMAT, Brazil
Dérek Bomfim Prates, UFVJM, ICET, Brazil
Jaqueline Da Silva, Federal University of Jequitinhonha and Mucuri Valleys, Institute of Science, Engineering and Technology, Brazil
Abstract: This paper presents a didactic construction process to observe the teaching and learning of mathematical contents related to the study of exponential functions in a students group enrolled in the first semester of the Science and Technology Bachelor's (STB) course of the Federal University of Jequitinhonha and Mucuri Valeys (UFVJM). As a contextualization tool strongly mentioned in the literature, Mathematical Modelling was used as a educational teaching tool to produce contextualization in the teaching and learning process of exponential functions to these students. In this sense, were used some simple models elaborated with the GeoGebra software and, to have a qualitative evaluation of the investigation and the results, we used Didactic Engineering as a methodology research. As a result of this detailed investigation some interesting details about the teaching and learning process were observed, discussed and detailed.
Acknowledgements: To CAPES for the Master Student fellowship and to FAPEMIG for the finantial support.
Was Polchinski wrong?Disributional Rindler spacetime with Levi-Cività connection induced a strong vacuum dominance. Unruh effect revisited.
Jaykov Foukzon, Israel Institution of Technology, Center for Mathematical Sciences, Israel
Abstract: The vacuum energy density of free scalar quantum field Φ in a Rindler distributional spacetime with distributional Levi-Cività connection is considered.It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background spacetime with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional spacetime such a Rindler distributional background spacetime, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional spacetimes with distributional Levi-Cività connection.In particular we obtain that the vacuum fluctuations <Φ²(δ)> has a singular behavior on a Rindler horizon δ₊=0:<Φ²(δ)>∼ δ⁻²,δ=c²/a,a→∞.Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski's account doesn't violation by the equivalence principle. https://arxiv.org/abs/0806.3026
Using Mathematical Models to Teach Functions to Secondary Students
Thamara Nepomucena, UFVJM, ICET, Brazil
Adaias Da Silva, UFVJM, PROFMAT, Brazil
Deborah Faragó Jardim, Federal University of Jequitinhonha and Mucuri Valleys, Institute of Science, Engineering and Technology, Brazil
Jaqueline Da Silva, Federal University of Jequitinhonha and Mucuri Valleys, Institute of Science, Engineering and Technology, Brazil
Abstract: The mathematical teaching in the basic education of the most of public Brazilian schools do not reach the goal. Several researches has shown that students finish their high school studies and start their universitary studies without the basic knowledge about functions. The lack of interest can be one of the main factors that causes a low achievement by the students children, young people or adults and this can be related to the teaching way. In general, the traditional teaching method does not stimulate the mathematical learning of these students, especially because it deals with a new students’ generation that is use to work with technology. In this sense, computational softwares and mathematical models has became important tools to help the student’s learning and can facilitate not only the teaching of quadratic functions but also another mathematical contents. The objective of this work was to understand the difficulties of the students with the quadratic functions, to analyze their comprehension about the related concepts and to evaluate the use of mathematical models with Geogebra as a teaching tool capable of providing an understanding of the some problems that are present in high school textbooks. The work was developed with a group of second year high school students in a public school in the state of Minas Gerais. After analyzing the students’ difficulties, based on the didactic transposition process, the mathematical and computational models were used in some intervention activities with the objective of complementing the teaching stimulating learning. As a result of the proposed activities there was a huge cognitive advance of the students related to the learning process because the use of a mathematical software with simple mathematical models helped them to understand the mathematical contents. Based on the students’ opinion it is possible to affirm that both techniques were a facilitator for the comprehension of the functions contents, stimulating their use in another studies activities involving mathematical and physics courses.
Acknowledgements: To Capes for the financial fellowship along the master studies of one of the authors.
Modelling Plane Geometry: the connection between Geometrical Visualization and Algebraic Demonstration
Lucas Pereira, UFVJM, PROFMAT, Brazil
Deborah Faragó Jardim, Federal University of Jequitinhonha and Mucuri Valleys, Institute of Science, Engineering and Technology, Brazil
Jaqueline Da Silva, Federal University of Jequitinhonha and Mucuri Valleys, Institute of Science, Engineering and Technology, Brazil
Abstract: Mathematics presents several factors that make science hardly understandable by the students when is taught in a traditional way. This traditional teaching focused on the teacher as a transmitter of knowledge leads the students to reach their goals by they own effort. In this way, the contents, teaching methodologies and the interpersonal relation between teacher and students do not have any relation with the student's academic life, without any contextualisation. Is very knowing in the literature that the use of mathematical modelling in the Plane Geometry teaching helps the students in their geometrical visualisation process. However, we must emphasise the contributions of this visualisation process to the students without distancing them to the algebraic thinking. Although some dynamic geometry softwares can not perform demonstrations, the techniques of modelling the behaviour of the geometrical construction leads the students to search for the proof of a given theorem. In this context, based on the concepts of Didactic Engineering as a research methodology, this work presents the teaching of Plane Geometry using mathematical models using GeoGebra, seeking to emphasise the importance of understanding the distinction between geometric visualisation and algebraic demonstration. The activities of this research were divided into three stages, where a diagnostic questionnaire was initially applied in the first stage, followed by the intervention where the students were submitted to dynamic activities with the software in the second stage, and finally a diagnostic questionnaire was applied for a better analysis of the data in the last stage.
Semantic similarity and analysis of the word frequency dynamics
Yulia Maslennikova, Kazan Federal univercity, radyophysics, Russian Federation
Vladimir Bochkarev, Kazan Federal University, Radiophysics, Russian Federation
Andrei Svetovidov, Kazan Federal University, Radiophysics, Russian Federation
Abstract: Analysis of words and word embeddings as parts of words in semantically linked groups is an important aspect in development of mathematical models for automatic text processing and, in particular, observation of the cultural evolution through language modification. Therefore, mutual study of frequency dynamics of synonymous word groups and semantically independent words is presented in this paper. Sets of synonymous adjectives were taken from WordNet, one of the largest lexical database in English. It includes more than 140 000 words, grouped into relatively small batch of synonyms. To obtain data on the word usage frequencies, Google Books Ngram database was involved. This corpus provides the opportunity to discover usage dynamics of words from over 5.2 billion books in 8 languages, issued in the period from 1583 to 2008. Our work is based on the approach of 1-grams frequency dynamics correlation analysis, where the degrees of correlation between sets of synonyms and sets of randomly selected unrelated words were compared. We examined the frequencies correlation of synonym pairs within each of 149 sets of synonyms and their corresponding antonymous groups of synonyms (298 sets overall), and also the correlation between words from each synonymous group and randomly picked group was computed. In order to acquire information on the correlation, we analyzed several measures of series correlation estimation. Furthermore, pairwise distances between vectors of synonyms and vectors of independent words were found. According to the data obtained, the highest accuracy was achieved with the Chebychev distance, providing the error probability of approximately 15%. Retrieved threshold of word proximity would serve as a basis for developing of semantically linked words recognizer.
Study of spin-crossover compound nanoparticles in the atom-phonon coupling model including a surface effect
Jamil Nasser , University of Versailles St. Quentin en Yvelines, LISV, France
Luc Chassagne, University of Versailles St. Quentin en Yvelines, LISV, France
Yasser Alayli, University of Versailles St. Quentin en Yvelines, LISV, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Abstract: A molecule of a spin-conversion compound has two electronic energy levels separated by Δ. The fundamental level is called low spin (LS) and the excited one is called high spin (HS)[1]. We study the thermal variation of the high-spin fraction, that is the fraction of molecules in the (HS) level, by using the atom-phonon coupling model [2,3] where we introduce the following surface effect: we assume that Δ has the value Δb for the molecules in the crystal bulk and the value Δse for those in the surface, with Δse < Δb. Both values depend on the compound, they do not vary with the crystal size. With this model, we can reproduce, at least qualitatively, two experimental results apparently contradictory and the disappearance and then the reappearance of the hysteresis loop when N, the number of atoms of the crystal, decreases. More, we can explain why the width of the hysteresis loop, decreases when N decreases [4] In our study, for any value of N, the entropy of the crystal is equal to zero at OK what is in agreement with the thirs law of Thermodynamics. References [1] A. Bousseksou, J. Nasser, J. Linares, K. Boukheddaden, F. Varret, J. Physique I, 2 (1992) 1381-1403 [2] J. Nasser, K. Boukheddaden, J. Linares, Eur. Phys. J. B, 39 (2004) [3] J. Nasser, S. Topcu, L. Chassagne, M. Wakim, B.Bennali, J. Linares,Y.Alayli, Eur. Phys. J. B, 115(2011) [4] H. Peng, S. Tricard, G. Félix, G. Molnar, W. Nicolazzi, L. Salmon, A. Bousseksou, Angewandte Zuschriften, 2014, 126, 11074-11078
Group classification of third order equations from the Riccati and Abel chain.
J C Ndogmo, University of Venda, Department of Mathematics and Applied Mathematics, South Africa
Abstract: The Lie pseudo-group of equivalence transformations is found for the family of third-order equations from the generalized version of the Riccati and Abel chain. This result is used to perform the complete group classification of the third order equations. This study reveals among others that no third order equation from the chain is linearizable, except when its expression is already linear. A simple characterization of the linear third order equations is given in terms of the parameter function of the family of equations considered.
MODEL OF PERSONAL CONSUMPTION UNDER CONDITIONS OF MODERN ECONOMY
Diana Rakhmatullina, Kazan (Volga region) Federal University, Department of Economic Methodology and History, Russian Federation
Elvira Akhmetshina, Kazan (Volga region) Federal University, Department of Economic Methodology and History, Russian Federation
Oksana Ignatjeva, Kazan (Volga region) Federal University, Department of Economic theory, Russian Federation
Abstract: In the conditions of the modern economy, in connection with the development of production, the expansion of the market for goods and services, its differentiation, active use of marketing tools in the sphere of sales, changes occur in the system of values and consumer needs. Motives that drive the consumer are transformed, stimulating it to activity. The article presents a mathematical model of personal consumption that takes into account modern trends in consumer behavior: - the consumer, making a choice, seeks to maximize the overall utility from consumption, physiological and socio-psychological satisfaction, in accordance with his expectations, preferences and conditions of consumption. The article proposes a formula for calculating the total utility; - the consumer is individual. The system of his preferences is formed under the influence of factors of a different nature. In the work identifies 11 types of consumers and the corresponding utility significance coefficients; - the consumer in the modern economy increasingly turns to loans in order to improve the overall level of satisfaction, which erases the clarity of the border of his budgetary opportunities. Our model takes this into account. In the paper also shows that the structure of consumer spending allows us to characterize and predict its further behavior in the market. Based on the proposed model and analysis of current trends in consumer behavior, conclusions and recommendations have been made that can be used by legislative and executive government bodies, business organizations, research centers and other structures to form a methodological and analytical tool for preparing a forecast model of consumpion.
Size effect on the three state thermal hysteresis of a 2D spin crossover nanoparticles
Salah ALLAL, University of Versailles St. Quentin en Yvelines, LATMOS, France
Devan Sohier, University of Versailles St. Quentin en Yvelines, LI-PaRAD, France
Thomas Dufaud, University of Versailles St. Quentin en Yvelines, LI-PARAD, France
Camille Harlé, University of Versailles St. Quentin en Yvelines, LATMOS, France
Pierre Dahoo, University of Versailles St. Quentin en Yvelines, LATMOS, France
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Abstract: In this report first we show, in the framework of the Ising-like model [1,2], a numerical simulation of a typical two step thermal transition obtained for a 12x12 square lattice: a "first-step hysteresis" for a high spin fraction Nhs between 0 – 0.5 and at a higher temperature a "second-step hysteresis" with Nhs between 0.5 and 1. Upon decreasing the number of molecules, the temperature range of the "second-step hysteresis" moves to a lower temperature, until with the square 4x4 lattice, a clear overlapped case with a three state behaviour is obtained. A detailed analysis of the role of the size system (4x4, 5x5, 6x6, 8x8 and 12x12) on the stability of this "Three state behaviour" is presented in this contribution. We study the influence of the surrounding environment on this specific thermal hysteresis. To solve the self-consistent equation related to the average value of the spin-operator <σ>, we use the density of the states calculated using a dynamic programming algorithm that will also be presented in this paper. References [1] Wajnflasz, J.; Pick, R., Low-spin-high-spin transitions in Fe2+ complexes. . J. Phys. Colloques 1971, 32, C1 [2] S. Guerroudj, R. Caballero, F. de Zela, C. Jureschi, J. Linares, K. Boukheddaden "Monte Carlo - Metropolis investigations of Shape and Matrix Effects in 2D and 3D Spin Crossover Nanoparticles", Journal of Physics Conference Series, 738 (2016) 012068
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.
Hydrodynamic instabilities at decay flow of nematic liquid crystals through the plane capillary of a variable gap.
Dina Shmeliova, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Sergey Pasechnik, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Arseniy Girgidov, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Gennady Maksimochkin, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Abstract: The shear flows of nematic liquid crystals (NLC) are characterized by non-Newtonian behavior and a number of specific hydrodynamic instabilities (HDI), arising due to a connection between the velocity gradient and the director. Previously [1,2], it was shown that usage of liquid crystals cells (LCS) of a variable gap provided effective way to study HDI in initially homeotropic LCS, which is connected with the escape of a director from the plane of quasi steady decay and oscillating Poiseuille flows. In this report we consider the possibility of a similar approach for a study of HDI in a specific type of a decay flow existing at a rise of NLC in the flat capillary of a variable gap. In this case the capillary can be replaced by a number of parallel channels of different gaps with different instant values of a pressure gradient, which induces a flow. The last feature differs such flow from the previously studied decay flow [1] with a constant value of a pressure gradient, applied to the channels of different thickness. The theoretical estimates for different initial geometries make possible to predict the dynamic of a capillary rise and time variations of local optical properties of NLC layer, connected with HDI. It can be used for explanation of the new experimental results, obtained at study of a capillary rise of NLC. [1] Pasechnik S.V., Chigrinov V.G., Shmeliova D.V., LIQUID CRYSTALS: VISCOUS AND ELASTIC PROPERTIES, 2009. С. 1-424. [2] Pasechnik S.V., Shmeleva D.V., Tsvetkov V.A., Krekhov A.P., Nasibullaev I.Sh., ORIENTATIONAL INSTABILITY IN A NEMATIC LIQUID CRYSTAL IN A DECAYING POISEUILLE FLOW, Journal of Experimental and Theoretical Physics. 2005. Т. 100. № 4. С. 804-810.
Acknowledgements: This work was supported by Ministry of Education and Science of Russian Federation - grant 3.9585.2017/8.9
A cryptographic hash function based on chaotic network automata
Jeaneth Machicao, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Odemir Bruno, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Abstract: Chaos theory has been used to develop several cryptographic methods relying on the pseudo-random properties extracted from simple nonlinear systems such as cellular automata (CA). Cryptographic hash functions (CHF) are commonly used to check data integrity. CHF "compress" arbitrary long messages (input) into much smaller representations called hash values or message digest (output), designed to prevent the ability to reverse the hash values into the original message. This paper proposes a chaos-based CHF inspired on an encryption method based on chaotic CA rule B1357-S2468. Here, we propose an hybrid model that combines CA and networks, called network automata, whose chaotic spatio-temporal outputs are used to compute a hash value. Following the Merkle and Damgard model of construction, a portion of the message is entered as the initial condition of the network automata, so that the rest parts of messages are iteratively entered to perturb the system. The chaotic network automata shuffles the message using flexible control parameters, so that the generated hash value is highly sensitive to the message. As demonstrated in experiments, the proposed model has excellent pseudo-randomness and sensitivity properties with acceptable performance when compared to conventional hash functions.
Acknowledgements: J. M. acknowledges a scholarship from the Brazilian agency CAPES (PROEX). O. M. B. acknowledges support from CNPq (Grant \#307797/2014-7 and Grant \#484312/2013-8) and FAPESP (grant \#14/08026-1).
Enhancement of the space of solutions of the kinetic-conformal Horava theory
Adrian Sotomayor, University of Antofagasta, Department of Mathematics, Chile
Alvaro Restuccia, University of Antofagasta, , Chile
Jorge Bellorín, University of Antofagasta, , Chile
Abstract: We show that in the Horava theory at the kinetic-conformal point there are more solutions of the field equations in the Hamiltonian formalism than in the original Lagrangian formalism. To hold this we add all the constraints, primary and secondary, to the Hamiltonian. There are certain configurations for the Lagrange multipliers associated to the secondary constraints leading to solutions that cannot be found in the original Lagrangian formulation. We show specific examples in vacuum and with a source. The solution with the source has homogeneous and isotropic spatial hypersurfaces.
Hadronization via gravitational confinement
Constantinos Vayenas, University of Patras, Chemical Engineering, Greece
Abstract: C.G. Vayenas1,2,* and D. Grigoriou1 1 LCEP, 1 Caratheodory St., University of Patras, Patras GR 26504, Greece 2 Division of Natural Sciences, Academy of Athens, 28 Panepistimiou Ave., GR-10679 Athens, Greece e-mail: cgvayenas@upatras.gr We analyze the thermodynamics and kinetics of baryogenesis using a Bohr-type rotating neutrino model in which the strong force is modeled as the gravitational force between ultrarelativistic neutrinos and the relativistic mass of these neutrinos becomes the rest mass of the gravitationally confined composite neutrino structure. In this work we derive a simple expression for the gravitational mass of the rotating neutrinos in terms of their total energy and rest mass. It is found that when the gravitational mass reaches the Planck mass, then the relativistic mass of the neutrinos equals the effective mass of u and d quarks.The model contains no adjustable parameters and leads to semiquantitative (within 1%) agreement with masses of baryons. It can also be extended by considering ultrarelavivistic rotating positron or electron-neutrino pairs, triplets or quartets whose mass is found to match within 2% that of W [1], Z and H bosons.The model also shows that hadronization is strongly exothermic (1.5 GeV/baryon formed) and is catalyzed by positrons, electrons and bosons. [1] Vayenas CG, Fokas AS, Grigoriou D (2016) On the structure, masses and thermodynamics of the W bosons. Physica A 450:37-48.
Acknowledgements: We thank Professor A. Fokas from University of Cambridge for numerous helpful discussions
Starobinsky model with f-essence
Shynaray Myrzakul, Al-Farabi Kazakh National University, Theoretical and nuclear physics, Kazakhstan
Sabit Bekov, Eurasian National University, General and Theoretical Physics , Kazakhstan
Kairat Myrzakulov, Eurasian National University, General and Theoretical Physics, Kazakhstan
Abstract: In this paper, we consider a cosmological model flat and homogeneous Universe for the Starobinsky model F(R)=\alpha R+\beta R^2, which non-minimally coupled with f-essence. For this model we obtained the field equations and considered particular solutions of the coupling and fermionic field functions. It is shown that the fermionic field can describes the nature of the universe.
Starobinsky model with a non-minimally coupled fermionic field
Yerlan Myrzakulov, L.N.Gumilyov Eurasian National University, General and Theoretical Physics, Kazakhstan
Abstract: In the present work, we investigate a Starobinsky model non-minimally coupled with the fermionic field for the Friedman-Robertson-Walker metric. For this model, a point-like Lagrangian and the equations of motion were obtained. To obtain cosmological solutions of these equations, we investigated the particular case of coupling and potential functions of the fermionic field.
Geometric plasticity at leaves from Ctenanthe oppenheimiana probed by measure of distances between stomata.
Humberto Antunes de Almeida Filho, Universidade de São Paulo, Physics, Brazil
Jeaneth Machicao, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Odemir Bruno, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Abstract: We measure the stomatal plasticity at \textit {Ctenanthe oppenheimiana} leaves based on distance between stomata pairs in microscopic images. The distance measurements revealed that the plasticity induced by environmental adaptations are measurable using the distance between neighbor stomata. Plants exposed to extreme light irradiation times from 24 to 4 hours per day, presented discernible relations between stomatal distances. The average distances between stomata pairs revealed a powerful tool to predict changes of plasticity of stomata according with different light acclimation conditions at Ctenanthe openheimiana plants.
Acknowledgements: H. A. A. F. acknowledges support from CNPQ (Conselho Nacional de Desenvolvimento Científico e Tecnológico) (Grants No.135137/2013-4). J. M. acknowledges a scholarship from the Brazilian agency CAPES (PROEX). O. M. B. acknowledges support from CNPq (Grant \#307797/2014-7 and Grant \#484312/2013-8) and FAPESP (grant \#14/08026-1).
Exact solution of F(R,T) model of gravity with a scalar field
Yerzhanov Koblandy, ENU, General and theoretical physics, Kazakhstan
Abstract: At present, in connection with a number of important discoveries in cosmology, the study of modified gravity models is popular. One of them is the F(R) model. Another similar model is F(T) gravity. Interest was aroused study the combined F(R,T) model of gravity. Another method is to use in the model some scalar fields. In this research, we solve the exact model that summarizes the F(R,T) gravity and the scalar field.
Approximate Bayesian Computation applied to Metrology for Nuclear Safeguards
Tom Burr, International Atomic Energy Agency, Information Management, Austria
Abstract: Approximate Bayesian Computation (ABC) is an inference option if a likelihood for the data is not available, but a model is available that outputs predicted observables for any specified input parameters. This paper reviews ABC and a few measurement methods used in nuclear safeguards, some of which have, and others of which do not have, corresponding likelihoods. A key aspect of metrology is uncertainty quantification (UQ), approached from physical first principles (“bottom-up”) or approached empirically by comparing measurements from different methods and/or laboratories (“top-down”). Although ABC is not commonly used in metrology, these example measurement methods illustrate advantages in ABC compared to current bottom-up approaches. ABC is also shown to be useful in top-down UQ. As a diagnostic, in bottom-up and top-down applications of ABC, the actual coverages of probability intervals are compared to the true coverages. If an ABC-based interval for a parameter is constructed to contain approximately 95% of the true parameter values, then it is important to verify that the actual coverage is close to 95%. It is shown that one advantage of ABC compared to other Bayesian approaches is its apparent robustness to miss-specifying the likelihood while maintaining good agreement between nominal and actual coverage.
Conservation laws of the Hirota-Maxwell-Bloch system and its reductions
Gaukhar Shaikhova, Eurasian National University, General and Theoretical physics, Kazakhstan
Kuralay Yesmakhanova, Eurasian National University, Department of Higher Mathematics, Kazakhstan
Guldana Bekova, Eurasian National University, , Kazakhstan
Sveta Ybyraiymova, Al-Farabi Kazakh National university, Department Higher Mathematics, Kazakhstan
Abstract: It is known that conservation law plays an important role in the study of nonlinear evolution equations and namely to integrability and constants of motion. In this paper, we construct infinitely many conservation laws for the Hirota-Maxwell-Bloch system and its reductions with symbolic computation from the Riccati form of the Lax pair.
Some cosmological solutions of F(T) gravity with f-essence
Tolkynay Myrzakul, Kazakh National University, Physics Department, Kazakhstan
Kairat Myrzakulov, Eurasian National University, General and Theoretical Physics, Kazakhstan
Abstract: In this work, we study the F(T) gravity with f-essence for the flat, homogeneous Friedman-Robertson-Walker universe. For this model, we have presented the point-like Lagrangian and the corresponding field equations. To describe the dynamics of the universe, we have investigated some cosmological solutions for F, K and h functions. It is shown that these solutions describe the late time accelerated expansion of the Universe.
The linear response function of a screw dislocation in a ferroelectrics
Viktor Dezhin, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Abstract: Small amplitude bending vibrations of a screw dislocation with arbitrary slip plane in an uniaxial ferroelectric is considered, the dislocation line is along the ferroelectric axis. To solve this problem the system of equations was made up. Fourier transform of the Peach-Koehler forces projection on the dislocation slip plane is obtained and a linear response function of a screw dislocation in a ferroelectric to an external force is found. The estimates of the additive to the dislocation effective mass and effective rigidity, the additional contribution to the damping of the dislocation vibrations are obtained.
Hipergeometric solutions to some nonhomogeneous equations of fractional order
Jorge Olivares Funes, University of Antofagasta, Departament of mathematics, Chile
Pablo Martin, Universidad de Antofagasta, Physics, Chile
Fernando Maass, Universidad de Antofagasta, Physics, Chile
Abstract: In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I0(x) , where I0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0< alpha < 1. Caputo dfinition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.
Acknowledgements: We thanks to the "Vicerrector de Investigacion" and the "Decano de Ciencias Basicas", of the "Universidad de Antofagasta" for support to this research.
PROGRAMMABLE LOGICAL ATOMIC GATE
Emil Gazazyan, Institute for Physical Research, Theoretical Physics, Armenia
Abstract: In this paper we demonstrate a simple realization of a programmable atomic gate in five-level atoms. The proposed scheme is based on the cyclic adiabatic population transfer resembling the technique of STIRAP and b-STIRAP in M-type system. In the present work we examine in detail the generalization of these population-transfer methods for five level diagrams in order to construct a tree-bit programmable atomic gate.
Acknowledgements: We are very grateful to Prof. Gayane Grigoryan for fruitful discussion. This work was supported by the SCS MES of Armenia (15T-1C066 theme) and IRMAS project.
Behavior of the solution of the Cauchy problem for an inhomogeneous hyperbolic equation with periodic coefficients
Hovik Matevossian, Federal Research Center "Computer Science and Control", Russian Academy of Sciences, Mathematical Physics and Mathematical Modeling, Russian Federation
Anatoly Vestyak, Moscow Aviation Institute - National Research University "MAI", Mathematical Modeling, Russian Federation
Abstract: We study the asymptotic behavior of the solution $u(x,t)$ of the Cauchy problem for a one-dimensional second-order hyperbolic equation with periodic coefficients (as $t\to\infty$) in which the initial data are zero, and the right-hand side of the equation has the form $f(x)\,exp(-i\omega t)$, where $\omega$ is real.
ASPECTS AND SOME RESULTS ON PASSIVITY AND POSITIVITY OF DYNAMIC SYSTEMS
Manuel De la Sen, UPV/EHU, Electricity and Electronics, Spain
Abstract: This paper is devoted to discuss various aspects of passivity results in dynamic systems and the characterization regenerative systems counterparts. In particular, the various concepts of passivity as standard passivity , strict input passivity , strict output passivity and very strict passivity ( i.e. Joint strict input and output passivity) are given and related to the storage function and the dissipation function . Then , the obtained results are related to external positivity of systems and positivity or strict positivity of the transfer matrices and transfer functions in the time- invariant case. On the other hand, it is discussed how to achieve or how eventually to increase the passivity effects via linear feedback by the synthesis of the appropriate feed-forward or feedback controllers or , simply, by adding a positive parallel direct input-output matrix interconnection gain.
F(T) gravity with scalar and fermion fields in (2+1) dimensions via Noether symmetry
Nurgissa Myrzakulov, Eurasian National University, General and Theoretical Physics, Kazakhstan
Abstract: In this paper, we will consider a modified F(T) gravity with scalar and fermion fields in (2+1) dimensions. The equations of motion for these models are obtained. Using the Noether symmetry approach, we determine the form of the coupling function and the potential.
A North Sea-Baltic Sea regional coupled models: Atmosphere, wind waves and ocean
Joanna Staneva, HZG, Institute for Coastal Research, Germany
Corinna Schrum, HZG, Coastal Systems, Germany
Abstract: The coupling of models is a commonly used approach when addressing the complex interactions between different components of earth system. In climate and forecasting research and activities, advanced models are needed and there is an urge towards the use of coupled modelling. This study presents the development of a new, high-resolution, coupled atmosphere, ocean and wave model system for the North Sea and the Baltic Sea, which is part of the Geestacht COAstal model SysTem GCOAST. We focus on the nonlinear feedback between strong tidal currents and wind-waves, which can no longer be ignored, in particular in the coastal zone where its role seems to be dominant. The proposed coupling parameterizations account for the feedback between of the upper ocean on the atmospheric circulation by accounting for the effects of sea surface temperature and the sea surface roughness. Several sensitivity experiments are performed to estimate the individual and collective effects of different coupling components. The performance of the coupled modelling system is illustrated for the cases of several extreme events. For example, the inclusion of wave coupling leads to decreases strong winds through wave dependent surface roughness or changes sea surface temperature, the mixing and ocean circulation; leading to better agreement with in-situ and satellite measurements. Comparisons with available atmospheric and oceanic observations showed that the use of the fully coupled system reduces the errors, especially under severe storm conditions. This justifies the further developments and implementation of the coupled model systems, for both, operational and climate, research and development activities.
Impact of telecommunication technologies on the middle class formation
Asiya Khusnullova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Svetlana Absalyamova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Rustem Sakhapov, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation
Chulpan Mukhametgalieva , Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Abstract: The article is devoted to the study of the impact of the information economy on the formation of the middle class. The paper identifies factors contributing to the increase in the share of the middle class in the transition to the information economy. The positive synergetic influence of telecommunication technologies on the formation of the middle class is considered through a possibility of using virtual spaces for labor and educational activities, a possibility of obtaining high returns in the form of dividends on intellectual capital, a qualitative change in the structure of needs, an access to new types of information services, etc. Authors develop a complex model of research of the middle class in the information economy, differing from those available using an expanded list of criteria. In addition to such widely used criteria as income level, level of education and self-identification, the criterion "degree of involvement in the information society" was introduced. The study substantiates that the transition to the information economy made an access to information and communication technologies one of the most significant criteria for social differentiation of society. On the basis of the model, an econometric estimate of the middle class has been carried out, which makes it possible to reveal the share of the middle class in modern society, dynamics of its development, as well as multicollinearity between spending on education, the Gini coefficient, access to information and telecommunication technologies and the size of the middle class.
GEOMETRIC AGGREGATION OPERATORS WITH INTERVAL VALUED PYTHAGOREAN TRAPEZOIDAL FUZZY NUMBERS WITH APPLICATION TO GROUP DECISION MAKING
Muhammad SHAKEEL, HAZARA UNIVERSITY MANSEHRA, MATHEMATICS, Pakistan
Abstract: Interval valued Pythagorean fuzzy number is a new tool for uncertainty and vagueness. It is a generalization of fuzzy numbers and intuitionistic fuzzy numbers. This paper deal with interval valued Pythagorean trapezoidal fuzzy numbers. In this paper we introduce interval valued Pythagorean trapezoidal fuzzy (IPTFN) numbers and some operation on IPTFN, and we also define different types of operators for aggregating interval valued Pythagorean trapezoidal fuzzy numbers. We present interval valued Pythagorean trapezoidal fuzzy weighted geometric (IPTFWG) operator, interval valued Pythagorean trapezoidal fuzzy ordered weighted geometric (IPTFOWG) operator and interval valued Pythagorean trapezoidal fuzzy hybrid geometric (IPTFHG) operator. Finally we develope a general algorithm for group decision making problem.
Geometry from stomata networks at leaves of the Ctenanthe oppenheimiana.
Humberto Antunes , Universidade de São Paulo, Instituto de Fisica de São Carlos, Brazil
Jeaneth Machicao, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Odemir Bruno, Universidade de São Paulo, Instituto de Física de São Carlos, Brazil
Abstract: We measure the stomatal plasticity at Ctenanthe oppenheimiana leaves based on distance between stomata pairs in microscopic images. Theoretical graphs were built according with distance thresholds as connectivity parameter. The distance measurements revealed that changes in stomatal plasticity induced by environmental adaptations are measurable using the distance parameters between neighbor stomata. The theoretical networks based at distances between stomata depends on how the connectivity can vary according with the threshold distances. Plants exposed to extreme light irradiation times from 24 to 4 hours per day, presented discernible relations between stomatal interdistances. The graphs related to average distances between stomata pairs revealed a powerful tool to predict changes of the geometric distribution of stomata at live Ctenanthe openheimiana plants.
Acknowledgements: Conselho Nacional de Desenvolvimento Científico e Tecnológico- (135137/2013-4)
Modeling of the dependence of magnetic elastomer’s deformation on the magnetic field
Dmitriy Solodkiy, FAR EASTERN FEDERAL UNIVERSITY, Theoretical and nuclear physics, Russian Federation
Abstract: Using the method of movable cellular automata, we have conducted the modeling of the dependence of magnetisation and deformation of the magnetic elastomer on the external magnetic field. This study have showed, that values of saturation deformation is greatly dependent on the distribution of the magnetic particles in non-magnetic matrix of elastomer. The comparison was made for two types of spatial distributions of magnetic particles: ordered (chain) and disordered (random). It turned out, that saturation deformation of elastomer with ordered distribution is almost 2 times higher than saturation deformation of elastomer with random distribution of magnetic particles.
Generalized Bell states maps physical systems' quantum evolution into a grammar for quantum information processing
Francisco Delgado, Instituto Tecnologico y de Estudios Superiores de Monterrey RFC: ITE430714KI0, Physics and Mathematics, Mexico
Abstract: Quantum information processing should be generated through the control of quantum evolution for physical systems used as resource. General Hamiltonian models comprising several systems as superconductin circuits, spin-spin couplings in ions and artificial anyons in electronic gases have a quantum dynamics which can be traslated into more natural languages for quantum information processing when they are expressed in terms of non-local basis, particularly the generalized Bell basis. On this terrain, this language lets to establish manipulation operations on the associated quantum information states in a more similar form as classical information processing does. This work shows how these kind of operations can be settled and implemented for quantum states design and quantum processing on the basement of a quantum dynamics expressed in terms of those non-local states.
An analytic relation between the fractional parameter in the Mittag-Leffler function and the chemical potential in the Bose-Einstein distribution through the analysis of the NASA COBE monopole data
Naomichi Suzuki, Matsumoto University, Department of comprehensive management, Japan
Abstract: In order to extend the Bose--Einstein (BE) distribution to fractional order, we turn our attention to the equation, $\partial f/\partial x = f+f^2$, which is proposed by Planck~\cite{Planck1900}, and satisfied with the stationary solution of the Kompaneets equation~\cite{Komp1957}. Substituting $1/R(x)$ for $f(x)$, we have $\partial R(x)/\partial x= R(x)+1$. Then, the Caputo fractional derivative~\cite{Caputo1967, Podlubny1999} with order $p$ ($p > 0$) is introduced in place of the partial derivative of variable $x$: % ${}_0^CD^p_x R(x) = R(x) + 1$. % The Caputo fractional derivative of function $R(x)$ for $m=1,2,\ldots$ is defined as \\ \qquad ${}^C_0\! D^p_x R(x) = \frac{1}{\Gamma(m-p)} \int_0^x (x-\tau)^{m-p-1} f^{(m)}(\tau) d\tau$, \quad $(m-1 \le p < m)$.\\ % If $p=m-1$, it reduces to the ordinary derivative, $\displaystyle{ {}^C_0\! D^p_x R(x) = d^{m-1} R(x)/dx^{m-1} }$. Under the initial condition, $R^{(j-1)}(0)=0$ ($j=1,2,\ldots, m$), we obtain $R(x)=E_p(x^p)$, where $E_p(x)$ denotes the Mittag--Leffler (ML) function defiend by, $E_p(x)=\sum_{k=0}^\infty \frac{x^k}{\Gamma(kp+1)}$. Then, the fractional BE distribution is given as $f(x) = 1/R(x) = 1/(E_p(x^p) - 1)~\cite{Biya2015}$, which is used to analyze the NASA COBE monopole data~\cite{Mather1994}. By the use of the integral representation of the ML function~\cite{Podlubny1999}, we obtain a new formula for the fractional BE distribution. Based on theanalysis of the NASA COBE monopole data, an identity $p\simeq e^{-\mu}$ is found~\cite{Biya2017}, where $\mu$ is the dimensionless constant chemical potential that was introduced to the BE distribution by the NASA COBE collaboration. \begin{thebibliography}{99} \bibitem{Planck1900} %[1] M. Planck, Verh. Deutsch. Phys. Ges. {\bf 2}, 202 and 237 (1900). \bibitem{Komp1957} %[2] A. S. Kompaneets, Sov. Phy. JETP {\bf 4}, 730 (1957); R. Weymann, Phys. Fluids {\bf 8}, 2112 (1965). \bibitem{Caputo1967} %[3] M. Caputo, Geophys. J. R. Astr. Soc. {\bf 13}, 529 (1967); M.~Caputo and F.~Mainardi, Riv. Nuov. Cim. (Ser. II), {\bf 1}, 161 (1971). \bibitem{Podlubny1999} %[4] I. Podlubny, \textit{Fractional Differential Equations} (Academic Press, San Diego, 1999). \bibitem{Biya2015} %[5] M. Biyajima, T. Mizoguchi and N. Suzuki, Physica {\bf A 440}, 129 (2015). \bibitem{Mather1994} %[6] J.C. Mather et al., Astrophys. {\bf J. 420}, 439 (1994); See also, D.J. Fixsen et al., Astrophys. {\bf J. 473}, 576 (1996). \bibitem{Biya2017} %[7] M. Biyajima, T. Mizoguchi and N. Suzuki, in preparation. \end{thebibliography}
Nonlinear distributional geometry and Colombeau analysis of gravitation singularities in distributional general relativity with distributional Levi-Civit`a connection
Jaykov Foukzon, Israel Institution of Technology, Center for Mathematical Sciences, Israel
Abstract: It seemed natural to identify gravitation singularities with singular values of metric or curvature components and their scalar combinations [1]. However, under formal and mathematically abnormal calculation which known from a very old physics handbooks [2]-[3], such a notion depends on choosing a reference frame and includes fictious singularities which being real for some observers are absent for others.In a nutshell, there is a widespread belief that there exist true physical singularities and unphysical,i.e.,coordinate singularities. We try to base our approach to the problem of gravitation singularities on the fact that a gravitation singularity leads by a natural way, directly to a singularity of a space-time structure in sense of Colombeau distributional geometry [4]-[6].We aim to describe gravitation singularities using mathematically rigorous approach via Colombeau nonlinear distributional space-time structures with distributional Levi-Civit`a connection.We pointed out that some important physical singularities which many years mistakenly considered as coordinate singularities. [7]-[8] [1] D. Ivanenko and G. Sardanashvily,Foliation analysis of gravitation singularities, Physics Letters A Volume 91, Issue 7, 27 September 1982, Pages 341-344. https://doi.org/10.1016/0375-9601(82)90428-5 [2] L. D. Landau and E. M. Lifshitz, The Classical Theory of Fields, 7th ed. (Nauka, Moscow, 1988; Pergamon, Oxford,1975). [3] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation (Freeman, New York, 1973; Mir, Moscow, 1977). [4] M, Kunzinger, R. Steinbauer,Foundations of a Nonlinear Distributional Geometry, Acta Applicandae Mathematica,April 2002, Volume 71, Issue 2, pp 179--206. [5] J.A. Vickers,Distributional geometry in general relativity,Journal of Geometry and Physics 62 (2012) 692--705. [6] R. Steinbauer, Nonlinear distributional geometry and general relativity, https://arxiv.org/abs/math-ph/0104041v1 [7] J. Foukzon,Distributional Schwarzschild Geometry from Non Smooth Regularization Via Horizon,British Journal of Mathematics & Computer Science, ISSN: 2231-0851, 11(1): 1-28, 2015, Article no.BJMCS.16961,DOI : 10.9734/BJMCS/2015/16961 [8] J. Foukzon, A. Potapov and E. Menkova,Distributional SAdS BH-Spacetime Induced Vacuum Dominance,British Journal of Mathematics & Computer Science 13(6):1-54, 2016, Article no.BJMCS.19235,DOI:10.9734/BJMCS/2016/19235
Honeycomb lattice heat capacity with long-range and short-range interactions
Petr Andriushchenko, Far Eastern Federal University, Department of theoretical and experimental physics, Russian Federation
Abstract: Abstract: Two series of samples which are consisting of various numbers of particles formed in hexagonal spin ice arrays, square and hexagonal (''from the center'') forms with the different radius of interaction were simulated. Models were considered with long-range (LR) and short-range (SR) dipole-dipole interaction. The temperature dependence of the heat capacity in LR interaction models shows anomalous character, there are two temperature peaks, ie, critical behavior of the system of dipoles in the region of Tc significantly changes. The first peak with increasing number of particles increases and the second peak reduces. The heat capacity peak of models with SR interaction with increasing number of particles is reduced. In models with SR interaction, the phase transition is absent, while models with LR interactions show the phase transition. An original order parameter allowing to separate the ordered phase from the disorder for LR model is proposed. The order parameter is a percolation cluster formed by vortices of hexagons in the lattice.
Quantum field theory in Snyder space
Salvatore Mignemi, Università di Cagliari, Mathematics, Italy
Abstract: We present an introduction to the definition of quantum field theory in Snyder space, a model of noncommutative geometry that preserves Lorentz invariance.
The Use of Logistic Model in RUL Assessment
Robert Gumiński, Warsaw University of Technology, Institute of Vehicles, Poland
Abstract: The paper takes on the issue of assessment of remaining useful life (RUL). The goal of the paper was to develop a method, which would enable use of diagnostic information in the task of reducing the uncertainty related to technical risk. Prediction of the remaining useful life (RUL) of the system is a very important task for maintenance strategy. In the literature RUL of an engineering system is defined as the first future time instant in which thresholds of conditions (safety, operational quality, maintenance cost, etc) are violated. Knowledge of RUL give of possibilities planning of testing and repair activities. Important in this task is building models of damage development. In presented work, logistic function will be used to model fatigue crack development. We must remember that very difficult is modeling of every phase of damage development. More effective is modeling of every phase of damage separately, especially including on-line diagnostic information. Particular attention was paid to the possibility of forecasting the occurrence of damage due to fatigue while relying on the analysis of the structure of a vibroacoustic signal.
Structure, electronic properties and design of materials: insights from electron density distribution and derived quantities.
Antoine Villesuzanne, CNRS, University of Bordeaux, Institute of Condensed Matter Chemistry of Bordeaux (ICMCB), France
Mike Whangbo, North Carolina State University, Dept of Chemistry, United States
Guosheng Shao, Zhengzhou University, State Centre for International Cooperation on Designed Low-carbon & Environmental Materials (CDLCEM), China
Werner Paulus, ICGM, University of Montpellier, Institute Charles Gerhardt, France
Abstract: The distribution of electron density in a molecule or a solid is a key quantity for rationalizing and predicting most physical (or chemical) phenomena ; it determines uniquely the energy of the system, which allowed the development of density functional theory (DFT) for the calculation of electronic structures. In solid state physics and chemistry, there are many possible post-treatments of the electron density distribution: charge partitioning methods (Bader's Atoms in Molecules theory, overlap population, Löwdin's natural orbitals,...), Electron Localization Function, Born effective charges, for example. Here, we discuss how electron density distribution, calculated within DFT, was used to address phenomena such as ion migration in ionic conductors (oxydes for application in fuel cells). Also, we present the development of energy density maps for the study of structural phase transitions and ion/vacancy migration energetics, and simple mathematical models of charge distribution in one- or two dimensional systems, for the rationalization of observed charge density wave patterns and superstructures. Finally, we propose a new extrapolation scheme for the estimation of surface energies in crystals, based on DFT calculations for oriented slabs.
Acknowledgements: The authors thank the National Agency for Research (ANR, France), the Technology Strategy Board (UK) and the State Key Research Programme for Fundamental Research (China)
QKD optical scheme calibration system
Vladimir Kurochkin, Russian Quantum Center (RQC), quantum communications group, Russian Federation
Alexander Duplinskiy, Russian Quantum Center (RQC), , Russian Federation
Alan Kanapin, Russian Quantum Center (RQC), , Russian Federation
Vasiliy Ustimchik, Russian Quantum Center (RQC), , Russian Federation
Yuri Kurochkin, Russian Quantum Center (RQC), , Russian Federation
Abstract: One-way quantum key distribution (QKD) optical schemes require active stabilization algorithms for continuous operation. To achieve this a mathematical model for a new optical scheme has been developed. The model uses Jones calculus to describe the polarization state evolution within the optical scheme. The developed algorithms have been successfully tested experimentally.
Acknowledgements: The support from Ministry of Education and Science of the Russian Federation in the framework of the Federal Program (Agreement 14.582.21.0009, ID RFMEFI58215X0009) is acknowledged.
Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers
Mohamed BOUALEM, UNIVERSITY OF BEJAIA, TECHNOLOGY, Algeria
Abstract: In this investigation, a single server feedback $M/M/1/N$ queueing system with vacation, balking, reneging and retention of reneged customers is analyzed. By considering the mathematical modeling, we examine the steady state probabilities and obtain the stationary distribution of the number of customers in the system when the server is in busy and on working vacation, we also study the effect of different parameters on the characteristics of the model and on total expected profits. Some important performance measures of the system by using the stationary distribution are obtained. By setting the appropriate parameters, some special cases are discussed. Furthermore, a numerical study of different performance measures and different types of costs involved with the change in diverse parameters of the system is carried out.
Modeling the Interdisciplinary in the Process of Training Physics
Tatyana Gnitetskaya, Far Eastern Federal University , The School of Natural Sciences, Russian Federation
Elena Ivanova, Far Eastern Federal University, The School of Natural Sciences, Russian Federation
Larisa Dubovaya, Far Eastern Federal University, School of Natural Sciences, Russian Federation
Yuliya Shutko, Far Eastern Federal University, The School of Natural Sciences, Russian Federation
Natalya Kovalchuk, Far Eastern Federal University, Department of General and experimental physics, Russian Federation
Elena Karnaukhova, FEFU, The Department of General and experimental physics, Russian Federation
Abstract: The information model of interdisciplinary links (Gnitetskaya T., 2016) allows to reach the interdisciplinary in the process of training physics. Presenting the fundamental physical term with semantic structure we can see that structure’s node(s) where interdisciplinary link(s) from physics to chemistry and vice versa could be established. Method of optimization the interdisciplinary content was described in this paper. Method based on quantity estimation of the information – an entropy, as characteristic of semantic structure graph. Results of entropy calculation for interdisciplinary content of term “atom structure”, corresponded to school physics’ level, were discussed.
Modeling Interdisciplinary Notion “Substance” with Information Model
Tatyana Gnitetskaya, Far Eastern Federal University , The School of Natural Sciences, Russian Federation
Elena Ivanova, Far Eastern Federal University, The School of Natural Sciences, Russian Federation
Natalya Kovalchuk, Far Eastern Federal University, Department of General and experimental physics, Russian Federation
Yuliya Shutko, Far Eastern Federal University, The School of Natural Sciences, Russian Federation
Larisa Dubovaya, Far Eastern Federal University, School of Natural Sciences, Russian Federation
Elena Karnaukhova, FEFU, The Department of General and experimental physics, Russian Federation
Abstract: In this paper the modeling fundamental notions in physics and chemistry based on the information model of interdisciplinary links was described. It was shown that introducing interdisciplinary information about notion substance from physics course to chemistry course didn’t stipulate the students’ overloading, because value of entropy in interdisciplinary content of chemistry slightly different from entropy in content without interdisciplinary information. A conclusion about necessity of addition the interdisciplinary content from physics to chemistry courses and vice versa has done. It was marked that compact proportions of semantic structures determine their fast loading ability. Therefore we recommend to practice the interdisciplinary semantic structures method in mobile and on-line kinds of learning.
An analysis of burn-off impact on the structure microporous of activated carbons formation
Mirosław Kwiatkowski, AGH University of Science and Technology, Faculty of Energy and Fuels, Poland
Abstract: The paper presents the results on the application of the uLBET numerical method as a tool for analysis of the microporous structure of activated carbons obtained from a bituminous coal. The uLBET method was employed particularly to evaluate the impact of the burn-off on the obtained microporous structure parameters of activated carbons.
Acknowledgements: The research is led within the AGH University of Science and Technology In Krakow grant No. 11.11.210.373.
An analysis of the influence of production conditions on the development of the microporous structure of the activated carbon fibres using the LBET method
Mirosław Kwiatkowski, AGH University of Science and Technology, Faculty of Energy and Fuels, Poland
Abstract: The paper presents the results of the research on the application of the new mathematical models of multilayer adsorption on heterogeneous surfaces with the unique numerical fast multivariant identification procedure as a tool for analysing the microporous structure of the activated carbon fibres obtained from polyacrylonitrile by chemical activation using potassium and sodium hydroxides. The novel method of the fast multivariate fitting of the mathematical models of multilayer adsorption on heterogeneous surfaces to the empirical adsorption data was employed particularly to evaluate the impact of the used activator and the hydroxide to polyacrylonitrile ratio on the obtained microporous structure of the activated carbon fibres.
Acknowledgements: The research is led within the AGH University of Science and Technology in Krakow grant No. 11.11.210.373.
Approximate Bayesian Computation in the estimation of the parameters of the Forbush decrease model.
Anna Wawrzynczak-Szaban, Siedlce University, Science Faculty, Institute of Computer Sciences, Poland
Piotr Kopka, National Centre for Nuclear Research, Poland, , Poland
Abstract: Realistic modeling of the complicated phenomena as Forbush decrease of the galactic cosmic ray intensity is a quite challenging task. One aspect is a numerical solution of the Fokker-Planck equation in five-dimensional space (three spatial variables, the time and particles energy). The second difficulty arises from a lack of detailed knowledge about the spatial and time profiles of the parameters responsible for the creation of the Forbush decrease. Among these parameters, the central role plays a diffusion coefficient. Assessment of the correctness of the proposed model can be done only by comparison of the model output with the experimental data of the galactic cosmic ray intensity. We apply the Approximate Bayesian Computation (ABC) methodology to match the Forbush decrease model to experimental data. The ABC method is becoming increasing exploited for dynamic complex problems in which the likelihood function is costly to compute. The main idea of all ABC methods is to accept samples as an approximate posterior draw if its associate modeled data is close enough to the observed one. In this paper, we present application of the Sequential Monte Carlo Approximate Bayesian Computation algorithm scanning the space of the diffusion coefficient parameters in the vicinity of the space where the Forbush decrease is created. The proposed algorithm is adopted to create the model of the Forbush decrease observed by the neutron monitors at the Earth in March 2002. The model of the Forbush decrease is based on the stochastic approach to the solution of the Fokker-Planck equation.
Acknowledgements: This work is supported by the Polish National Science Centre grant awarded by decision number DEC- 2012/07/D/ST6/02488.
Modelling of pulsed electron beam induced graphite ablation: Sublimation versus melting.
Muddassir Ali, Laurentian University, Bharti School of Engineering, Canada
Redhouane Henda, Laurentian University, School of Engineering, Canada
Abstract: Pulsed electron beam ablation (PEBA) has recently emerged as a very promising technique for the deposition of thin films with superior properties. Interaction of the pulsed electron beam with the target material is a complex process, which consists of heating, phase transition, and erosion of a small portion from the target surface. Ablation can be significantly affected by the nature of thermal phenomena taking place at the target surface, with subsequent bearing on the properties, stoichiometry and structure of deposited thin films. A two stage, one-dimensional heat conduction model is presented to describe two different thermal phenomena accounting for interaction of a graphite target with a polyenergetic electron beam. In the first instance, the thermal phenomena are comprised of heating, melting and vaporization of the target surface, while in the second instance the thermal phenomena are described in terms of heating and sublimation of the graphite surface. In this work, the electron beam delivers intense electron pulses of ~100 ns with energies up to 16 keV and an electric current of ~400 A to a graphite target. The temperature distribution, surface recession velocity, ablated mass per unit area, and ablation depth for the graphite target are numerically simulated by the finite element method for each model. Based on calculation findings and available experimental data, ablation appears to occur mainly in the regime of melting and vaporization from the surface.
Multiscale Structure of Polynomial Dynamics: From Localization to Pattern Formation
Antonina Fedorova, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation
Michael Zeitlin, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation
Abstract: We consider a wavelet based multiscale description for nonlinear optimal dynamics (energy minimization in a high power electromechanical system as a key example). In a particular case, we have the solution as a series on shifted Legendre polynomials parametrized by the solutions of the reduced algebraical systems of equations. In the general case, we represent the solution via multiscale decomposition in the base of various families of compactly supported wavelets. In this case the solution is parametrized by solutions of two reduced algebraic problems, one as in the first case and the second one is some linear problem obtained from the popular wavelet constructions: Fast Wavelet Transform, Stationary Subdivision Schemes, the method of Connection Coefficients. Such a machinery allows us to consider maximally localized bases in the underlying functional spaces together with most sparse representation for all type of operators involving in the initial set-up. All that provides the best possible convergence properties and as a result our numerical modeling is more flexible and saves CPU time. In addition, the final representation is parametrized by the reduced pure algebraic construction (the so-called general dispersion relations) and allows us to solve the dynamical or optimal control problems (energy minimization, e.g.)in a most effective way.
Wigner Quasiclassics via Multiresolution: Beyond Gaussians
Michael Zeitlin, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation
Antonina Fedorova, IPME RAS, Mathematical Methods in Mechanics Group, Russian Federation
Abstract: We present the application of our variational-multiscale approach to numerical/analytical calculations in the general quasi-classical set-up. The starting points are Wigner-Weyl-von Neumann framework as well as Moyal (naive) deformation quantization. Our technique allows to cover all complicated underlying features of compex quantum dynamics based on the proper choice of background functional spaces which determine dynamical properties together with the internal structure of pseudo-differential operators incorporated in the full hierarchy of Wigner-like equations describing the evolution of the quasiprobability beyond trivial gaussian-like area with pure postitive Wigner functions. The choice of hidden underlying symmetry and its representation on the orbits of proper actions provide us with the filtration of the background Hilbert space of states which implies the whole tower of internal hidden scales by using multiresolution decomposition. All that allows to consider maximally localized quantum states and most sparse representation for all set of observables. At the same time the orbit structure allows to consider basic non-local phenomena like entanglement with possible subsequent decoherence. Our main applications in this consideration are related with a description of quantum properties in nonlinear beam dynamics, both in accelerator and plasma physics but such general background provides all possibilities to describe the modeling of prototypes of any future quantum devices.
Dynamics of nanoparticle concentration in nanofluids under laser light field
Victor Krishtop, Far Eastern State Transport University, Physics, Russian Federation
Polina Vinogradova, Far Eastern State Transport University, Mathematics , Russian Federation
Abram Livashvili, Far Eastern State Transport University, Mathematics , Russian Federation
Galina Kostina, Far Eastern State Transport University, Mathematics , Russian Federation
Tatiana Bryukhanova, Pacific National University, Physics, Russian Federation
Abstract: The dynamics of the concentration of a nanofluids placed in a light field with a Gaussian intensity profile is studied theoretically. The investigation is based on the analytical and numerical solutions of the system of linearized heat conduction and convection-diffusion equations. The convection-diffusion equation contains terms that correspond both to the Soret effect and to the transfer of nanoparticles, caused by the action of a light field on them (electrostriction). The dependence of the coefficient of thermal conductivity of the medium on the concentration is taken into account. It is shown that under these conditions single traveling waves appear in the medium, the velocity of which depends not only on the thermal physical parameters of the medium, but also on the polarization of the particles. Conditions, under which the stratification of the medium is possible, are found.
Acknowledgements: Work was supported by Ministry of education and science of Khabarovskiy krai (Russia)
Electrically induced shear flows of liquid crystals confined to porous polymer films for THz application
Dina Shmeliova, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Sergey Pasechnik, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Olga Semina, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Alexander Dubtsov, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Valentin Tsvetkov, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Sergey Trifonov, Moscow Technological University, Problem laboratory of molecular acoustics, Russian Federation
Abstract: In this report we present a new approach based on usage of electro-osmotic flows, arising in porous polymeric films filled with liquid crystals, to control electromagnetic waves of terahertz (THz) frequency range. Two possible variants of realization of such approach are considered. In the first case the sample of porous film, connected with a traditionally used plane LC cell, acts as an electro-hydrodynamic pump. It provides a declination of LC orientation from the initial state and corresponding changes of the refractive index of LC media. Usage of the previously obtained results [1] on electro-kinetic phenomena in porous PET films, filled with a standard liquid crystal 5 CB, makes possible to calculate the parameters of linear response of a plane layer on the shear flow arising in the plane cell. The possible influence of nonlinear phenomena in shear flows [2] will be also considered. The second case is connected with a possibility of a direct influence of an electro-osmotic flow on LC confined to cylindrical pores. The threshold field strength, needed to change the initial orientation of LC, as a function of a pore’s will be estimated. The particular examples of possible terra fluidic devices, based on electro-osmotic flows of LC, will be considered. [1] Chopik A., Pasechnik S., Semerenko D., Shmeliova D., Dubtsov A., Srivastava A.K., Chigrinov V., ELECTRO-OPTICAL EFFECTS IN POROUS PET FILMS FILLED WITH LIQUID CRYSTAL: NEW POSSIBILITIES FOR FIBER OPTICS AND THZ APPLICATION, Optics Letters. 2014. Т. 39. № 6. С. 1453-1456. [2] Pasechnik S.V., Chigrinov V.G., Shmeliova D.V., LIQUID CRYSTALS: VISCOUS AND ELASTIC PROPERTIES, 2009. С. 1-424.
Acknowledgements: This work was supported by Ministry of Education and Science of Russian Federation, identification number- RFMEFI58316X0058.
Generalized logistic map and its application in chaos based cryptography
Marcin Lawnik, Silesian University of Technology, Faculty of Applied Mathematics, Poland
Abstract: The logistic map is commonly used in, for example, chaos based cryptography. However, its properties do not render a safe construction of encryption algorithms. Thus, the scope of the paper is a proposal of the generalization of a logistic map by means of a well recognized family of chaotic maps. In the next step, an analysis of Lyapunov exponent and the distribution of a iterative variable are studied. The obtained results confirm that the analyzed model can safely and effectively replace a classic logistic map for applications involving chaotic cryptography.
Crossover to first-order transition in XY model due to higher-order interactions
Milan Zukovic, Institute of Physics, Faculty of Science, P. J. Safarik University, Department of Theoretical Physics and Astrophysics, Slovakia (Slovak Republic)
Abstract: The effect of inclusion of higher-order interactions in the XY model on critical properties is studied by Monte Carlo simulations. It is found that an increasing number of the higher-order terms in the Hamiltonian modifies the shape of the potential, which beyond a certain value leads to the change of the nature of the transition from continuous to first order. The evidence for the first-order transition is provided in the form of the finite-size scaling and the energy histogram analysis. A rough phase diagram is presented as a function of the number of the higher-order interaction terms.
Acknowledgements: This work was supported by the Scientific Grant Agency of Ministry of Education of Slovak Republic (Grant No. 1/0331/15) and the scientific grants of Slovak Research and Development Agency provided under contract No. APVV-0132-11 and No. APVV-14-0073.
Lorenz curves in a new science-funding model
Ding-wei Huang, Chung Yuan Christian University, Physics, Taiwan, Province Of China
Abstract: Recently, J. Bollen et al. have suggested a new approach to fund science. The idea is to fund every scientist equally and to ask all scientists to give a fraction of their funding to other scientists. The more one receives funding from others, the more one gives away funding to others. Every scientist serves as a funding agency to distribute a small amount of funding. As the funding circulates fluidly in the community, the system can potentially be fairer and more efficient. The funding distribution is expected to converge toward an optimal result favored by the entire community of scientists. Along this line, we propose an agent-based model to theoretically and systematically explore the implications of this approach. We introduce various parameters and examine their effects. The concentration of funding is shown by the Lorenz curves and the Gini coefficient. In this model, all scientists are treated equally and follow the well-intended regulations. All scientists give a fixed ratio of their funding to others. The fixed ratio becomes an upper bound for the Gini coefficient. It seems that the concentration of funding can be effectively suppressed, since the Gini coefficient can be easily controlled by adjusting the ratio. In some parameter range, the fluidity of funding is significant and as desired. In other parameter range, the undue concentration of funding still happens swiftly. We show that the seemingly perfect regulations cannot prevent the undesired results from happening, where a minority of scientists receives the majority of funding. Phase transitions between different regimes are discussed. References: J. Bollen, D. Crandall, D. Junk, Y. Ding, and K. Borner, Scientometrics 110 (2017) 521. J. Bollen, D. Crandall, D. Junk, Y. Ding, and K. Borner, EMBO reports 15 (2014) 131.
RMC refinements of 3D local atomic structures using multiple data sets: achievements and challenges.
Victor Krayzman, NIST, MML, United States
Abstract: Reverse Monte Carlo (RMC) refinements of structural models using X-ray/neutron total scattering data collected on powder samples provide 3D snapshots of atomic configurations. To perform a refinement, a large supercell (up to 1000000 atoms) with periodic boundary conditions is constructed per an average-structure model (obtainable from Bragg reflections) and experimental signals are calculated from the atomic coordinates. During the refinements, atoms are selected at random and displaced in random directions by a certain distance until the relevant signals calculated after each atomic move match the experimental data. Both “good” and “bad” moves are accepted with the acceptance probability determined using a version of the Metropolis algorithm. X-ray and/or neutron total scattering data, being determined by a superposition of all atomic pair correlation functions in a material, often lack chemical and directional selectivity. To mitigate these deficiencies, we implemented simultaneous fitting of multiple complementary datasets, including the total scattering, chemically selective Extended X-ray Absorption Fine Structure (EXAFS) data, patterns of diffuse scattering observed in single crystals of the same material, and several other types of information. In this presentation, we will describe the algorithms and strategies employed in the combined-technique refinements, present their applications to structural analysis in several complex solid solutions, and outline the outstanding challenges.
Applicability of the lattice Boltzmann method to determine the ohmic resistance in equivalent resistor connections
Mayken Espinoza-Andaluz, Escuela Superior Politecnica del Litoral, Centro de Energias Renovables y Alternativas, Ecuador
Abstract: Knowing the ohmic resistance of the materials allow to know in advance its electrical behavior when a potential difference is applied, and therefore the prediction of the electrical performance can be achieved in a most certain manner. Although the Lattice Boltzmann method (LBM) has been applied to solve several physical phenomena in complex geometries, it has only been used to describe the fluid phase, but applicability studies of LBM on the solid-electric-conducting material have not been carried out yet. The purpose of this paper is to demonstrate the accuracy of calculating the equivalent resistor connections using LBM. Several series and parallel resistor connections are effected. All the computations are carried out with 3D models, and the domain materials are designed by the authors.
MATHEMATICAL MODELLING OF COMPOSITE FRAME PRODUCTION USING AN INDUSTRIAL ROBOT
Michal Petrů, Technical University of Liberec, Department of Machinery Construction, Czech Republic
Jaroslav Mlynek, Technical University of Liberec, Department of Mathematics, Czech Republic
Tomas Martinec, Technical University of Liberec, Institute for Nanomaterials, Advanced Technology and Innovation, Department of Physical Measurements, Czech Republic
Abstract: The article deals with quality aspects of frame composite production. This type of composite is often used, for example, in the aerospace and automotive industry. The material properties of the frame and fibers wound on the frame are important quality factors of the composite production. The quality of the composite depends greatly alsoon the correct winding angles of the fibers on the frame and on the homogeneity of the individual winding layers. The realisation of these two conditions is related to determining the correct trajectory of the industrial robot, which is part of the composite production technology. This paper presents the material properties of the polyurethane frame and the wound fibers and a calculation method for determining the optimized trajectory of industry robot in the process of a frame composite made by winding a carbon or glass fibers on a polyurethane frame. The composite frame with a circular cross-section is attached to the end-effector of the robot and successively passes through the fibre-processing head during the winding process, usually with three layers of winding. Each layer of fibers is wound onto the frame at a different angle. Quality of production depends significantly on the correct winding of fibers on a polyurethane frame. It is especially necessary to ensure correct angles of the fiber windings on a frame and the homogeneity of individual winding layers. It is also required to solve the problem of the passage rate of composite frame through the winding head and correction of rotational speeds of the moving parts of the winding head to ensure the right winding angles. Differential evolution algorithm is applied to optimization of the robot-end-effector trajectory to achieve optimal angles of windings of fibers on the frame. The matrix calculus is used in the optimization algorithm (especially rotation and translation matrices). A presented computational method allows to find the optimized 3D trajectory of the end-effector of an industrial robot in the production of a frame composite. Software tools offered by suppliers for the purposes of described production process of the composite are not currently available. The algorithm that calculates the exact optimized trajectory of the robot can also be applied to other production processes using industrial robots. This approach for determining the trajectory of the robot is substantially more effective than repeated search of suitable trajectory using the control panel (teach pendant) of the robot. The calculation of the optimal trajectory of the end-effector of the robot is programmed and tested in the Delphi development environment. The described algorithm can be created in any programming language and is applicable to any industrial robot. Using the described algorithm to determine the optimized robot trajectory does not cause any additional production costs to the composite manufacturer.
Acknowledgements: The results of this project No. LO1201 were obtained through the financial support of the Ministry of Education, Youth and Sports, Czech Republic in the framework of the targeted support of the “National Programme for Sustainability I”.
A mathematical model for the occurrence of historical events
Teruaki Ohnishi, Institute of Science and Technology for Society, Urayasu Branch, Japan
Abstract: A mathematical model was proposed on the frequency distribution of historical inter-event time τ. A basic ingredient was constructed by assuming the significance of a newly occurring historical event depending on the magnitude of a preceding event, the decrease of its significance by oblivion during the successive events, and an independent Poisson process for the occurrence of the event. The frequency distribution of τ was derived by integrating the basic ingredient with respect to all social fields and to all stake holders. The function of such a distribution was revealed as the forms of an exponential type, a power law type or an exponential with cut-off type depending on the values of constants appearing in the ingredient. The validity of this model was studied by applying it to the two cases of Modern China and Northern Ireland Troubles, where the τ distribution varies depending on the different countries interacting with China and on the different stage of history of the Troubles. This indicates the historical events consisted from many components with such different types of distributions of τ, similarly to the cases of other general human activities.
Approximate Bayesian Computation applied to Metrology for Nuclear Safeguards
Tom Burr, International Atomic Energy Agency, Information Management, Austria
Claude Norman, IAEA, SGIM, Austria
Thomas Krieger, Julich, , Germany
Abstract: Abstract. Approximate Bayesian Computation (ABC) is a candidate approach when an explicit likelihood for the data is not available, but there is a model that outputs predicted observables for specified input parameters. This paper briefly reviews ABC and then describes a few measurement methods used in nuclear safeguards, some of which have, and others of which do not have corresponding likelihoods. A key aspect of metrology is uncertainty quantification (UQ), whether approached from physical first principles (“bottom-up”) or empirically by comparing measurements from different methods and/or laboratories (“top-down”). Although ABC is not yet commonly used in metrology, these example measurement methods in nuclear safeguards illustrate advantages in using ABC compared to current bottom-up approaches. ABC is also shown to be useful in top-down UQ approaches. As a diagnostic, in bottom-up and top-down applications of ABC, the actual coverages of probability intervals are compared to the true coverages. If an ABC-based interval for a parameter is constructed to contain approximately 95% of the true parameter values, then it is important to verify that the actual coverage is close to 95%. It is shown that one advantage of ABC is its apparent robustness to misspecifying the likelihood while still maintaining good agreement between nominal and actual probability interval coverage compared to other Bayesian approaches
Gauge symmetries for a coupled Korteweg-de Vries system
Alvaro Restuccia, University of Antofagasta, , Chile
Adrian Sotomayor, University of Antofagasta, Department of Mathematics, Chile
Abstract: We construct a gauge invariant action for a parametric coupled Korteweg-de Vries system whose field equations are an integrable system in the sense that it has an infinite sequence of conserved quantities.
Acknowledgements: We are partially supported by Fondecyt 1161192, Chile.
Accurate Analytic Approximation to the Modified negative fractional order Bessel function I−2/3(x) ( P. Martin ,J.Olivares and F. Maass )
Pablo Martin, Universidad de Antofagasta, Physics, Chile
Abstract: Modified Bessel functions appear in several areas of Physics as Electrodynamics, Optics, Quantum Mechanics and others. Its power series and asymptotic expansions are known, but its calculation is not easy, mainly for negative and fractional order functions. Here an analytic approximation have been found for the modified Bessel function I−2/3(x), following a new procedure, which could be also applied to other Bessel functions. The analytic approximation here found is valid for all positive value of the variable, and the accuracy is high notwithstanding its simplicity. This technics is different to the usual way to obtain polynomial approximations valid only for a specified interval of the variable. The approximation here found is I_□((-2)/3)(x)= (x^□((-2)/3) cosh⁡(x))/(1,6873〖(1+x^2)〗^□((-1)/12) ) (1+0,9066x^2)/(1+〖0,6736x〗^2 ) The maximum relative error of this approximation is about 2% at x= 1.5, however outside a short interval around that value, the relative error is less than 1%. Because of this small error the approximation here found can be used in most of the applications of this function, and furthermore can be differentiated and integrated as the actual function. This fractional Bessel function is also connected with the Airy function, thus increasing the number of applications. The method here presented uses rational functions as Pad´e, buy now combined with other elementary functions. Power series and asymptotic expansion are also used simultaneously as in previous work[1], but some improvements have been also introduced. References [1] P. Martin, J. Olivares and A. Sotomayor, Rev. Mex. F´ısica 63, 130 (2017).
Short DNA fragments shrink and stretch when over-twisted
marco zoli, university of camerino, physics, Italy
Abstract: Bending and twisting flexibility of the helix are essential to the DNA packaging in chromosomes, to the DNA-protein binding and to the formation of those transient local base pair openings along the chain which regulate DNA replication and transcription. Experimental advances in single molecule micro-manipulation techniques over the last decades have permitted achieving substantial knowledge of the DNA flexibility properties mostly by sampling the molecule response to applied mechanical deformations. Studies of DNA cyclization properties have also indicated that DNA maintains an intrinsic flexibility at length scales which are smaller than the typical persistence length thus questioning, at such scales, the applicability of traditional worm-like-chain models. For short DNA molecules, all-atomistic simulations and mesoscopic models provide useful analytical tools as they can treat the helix at the level of the base pair and include those large fluctuational effects which shape the helix flexibility properties. We address these issues by reviewing a computational method, based on the path integral formalism, developed in the last years both for linear and circular helicoidal molecules [1-3]. The method is applied to a mesoscopic Hamiltonian model which incorporates, for a helical molecule in a solvent potential, both the inter-strand hydrogen bond interactions and the intra-strand stacking interactions. The model also accounts for the bending and twisting fluctuations between adjacent base pairs along the molecules stack. The base pair separations are considered as trajectories in the path configuration space and the total partition function is computed by summing in the path space over a broad ensemble of base pair configurations consistent with the physical requirements of the model potential. Some recent results regarding the cyclization probabilities of molecules with about 100 base pairs [4] and the elastic response of short chains to external loads [5, 6] are presented. [1] M. Zoli, Soft Matter 10, 4304-4311 (2014). [2] M. Zoli, The Journal of Chemical Physics 141, 174112 (2014). [3] M. Zoli, Europhysics Letters 110, 18001 (2015). [4] M. Zoli, The Journal of Chemical Physics 144, 214104 (2016). [5] M. Zoli, Physical Chemistry Chemical Physics, 18, 17666 (2016). [6] M. Zoli, Journal of Physics: Condensed Matter 29, 225101 (2017).
Identification of environment symmetry for iron centers in aluminosilicates by EPR
Evgeny Apushkinskiy, Peter the Great St. Petersburg State Polytechnic University , Experimental Physics, Russian Federation
Boris Popov, Peter the Great St. Petersburg Polytechnic University, Experimental Physics, Russian Federation
Vladimir N. Romanov, Peter the Great St. Petersburg Polytechnic University, Experimental Physics, Russian Federation
Vladimir Saveliev, Peter the Great St. Petersburg Polytechnic University, Experimental Physics, Russian Federation
Vladimir Sobolevskiy, Peter the Great St. Petersburg Polytechnic University, Experimental Physics, Russian Federation
Abstract: We study an angular dependence of EPR spectra of the own defects in topaz (Al2[SiO4][F,OH]2). The topaz crystal structure is built of silicon-oxygen tetrahedral (SiO4) and octahedral aluminum surrounded by four oxygen ions and fluorine ions or a hydroxyl group. There are two types of substitution defects in topaz, such as octahedral and tetrahedral, depending on the location of the impurity ion. The point defects with octahedral symmetry arise on local substitution of aluminum (Fe3+ → Al3+), while tetrahedral coordinated centers are formed by substitution of silicon (Fe3+→ Si4+) in the silicon-oxygen tetrahedral (SiO4). To determine the symmetry of the impurity centers, the angular dependence of the EPR spectrum is calculated. The excited energy states for defects are determined by the magnitude of the g-factor shift. These states equal 1.6 eV and 3.2 eV, respectively. A super-hyperthin structure (SHTS) of the EPR lines of iron has been observed. This SHTS is determined by the magnetic moments of the fluorine nuclei F19 located in the first coordination sphere of the paramagnetic iron center. The models of the three new paramagnetic centers in topazes are suggested, one of them being of orthorhombic symmetry for aluminum substitution and the two others being of tetragonal symmetry for silicon substitution with oxygen vacancies.
Physical Description of Image Conception
Yehuda Roth, Oranim College, Science, Israel
Abstract: We describe a non-linear quantum approach describing a way of conceiving images. Our primary assumption is that although images mostly appear as mixed photon states, each image can be represented by a single coherent photon state. Thus, integrating non-linear dynamics with quantum mechanics, we show how an image that was originally described in a mixed-state form, can be transformed into the pure state description. Being in the pure state phase is regarded as the image's conceived stage.
Effect of surface condition on oxidation kinetics of Ni-base superalloy
Wojciech J. Nowak, Rzeszow University of Technology, Department of Material Science, Poland
Abstract: The materials used at high temperature, like in gas turbines or jet engines, need to fulfill a number of requirements, e.g. high creep strength and oxidation resistance at a wide range of operating temperatures, environments and loading condition as well as a suitable ductility at low temperature. Such a properties are obtained in Ni-base superalloys, due to their microstructure consisting of thermodynamically stable γ-Ni matrix with combination of strengthening γ’-Ni3Al phase. However, when one expose the alloys at high temperature, an oxidation process occurs and the material starts to form an oxide scale. The Ni-Cr-Al based alloys can be classified into the three groups of materials in term of formed oxide scales: NiO-forming, chromia forming and an alumina forming alloys. Formation of protective oxides like Al2O3 or Cr2O3 substantially increase the lifetime of the component exposed at high temperature. To provide a resistance against oxidation a protective coatings such as MCrAlY (where M is mainly Ni or Co) or β-NiAl which are an alumina forming materials are applied. However, coatings production is time consuming, results in additional component costs, and can negatively affect alloy mechanical properties, such as fatigue strength. Therefore, another, cheaper method to force material to form a protective oxide scale is proposed in the present study. Namely, a different surface preparation of a Ni-base superalloys, like grinding, polishing, sand blasting etc. on oxide scale formation during exposure at high temperature in Ar-O2 atmosphere will be presented. The model describing the effect of surface treatment on oxidation kinetics and oxide scale formation will be introduced as well.
Acknowledgements: This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665778
The Kirkendall shift during ternary reactive diffusion process - entropy production principle
Bartek Wierzba, Rzeszow University of Technology, Materials Science, Poland
Abstract: In this paper the phenomenological process related to the evolution of the ternary multiphase systems is discussed. The entropy production principle is proposed to choice the reaction path during such diffusion process by means of numerical simulations. The bi-velocity method of the three-component multi-phase system is shown. The simulations present the local entropy production determines the diffusion path in ternary system. The simulations results will be compared with the experiments of diffusion in Fe-Ni-Ti system.
Acknowledgements: This work has been supported by the National Science Centre (NCN) in Poland, decision number 2014/15/B/ST8/00120.
Mathematical modeling of polymer flooding using unstructured Voronoi grid
Bulgakova Guzel, Ufa State Aviation Technical University, Mathematics, Russian Federation
Abstract: Nowadays the part of unconventional oil in the total oil reserves in world is more than 60% and continues to grow. Effective recovery of such oil necessitates development of enhanced oil recovery techniques such as polymer flooding. Polymer flooding simulation software is expensive and most of the products uses only rectangular grid for calculations. The study investigated the model of polymer flooding with effects of adsorption and water salinity. The model takes into account six components that includes elements of the classic black oil model. These components are polymer, salt, water, dead oil, dry gas and dissolved gas. The equations of the model and the problem statement are formulated. Solution of the problem is obtained by finite volume method on unstructured Voronoi grid using fully implicit scheme. The discretized nonlinear equations are solved by the Newton’s method. To compare several different grid configurations numerical simulation of polymer flooding is performed. The oil rates obtained by a hexagonal locally refined Voronoi grid are shown to be more accurate than the oil rates obtained by a rectangular grid with the same number of cells. The latter effect is caused by high solution accuracy near the wells due to the local grid refinement. Minimization of the grid orientation effect caused by the hexagonal pattern is also demonstrated. However, in the inter-well regions with large Voronoi cells flood front tends to flatten and the water breakthrough moment is smoothed.
Acknowledgements: This study was supported by the Russian Foundation for Basic Research (Project 17-41-020226 r_a).
Magnetic Soliton for Single-Ion Anisotropy in SU(3) Group
Yousef Yousefi, Payame Noor University, Physics, Iran, Islamic Republic Of
Abstract: We discuss system with Single-Ion anisotropy Hamiltonian with nearest neighbor exchange within a mean field approximation process that observed in compositions like CSNiF3. We drive Lagrangian and equations describing this model with Path integral technic by using coherent states in real parameters. for small linear excitation from the ground state, dispersion equations of spin wave of dipole and quadrupole branches obtained. If the Single-Ion anisotropy coefficient is zero, we have only dipole dispersion branch and there is no quadruple dispersion. In other word, quadruple dispersion branch obtained only when there is anisotropy term in Hamiltonian. In final, soliton solution for quadrupole branches for these linear equations calculated. This soliton is the solution of nonlinear Klein-Gordon equation and have the form of Hylomorphic soliton. These solitons are like Q-ball solitons. Also this soliton is of the kind of non-topologic ones because their boundary values in ground and infinity are the same from the topological point of view.
Numerical Procedure for Modeling of Light Emitting Diode with Mesh-Like Electrode
Yohei Nishidate, University of Aizu, Computer Science and Engineering, Japan
Abstract: A computational procedure is presented for numerical modeling of the light emitting diode (LED) with top p-electrode designed as a mesh with the strips of rectangular cross section. Isotropic light emission in the LED's active region and light reflection from the bottom electrode are considered. Three-dimensional Laplace equation for electric potential is solved by finite element method. The numerical model incorporates mapped infinite element to account for potential decay far away from the LED structure and finite element model developed for boundary condition at semiconductor-air interface in the mesh opening. Simulation results demonstrate the effect of the mesh's geometrical parameters on the total output power.
Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma
Mikhail Tokar, Institute für Energie- und Klimaforschung (4) - Plasma Physics, Forschungszentrum Jülich GmbH, Germany
Abstract: The recombination of plasma charged components, electrons and ions of hydrogen isotopes, on the wall of a fusion reactor is a source of neutral molecules and atoms, recycling back into the plasma volume. Here neutral species participate, in particular, in charge-exchange (c-x) collisions with the plasma ions and, as a result, atoms of high energies and chaotically oriented velocities are generated. Some fraction of these hot atoms hit the wall and get into openings of ducts, guiding to diagnostic installations, e.g., first mirrors. To assess the intensity of installation erosion and develop approaches to reduce it to a sufficiently low level, the behavior of c-x atoms in the plasma and duct has to be modeled by solving a kinetic equation for the atom velocity distribution function. Normally this is done by statistical Monte Carlo methods which, however, are very time consuming if a reasonably small level of accident errors has to be attained. This is an obstacle to perform extensive enough studies to find, e.g., the most optimal duct geometry. Recently [1], in a one-dimensional case an iterative procedure to solve one-dimensional kinetic equation, being alternative to Monte Carlo methods, has been tremendously accelerated, at least by a factor of 30-50, without any noticeable loss of the computation accuracy, by applying the approximate pass method for the involved calculation of integrals in the velocity space including the Maxwellian distribution function of plasma ions. In the present contribution the method elaborated in [1] is developed further to solve a 2-D kinetic equation, used by describing the transport of c-x atoms in the vicinity of an opening in the wall. This allows to firmly determine the energy spectrum of c-x atoms penetrating into circular ducts and assess the erosion rate of installations there. On the basis of calculations done an optimized geometry of the duct is proposed, allowing to take into account both the depletion of atom population near wide openings and reduced aperture of narrow ducts. The results of kinetic modeling are compared with those obtained with the diffusion description for c-x atoms, being relevant under plasma conditions of low temperature and high density, where the mean free path length between c-x collisions is much smaller than that till the atom ionization by electrons. It is demonstrated that this approximation, allowing very fast calculations, can be applied for rough estimates, with an error up to 30%, even for a hot plasma in the scrape-off layer of a fusion reactor. [1] M. Z. Tokar, “Scrape-off layer modeling with kinetic or diffusion description of charge-exchange atoms”, Phys. Plasmas., 23, 122512 (2016).
Explanation of Rotation Curves in Galaxies and Clusters of Them, by Generalization of Schwarzschild Metric and Combination with MOND, eliminating Dark Matter
Spyridon Vossos, NKUA, Chemistry, Greece
Elias Vossos, NKUA, Physics, Greece
Abstract: Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury’s orbit, Shapiro time delay etc [1]. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter [2-6]. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable Interpolating function (μ) in Milgrom’s Law [7-11]. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). Then, we are limited to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which has two terms. The first is significant, near to Schwarzschild radius, while the second is significant at very long distance from the center of gravity. This second term is associated with the Interpolating function (μ). With that, a new relativistic potential is obtained (let us call 2nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a specialization at very long distance of a pure Relativistic Gravitational Interaction associated with Lorentz metric. This relativistic potential and the corresponding metric of spacetime have been obtained by the light of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metric [12,13]. Of course, may also be applied by scientists who prefer the hyperbolic geometry of Classic Relativity (CR).
Diffusion of neutrons in the toroidal nuclear electrogenerator
Vladimir Tertychny-Dauri, Saint-Petersburg National Research University of Information Technologies, Mechanics and Optics, Physics and Engineering, Russian Federation
Abstract: Diffusion of neutrons in the toroidal nuclear electrogenerator (nuclegen) is investigated. Important conclusion about the practically complete absence of the diffusion of neutrons and charged fission particles through the external boundary under toroidal motion is substantiated by the solution of corresponding equation diffusion with the aid of Fourier's standard division method.
Correction to the Wills-Harrison approach: Influence on the Fe-based liquid alloys thermodynamics
Nikolay Dubinin, Ural Federal University, Engineering centre , Russian Federation
Abstract: Some years ago, we applied the Wills-Harrison (WH) [1] approach in conjunction with the variational method of the thermodynamic perturbation theory to calculate thermodynamic properties of Fe-Co and Fe-Ni liquid alloys [2, 3]. Later, we introduce the correction to the WH model due to the non-diagonal coupling between d electrons on different atoms and applied this correction to investigate the WH effective pair interactions in liquid Fe, Co and Ni [4]. Here, the influence of this correction on the thermodynamics of Fe-Co and Fe-Ni liquid alloys near their melting temperatures at different component concentrations is studied. This work is supported by the federal target project “R&D for Priority Areas of the Russian Science-and-Technology Complex Development for 2014-2020”, government contract № 14.578.21.0200 on the subject “Development of ceramic components and parts production by selective laser melting technology, using innovative diagnostic processes of products and methods” (Application Code «2016–14–579–0009–3076»). 1. J.M. Wills, W.A. Harrison, Phys. Rev. B 28, 4363 (1983). 2. N.E. Dubinin, L.D. Son, N.A. Vatolin, J. Phys.: Condens. Matter 20, 114111 (2008). 3. N.E. Dubinin, J. Phys.: Conf. Ser. 144, 012115 (2009). 4. N.E. Dubinin, J. Phys.: Conf. Ser. 338, 012004 (2012).
Acknowledgements: This work is supported by the federal target project “R&D for Priority Areas of the Russian Science-and-Technology Complex Development for 2014-2020”, government contract № 14.578.21.0200 (Application Code «2016–14–579–0009–3076»).
Understanding dynamics of Martian winter polar vortex with ”improved” moist-convective shallow water model
Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Earth and Planetary Sciences, France
Abstract: We show how the salient features of the atmospheres of Mars and Saturn, namely the surprising symmetry and stability of Martian polar vortex, and the longevity of the hexagonal vortex at the North pole of Saturn, which is being observed for decades, can be explained with the help of a simple shallow-water type model resulting from vertical averaging of primitive equations of planetary atmospheres, with addition of phase transitions of water, and mosit convection, for Saturn, and addition of phase transitions of CO2 with dust nuclei, for Mars. Thus "improved" multi-phase rotating shallow water model allows for detailed stability analysis of vortex structures, and for efficient finite-volume numerical implementations and high-resolution long-time simulations at low cost. The former are used to identify the unstable modes of polar vortices, and the latter - to follow nonlinear evolution of the instabilities and life-cycles of the resulting structures.
Quantized Vector Potential and the Photon Wave-function
CONSTANTIN MEIS, CEA - Saclay, National Institute for Nuclear Science and Technology, France
Pierre Dahoo, University of Versailles St. Quentin en Yvelines, LATMOS, France
Abstract: The permanent violation of Bell’s inequality by the experimental evidence with single photon states has demonstrated that hidden variables within a local representation are excluded. However, new variables within a non-local representation for the photon through a real wave function are not explicitly excluded. We consider here the vector potential, enhanced at a single k-mode photon state beyond the standard description in QED, with the quantized amplitude proportional to the angular frequency times a quantization constant. Within this representation the vector potential function for a k-mode and lamda-polarization photon satisfies the classical electromagnetic wave propagation equation as well as Schrodinger’s equation for the relativistic massless Hamiltonian and finally a quantum equation for the vector potential amplitude operator. Consequently, taking into account the left (L) and right (R) circularly polarized states for a single photon we define a six components function as a general wave function for a k-mode photon in a non-local representation that can be suitably normalized. It is shown that the established photon wave function satisfies Schrodinger’s equation with the relativistic massless Hamiltonian coupled to Pauli spin 1 matrices. We deduce that the square of the modulus of this wave function gives the energy density at a given coordinate while the probability for detecting a k-mode photon around a point on the propagation axis depends on the fourth power of the angular frequency Furthermore, the amplitudes of the electric and magnetic fields of single k-mode photon are also expressed through the square of the angular frequency. This representation confers precise properties to a single photon state opening perspectives for further experimental investigations in order to understand the real nature of a single photon state.
Chemical sensor array modeling using multivariable partial differential equations: comparison between conducting polymer and metal oxide based resistive sensors
Abdelaziz Abbas, Centre de Recherche en Technologies Industriels (CRTI), Division de caractérisation et instrumentation, Algeria
ahmed mebtouche, Centre de Recherche en Technologies Industriels (CRTI), , Algeria
Abstract: In the presented paper, the interactions between a chemical sensor array and a gas mixture were investigated. A partial differential equations that contain several variables, and connects the partial sensitivities of the sensor array elements with the input variables (concentrations of the gas mixture components), have been developed. Furthermore, the solutions of the differential equations were deduced. We were especially interested for resistive sensors based on conducting polymers and metal oxide sensitive layers (or films), we made a comparison between them .
Variable dissipation dynamical systems: integrability and analysis
Maxim V. Shamolin, Lomonosov Moscow State University, Institute of Mechanics, Russian Federation
Abstract: In this activity, we systematize some results on the study of the equations of spatial motion of dynamically symmetric fixed rigid bodies-pendulums located in a nonconservative force fields. The form of these equations is taken from the dynamics of real fixed rigid bodies placed in a homogeneous flow of a medium. In parallel, we study the problem of a spatial motion of a free rigid body also located in a similar force fields. Herewith, this free rigid body is influenced by a nonconservative tracing force; under action of this force, either the magnitude of the velocity of some characteristic point of the body remains constant, which means that the system possesses a nonintegrable servo constraint, or the center of mass of the body moves rectilinearly and uniformly; this means that there exists a nonconservative couple of forces in the system. We also review both new results and results obtained earlier. Problems examined are described by dynamical systems with so-called variable dissipation with zero mean. The problem of the search for complete sets of transcendental first integrals of systems with dissipation is quite topical; a large number of works are devoted to it. We introduce a new class of dynamical systems that have a periodic coordinate. Due to the existence of nontrivial symmetry groups of such systems, we can prove that these systems possess variable dissipation with zero mean, which means that on the average for a period with respect to the periodic coordinate, the dissipation in the system is equal to zero, although in various domains of the phase space, either the energy pumping or dissipation can occur. Based on the facts obtained, we analyze dynamical systems that appear in dynamics of a multi-dimensional rigid body and obtain a series of new cases of complete integrability of the equations of motion in transcendental functions, which can be expressed through a finite combination of elementary functions. As applications, we study dynamical equations of motion arising in the study of the plane and spatial dynamics of a rigid body interacting with a medium and also a possible generalization of the obtained methods for the study of general systems arising in the qualitative theory of ordinary differential equations, in the theory of dynamical systems, and also in oscillation theory.
Acknowledgements: Institute of Mechanics, Lomonosov Moscow State University
Fake images detection using neural networks
Yulia Maslennikova, Kazan Federal univercity, radyophysics, Russian Federation
Iliya Korchagin, Kazan Federal univercity, , Russian Federation
Abstract: Today, there are few effective services and software that provide reliable detection of digital images photomontage. This paper provides the adaptive algorithm for the recognition of fake digital images using artificial neural networks. First of all, special database was prepared, that includes different types of original and fake images: raw and scanned copies of text documents with different manipulation (like fake signatures and seals). Database included more than 50 different images. The proposed recognition algorithm is based on the analysis of statistical properties of the JPEG artifacts. Any manipulation with an image provides additional distortion to the image. The first step of algorithm is the selection and removal of all significant objects on the image (letters), the second step is the analysis of JPEG artifacts density function, and the final step is cluster analysis of desity functions to identify suspicious areas on the image. For cluster analysis the self - organizing map neural network was used. The accuracy of the proposed adaptive recognition system is following: the 1st type error (false alarm) – 10%; the 2nd type error – 7%.
Statistical homogeneity tests applied to large data sets from high energy physics experiments
Jakub Trusina, Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Czech Republic
Jiri Franc, Czech Technical University in Prague, , Czech Republic
Vaclav Kus, Czech Technical University in Prague, (Department of mathematics), Czech Republic
Abstract: Tests for homogeneity are used in high energy physics for verification of simulated Monte Carlo samples, if they have the same distribution as measured data from a detector. Kolmogorov-Smirnov, $\chi^2$, and Anderson-Darling tests are the most used techniques to test the samples' homogeneity. Since MC generators produce plenty of entries from different models, each entry is weighted. One way of testing the homogeneity is by binning. If we do not want to lose any information, we can use generalized tests based on weighted empirical distribution function. In this paper, we proposed such generalized weighted homogeneity tests and introduce some of their asymptotic properties. We present results from a numerical analysis which focuses on estimations of type-I error and power of test. Finally, we show an application of these tests for homogeneity to a data from experiment D0 in Fermilab.
First-principles analysis of polaron absorptions in alkali tungsten bronzes
Satoshi Yoshio, Sumitomo Metal Mining Co.,Ltd., Computer Aided Engineering and Development Dept., Japan
Keisuke Machida, Sumitomo Metal Mining Co.,Ltd., , Japan
Koichiro Maki, Sumitomo Metal Mining.Co.,Ltd., , Japan
Kenji Adachi, Sumitomo Metal Mining Co., Ltd., Ichikawa Research Center, Japan
Abstract: Alkali tungsten bronzes have drawn much attention in relation to metal-nonmetal transitions, superconductivity, photocatalysts, electrochromic devices, etc., and recently to solar control filters with high visible transparency and strong near-infrared (NIR) absorptions as nanoparticles. The origins of those optical properties, with special attention to polaron absorptions, have been sought in this study by first-principles calculations for Cs-doped hexagonal tungsten bronze (HTB) nanoparticles. Incorporating the Drude term and using the screened exchange method, the dielectric functions of Cs-HTB have been calculated that reproduced the measured values with good precision except for the polaron peak in the imaginary part. By introducing oxygen defects, however, electrons are localized with a narrow band at 0.5 eV below the Fermi energy, and the resulting electronic excitation provides a good account of the experimental polaron absorption. It became clear that the polaron absorption is initiated and amplified by the oxygen defects, as confirmed experimentally by the strong dependence of the peak intensity on the amount of oxygen defects. Optical absorption of Cs-HTB at low energy is caused by plasmons and polarons. We have modeled the itinerant and localized electrons caused by the oxygen defects. The experimentally derived binding energy of the polaron absorptions has coincided with the calculated activation energy of oxygen hopping in Cs-HTB, which enabled to construct the atomic models of polaron excitations.
Dual Energy Tomosynthesis breast phantom imaging
Vaia Koukou, University of Patras, Department of Medical Physics, Faculty of Medicine, Greece
Niki Martini, University of Patras, Department of Medical Physics, Faculty of Medicine, Greece
George Fountos, Technological Educational Institute of Athens, Biomedical Engineering, Greece
Gerasimos Messaris, University Hospital of Patras, Department of Medical Physics, Greece
Christos Michail, Technological Educational Institute of Athens, Biomedical Engineering, Greece
Ioannis Kandarakis, Technological Educational Institute of Athens, Biomedical Engineering, Greece
George Nikiforidis, University of Patras, Medical Physics, Greece
Abstract: Dual energy (DE) imaging technique has been applied to many theoretical and experimental studies. The aim of the current study is to evaluate dual energy in breast tomosynthesis using commercial tomosynthesis system in terms of its potential to better visualize microcalcifications (μCs). The system uses a tungsten target X-ray tube and a selenium direct conversion detector. Low-energy (LE) images were acquired at different tube voltages (28, 30, 32 kV), while high-energy images at 49 kV. Fifteen projections, for the low- and high-energy respectively, were acquired without grid while tube scanned continuously. Log-subtraction algorithm was used in order to obtain the DE images with the weighting factor, w, derived empirically. The subtraction was applied to each pair of LE and HE slices after reconstruction. The TORMAM phantom was imaged with the different settings. Four regions-of-interest including μCs were identified in the inhomogeneous part of the phantom. The μCs in DE images were more clearly visible compared to the low-energy images. Initial results showed that DE tomosynthesis imaging is a promising modality, however more work is required.
Acknowledgements: his work was supported by Grant Ε.040 from the Research Committee of the University of Patras (Programme K. Karatheodori).
Correlated electron dynamics in the parallel and antiparallel spin states of simple confined electron systems
Tokuei Sako, Nihon University, College of Science and Technology, Japan
Abstract: Correlated dynamics of a few electrons confined in a two-dimensional nanoscale potential well with circular symmetry has been studied relying on the full configuration interaction wave function supplemented by high angular momentum basis functions. The probability density distributions in the internal space obtained by integrating the squared norm of the wave function over the angular coordinate corresponding to the overall rotation have been carefully examined for different spin states sharing the same orbital configuration. The results show distinct angular dependence in the nodal patterns among different spin states, that becomes appreciable towards the strong limit of confinement where dynamic correlation would disappear. This counter-intuitive trend of the angular dependence in the strong limit of confinement is rationalized on the basis of Fermi and conjugate Fermi holes.
Acknowledgements: This study has been supported in part by the Grants-in-Aid for Scientific Research (No. 15K05396) from Japan Society for the Promotion of Science, the Grants-in-Aid for Scientific Research on Innovative Areas (No. 25110006) from the Ministry of Education, Science, Sports and Culture (MEXT) and by the MEXT-Supported Program for the Strategic Research Foundation at Private Universities (Nihon University, 2013-2017).
Numerical simulation in nonlinear dynamic systems with retiming of motions of individual components
Daria Apushkinskaya, Saarland University, Mathematics, Germany
Evgeny Apushkinskiy, Peter the Great St. Petersburg State Polytechnic University , Experimental Physics, Russian Federation
Abstract: We study differential equations describing nonlinear processes in dynamical systems (macro-systems) that consist of a large number of components (micro-systems) and allow a synchronisation in behaviour of these components. In physics, these processes underlie the echo phenomena. An empirical solution of such equations is proposed. A solution is given in the form of power series of the spectra of external perturbations acting on a macro-system. Numerical simulations of this solution give a good agreement with a number of experimentally observed echo phenomena.
EFFECT OF THICKNESS ON THE MAGNITUDE OF SPONTANEOUS POLARIZATION IN THIN FERROELECTRIC FILMS © O.G.Maksimova., O.S.Baruzdina, E.A.Maksimova Cherepovets State University,Cherepovets,Russia E-mail: og62@mail.ru
Olga Maksimova, Cherepovets State University, Department of Physics, Russian Federation
Abstract: To describe the ferroelectric phase transition,3D- Ising model is widely used, which takes into account the interactions of particles within a given correlation radius [1]. We used the interaction energy of dipoles that describesbythe potential orientation interactions (as in the Ising model) with the additional term representing the Lennard-Jones potential. The average distance between the dipoles and the values of the interaction constants were determined by the Monte Carlo method from the condition of the minimum of the potential energy when solving the self-consistency problem. It is shown that, with decreasing the depth of the well or the increase of temperature, the average distance between the dipoles decreases.This leads to theshift of the phase transition point in comparison with 3D-Ising model. Under the internal electric field caused by spontaneous polarization, free electrons in thin ferroelectrics film move to the outer surface of the film and create an additional depolarizing field [2] whose magnitude depends on the value of the long-range orientation order. For solving the self-consistency problem, the effect of the depolarizing field on the order parameter in a thin ferroelectric film is considered.Dependences of the polarization of the ferroelectric film on the temperature at different values of its thickness and the depth of the potential well are calculated. It is shown that the effective thickness of the surface layer in thin film increases with increasing temperature. Near the phase transition point, its thickness increases infinitely. The critical value of the film thickness is determined whenthe spontaneous polarization is absent. 1.A. L. Pirozerskiĭ, E. V. Charnaya. Ising model for a ferroelectric phase transition in a system of interacting small particles.Physics of the Solid State. 52 3 (2010). 2.J.Paul, T. Nishimatsu, Y. Kawazoe and, U.V.Waghmare. Ferroelectric phase transitions in ultrathin films of BaTiO3. Phys. Rev. Lett.,99.077601/1-4(2007).
MODELING OF LIGHT SCATTERING BY TEXTURED POLYMER COATINGS OF ROLLED METAL
Andrei Maksimov, Cherepovets State University, Department of Physics, Russian Federation
Abstract: Rough surfaces play an essential role in many physical phenomena including wave scattering, friction, adhesion, electrical conductivity, capacitance and heat transport, and in applications ranging from thin films to sensors [1]. Light scatter, which is faster and less invasive than SPM, can also measure surface roughness via the inverse wave scattering method [2]. The statistical characteristics of light intensity fluctuations arising in the scattering of waves on textured polymer coatings of rolled metal on the base screen model with a random phase for surface with one-dimensional roughness are studied. In the frame of the Kirchhoff method, the average coefficient of light scattering, scattering diagrams for the coating surface are numerically calculated for various values of surface roughness and falling angles. The results of the research made it possible to develop a convergence technique for such a metal roll allowing identifying a correspondence between the color and the texture of the sample surfaces. 1.M. Zamani, F. Shafiei, S. M. Fazeli, M. C. Downer, and G. R. Jafari. Phys. Rev. E 94, 042809 2. G. R. Jafari, S. M. Mahdavi, A. Iraji Zad, P. Kaghazchi, Surf. Interface Anal. 37 (7) (2005) 641-645.
The Anisotropy Studies of Galactic Cosmic Rays in diffuse Galactic Magnetic Field.
Pantea Davoudifar, Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of)
Keihanak Rowshan Tabari, Research Institute for Astronomy and Astrophysics of Maragha, , Iran, Islamic Republic Of
Abstract: A previously developed model of Galactic magnetic field with Kolmogorov spectrum of field line irregularities is used to study the anisotropy amplitudes of cosmic rays below a PeV. The sources were considered to be Type II SN with a cylindrical symmetry in the Galactic disk. The Galaxy is considered to have a giant halo with a radius of 100 Mpc. As a standard method the anisotropy amplitudes are calculated using cosmic rays flux vector. The simulation results were studied in two cases A and B for primary protons and primary Iron nuclei.
Data collection system for a wide range of gas-discharge proportional neutron counters
Vladimir Oskomov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Alexandr Sedov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Nurzhan Saduyev, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Orazaly Kalikulov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Inesh Kenzhina, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Ernar Tautaev, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Yerzhan Mukhamejanov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Vyacheslav Dyachkov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Shynbolat Utey, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Abstract: This article describes the development and creation of a universal system of data collection to measure the intensity of pulsed signals. As a result of careful analysis of time conditions and operating conditions of software and hardware complex circuit solutions were selected that meet the required specifications: frequency response is optimized in order to obtain the maximum ratio signal/noise; methods and modes of operation of the microcontroller were worked out to implement the objectives of continuous measurement of signal amplitude at the output of amplifier and send the data to a computer; function of control of high voltage source was implemented. The preliminary program has been developed for the microcontroller in its simplest form, which works on a particular algorithm.
Acknowledgements: This work was supported by grant #3838/GF4 of the Ministry of Education and Science of Kazakhstan.
Numerical Simulation of a device with two Spin Crossover: Application for Temperature and Pressure sensors
Jorge Linares, University of Versailles St. Quentin en Yvelines, GEMAC, France
Salah ALLAL, University of Versailles St. Quentin en Yvelines, LATMOS, France
Pierre DAHOO, University of Versailles St. Quentin en Yvelines, LATMOS, France
Yann GARCIA, Université Catholique de Louvain, IMCN/MOST, Belgium
Abstract: The spin-crossover (SCO) phenomenon is related to the ability of a transition metal to change its spin state. For Iron (II) SCO complexes the changes are between the diamagnetic low-spin (S=0) and the paramagnetic high-spin (HS S=2) states [1]. In this contribution we simulate the High-Spin Fraction (Nhs) for different set values of temperature and pressure that are meant to be measured by a device using two SCO characterized by weak elastic interactions. We improve the calculation given by Linares et al [2], taking also into account different changes in the volume (VHS, VLS) of the SCO. We perform all the calculations in the frame work of a Ising-like model solved in the mean-field approximation. The two SCO show in this case ("weak elastic interactions") gradual spin transitions and thus from the optical properties, together with the calibration obtained by the calculations shown in this article, both temperature and pressure values can be measured.
Acknowledgements: CHAIR Materials Simulation and Engineering, UVSQ, Université Paris Saclay is gratefully acknowledged.
Helical inward convection in toroidal magnetized plasmas
Madalina Vlad, National Institute of Laser Plasma and Radiation Physics, Plasma and Fusion, Romania
Florin Spineanu, National Institute of Laser Plasma and Radiation Physics, Plasma and Fusion, Romania
Abstract: We discuss a mechanism that is able to transport heavy impurity ions from the edge of a toroidal magnetically confined plasma to the core. It consists of the combination of a spontaneous rotation and the localized baroclinic vorticity generation. The geometry of the problem is similar to the smoke ring with the particularity that there may be strong rotation in the toroidal direction. The problem has unexpected general features, like: excitation of a purely growing instability which modulates the radial transport of heat, whose manifestation is the spontaneous rotation in the poloidal (meridional) plane. It is connected with the exact integrability of the Nonlinear Schrodinger Equation, here derived as the envelope equation for the radial fluxes. The meridional inhomogeneity is the source of rotation (the mechanism is Stringer spontaneous spin-up, which in plasma physics is a “neoclassical” effect). The baroclinic generation of vorticity is imposed by the poloidal variation of the density (again a “neoclassical” characteristic) combined with equilibrium radial gradient of the pressure. These two effects transport heavy ions from the edge the axis. The importance of this inward convection is underlined: a small contamination of the core plasma is able to suppress the thermonuclear reactions. The examination of such processes is therefore essential for the success of the fusion plasma. This work is however interdisciplinary: it involves integrability, fluid vorticity and plasma confinement.
Acknowledgements: This work is supported by the contract C5-04 IFA-CEA and by WPJET1-C.
To the problem of decomposition of initial-boundary-value problems in mechanics
Mikhail Nikabadze, Lomonosov Moscow State University, Mechanics and Mathematics, Russian Federation
Abstract: The problems of decomposition of initial-boundary value problems in the classical (micropolar) three-dimensional theory of elasticity are considered. In addition, similar problems are considered for the theory of thin bodies with one and two small dimensions when using systems of orthogonal polynomials and shell theories obtained from the corresponding three-dimensional theories. In particular, the first initial-boundary value problem for bodies with an arbitrary boundary is split, and also the second and third (mixed) initial-boundary value problems for bodies with a piecewise-plane boundary for different anisotropy are split. From the decomposed equations of the classical (micropolar) three-dimensional theory, the corresponding decomposed equations of the theory of prismatic bodies with one small dimension of constant thickness in displacements (displacements and rotations) are obtained. From the latter equations, in turn, the equations are derived in the moments of unknown vector-functions with respect to any system of orthogonal polynomials. The systems of the equations of various approximations in the moments with respect to the systems of Legendre and Chebyshev polynomials are obtained. On the basis of the constructed tensor-operator of cofactors for the operator of any of these systems of equations these systems split and for each moment of the unknown vector-function a high order elliptic type equation is obtained (the system order depends on the order of approximation), the characteristic roots of which are easily found. Using the Vekua method, one can obtain their analytical solutions.
Acknowledgements: this research was supported by the Shota Rustaveli National Science Foundaiton (project no. DI-2016-41) and the Russian Foundation for Basic Research (project no. 15-01-00848-a)
Tropical cyclones influence on total electron content variations
Dmitry Voloskov, Kazan (Volga region) Federal Universty, Institute of Physics, Russian Federation
Yulia Maslennikova, Kazan Federal univercity, radyophysics, Russian Federation
Vladimir Bochkarev, Kazan Federal University, Radiophysics, Russian Federation
Abstract: A number of studies provide evidence of meteorological effects presence in ionosphere parameters variations. However, most of them focus on local correlations, not considering spatial effects. In this study we propose a new method based on conjoint principal component analysis. This method allows studying spatial correlations between parameters as well as temporal ones. Tropical cyclones are one of the most important meteorological phenomena. Their effect in ionosphere parameters variations are being investigated. Global total electron maps as assessment of ionospheric condition and meteorological reanalysis maps were analysed using proposed approach.
On efficiency of fire simulation realization: parallelization with greater number of computational meshes
Lukas Valasek, Institute of Informatics, Slovak Academy of Sciences, Parallel Computational Methods and Algorithms, Slovakia
Abstract: Current applications of computer fire simulation belong to computationally demanding tasks which require efficient realization on high-performance computers. Contemporarily fire simulation systems are capable to utilize the knowledge of the Computational Fluid Dynamics theory and to model fires involving most of relevant physical and chemical processes related to fire. They allow to use advantages of a computer platform available and utilize various parallelization modes. In this paper efficiency of fire simulation realization on a computer cluster using the Fire Dynamics Simulator (FDS) system is discussed. The parallel MPI version of FDS is used for testing efficiency of four strategies of cluster computational resources allocation for a corridor fire simulation using greater number of computational cores. Five simulations with different number of computational meshes were realized on the HPC cluster at Institute of Informatics, Slovak Academy of Sciences in Bratislava (Slovakia) using the four allocation strategies. The simulation results indicate that all tested allocation strategies are of the same efficiency in the case that the number of cores used for given simulation calculation is a multiple of the number of cores in computer cluster node. In the case that the number of used cores is not equal to any cluster node cores number multiple, two from the four tested allocation strategies provide more efficient calculations, however, this difference decreases with increasing number of used computational cores for the case of greater cores number.
Energy parameters of transport processes in a LaF3 crystal doped with aluminum.
Georgiy Nujdov, TGTU, Physics of multiphase systems, Uzbekistan
Abstract: The article presents the results of quantum-chemical calculations of the potential relief of a lattice of a LaF3 super ionic crystal doped with aluminum. The potential relief of the lattice during the migration of the fluorine ion in the vicinity of the embedded aluminum ion is shown. A significant decrease in the effective barrier Ed and the energy of disordering of the lattice Ea are found. The most probable configurations of ensembles of aluminum ions were also found and the energy parameters of the migration of the fluoride ions nearest to them were calculated.
Investigation of humidity using the muon component of cosmic rays
Vladimir Oskomov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Alexandr Sedov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Nurzhan Saduyev, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Orazaly Kalikulov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Inesh Kenzhina, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Aisha Naurzbayeva, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Nazgul Alimgazinova, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Askhat Zhumabaev, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Saken Shinbulatov, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Nurzhan Erezhep, Institute of Experimental and Theoretical Physics of Al-Farabi Kazakh National University, Laboratory of Cosmic Rays Variations, Kazakhstan
Abstract: Determination of humidity is one of the most important types of hydrometeorological and glaciological observations performed in agriculture, hydropower and water supply. The work is devoted to the development of physical basis of moisture determination method, based on attenuation of the flux of cosmic-ray muons. The relationship between the intensity of muons registered in the underground room of the Tien Shan mountain research station (Almaty) and relative humidity was studied. The results of studies show that the values of the normalized mutual correlation function between the rows of muon intensity and relative humidity vary from 0.3 to 0.7, depending on the coincidence scheme. The data obtained from the muon telescope located at the the Tien Shan mountain research station was used in the work.
Acknowledgements: This work was supported by grant #3842/GF4 of the Ministry of Education and Science of Kazakhstan.
Propagation of Ultra High Energy Cosmic Rays from Galactic Sources in a Fractal Interstellar Medium and Origin Studies
Pantea Davoudifar, Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of)
Keihanak Rowshan Tabari, Research Institute for Astronomy and Astrophysics of Maragha, , Iran, Islamic Republic Of
Abstract: Cosmic rays propagation within the Galaxy is simulated considering a fractal-like distribution of matter and magnetic fields. In such an anomalous diffusion process, the sources of ultra-high energy particles were considered to be galactic pulsars. The coordinate and birth times of sources were chosen from SN and pulsar catalogues. From these sources the primary spectrum of cosmic rays (H, He, CNO, Ne-Si, Fe) in the range EeV and above were reproduced. The resulted spectrum is used to discuss about the change in cosmic ray sources form Galactic to Extragalactic.
Modeling of traction-coupling properties of wheel propulsor
Rustem Sakhapov, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation
Regina Nikolaeva, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Marat Makhmutov, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Muhammat Gatiyatullin, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Abstract: In conditions of operation of aggregates on soils with low bearing capacity, the main performance indicators of their operation are determined by the properties of retaining the functional qualities of the propulsor. Therefore, the parameters of the anti-skid device can not be calculated by only one criterion. The equipment of propellers with anti-skid devices, which allow to reduce the compaction effect of the propulsion device on the soil, seems to be a rational solution to the problem of increasing traction and coupling properties of the driving wheels. The mathematical model is based on the study of the interaction of the driving wheel with anti-skid devices and a deformable bearing surface, which takes into account the wheel diameter, skid coefficient, the parameters of the anti-skid device, the physical and mechanical properties of the soil. As a basic mathematical model that determines the dependence of the coupling properties on the wheel parameters, the model obtained as a result of integration and reflecting the process of soil deformation from the shear stress is adopted. The total value of the resistance forces will determine the force of the hitch pressure on the horizontal soil layers, and the value of its deformation is the degree of wheel slippage. When the anti-skid devices interact with the soil, the traction capacity of the wheel is composed of shear forces, soil shear and soil deformation forces with detachable hooks. As a result of the interaction of the hook with the soil, the latter presses against the walls of the hook with the force equal to the sum of the hook load and the resistance to movement. During operation, the linear dimensions of the hook will decrease, which is not taken into account by the safety factor. Abrasive wear of the thickness of the hook is approximately proportional to the work of friction caused by the movement of the hook when inserted into the soil and slipping the wheel.
Mathematical model of highways network optimization
Rustem Sakhapov, Kazan State University of Architecture and Engineering, Road Construction Machinery, Russian Federation
Regina Nikolaeva, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Muhammat Gatiyatullin, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Marat Makhmutov, Kazan State University of Architecture and Engineering, Department of road construction machinery, Russian Federation
Abstract: The article deals with the issue of highways network design. Studies show that the main requirement from road transport for the road network is to ensure the realization of all the transport links served by it, with the least possible cost. The goal of optimizing the network of highways is to increase the efficiency of transport. It is necessary to take into account a large number of factors that make it difficult to quantify and qualify their impact on the road network. In this paper, we propose building an optimal variant for locating the road network on the basis of a mathematical model. The article defines the criteria for optimality and objective functions that reflect the requirements for the road network. The most fully satisfying condition for optimality is the minimization of road and transport costs. We adopted this indicator as a criterion of optimality in the economic-mathematical model of a network of highways. Studies have shown that each offset point in the optimal binding road network is associated with all other corresponding points in the directions providing the least financial costs necessary to move passengers and cargo from this point to the other corresponding points. The article presents general principles for constructing an optimal network of roads.
Small-angle scattering from 3D Sierpinski tetrahedron generated using chaos game
Azat Slyamov, Joint Institute for Nuclear Research, Bogolyubov Laboratory of Theoretical Physics, Russian Federation
Abstract: We approximate a three dimensional version of deterministic Sierpinski gasket (SG), also known as Sierpinski tetrahedron (ST), by using the chaos game representation (CGR). Structural properties of the fractal, generated by both deterministic and CGR algorithms are determined using small-angle scattering (SAS) technique. We calculate the corresponding monodisperse structure factor of ST, using an optimized Debye formula. We show that scattering from CGR of ST recovers basic fractal properties, such as fractal dimension, iteration number, scaling factor, overall size of the system and the number of units composing the fractal.
Simulation of small-angle scattering patterns using a CPU-efficient algorithm
Eugen Anitas, Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Russian Federation
Abstract: Small-angle scattering (of neutrons, x-ray or light; SAS) is a well-established experimental technique for structural analysis of disordered systems at nano and micro scales. For complex systems, such as super-molecular assemblies or protein molecules, analytic solutions of SAS intensity are generally not available. Thus, a frequent approach to simulate the corresponding patterns is to use a CPU-efficient version of the Debye formula. For this purpose, in this paper we implement the well-known DALAI algorithm in Mathematica software. We present calculations for a series of 2D Sierpinski gaskets and respectively of pentaflakes with various scaling factors, obtained from chaos game representation.
Structural characterization of nano and micro-fractals using lacunarity analisys and small-angle scattering.
Azat Slyamov, Joint Institute for Nuclear Research, Bogolyubov Laboratory of Theoretical Physics, Russian Federation
Abstract: The paper presents structural characterization of deterministic nano and micro-fractals using the lacunarity analisys. We show that for the considered mass-fractal models, the lacunarity spectrum reveals the main structural parameters of the fractal, such as overall size of the system, iteration number, scaling factor and the size of basic units. We confirm the obtained results with the well known small-angle scattering (SAS) technique.
Finding exact constants in a Markov model of Zipf’s law generation
Vladimir Bochkarev, Kazan Federal University, Radiophysics, Russian Federation
Eduard Lerner, Kazan Federal University, Data Analysis and Operations Research, Russian Federation
Anton Nikiforov, Kazan Federal University, Data Analysis and Operations Research, Russian Federation
Alexander Pismenskiy, Kazan Federal University, Data Analysis and Operations Research, Russian Federation
Abstract: According to the classical Zipf’s law, the word frequency is a power function of the word rank with an exponent $-1$. The objective of this work is to find multiplicative constant in a Markov model of word generation. Previously, the case of independent letters was mathematically strictly investigated in [1]. Unfortunately, the methods used in this paper cannot be generalized in case of Markov chains. The search of the correct formulation of the Markov generalization of the results [1] was performed using experiments with different ergodic matrices of transition probability $P$. Combinatory technique allowed taking into account all the words with probability of more than $e^{-300}$ in case of 2 by 2 matrices. It was experimentally proved that the required constant in the limit is equal to the value reciprocal to conditional entropy of matrix row $P$ with weights presenting the elements of the vector $\pi$ of the stationary distribution of the Markov chain. [1] Bochkarev V.V. and Lerner E.Yu. 2017 International Journal of Mathematics and Mathematical Sciences Article ID 914374.
Acknowledgements: This work was supported by the Russian Foundation for Basic Research, Grant no. 15-06-07402. The research of the first author was supported by the Russian Government Program of Competitive Growth of Kazan Federal University.
Simple method to improve comb frequency characteristic in passband and folding bands
Gordana Jovanovic Dolecek, INAOE, Electronics, Mexico
Abstract: The simplest decimation filter is comb filter which does not require multipliers for its implementation. The filter must have flat frequency characteristic in the passband of interest and high attenuation in the so called folding bands ( bands around the comb zeros), in order to avoid deterioration of the decimated signal. However, comb filter has droop in the passband and a low attenuation in the folding bands. Different methods have been proposed to improve comb frequency characteristic in passband, folding bands, and in both passband and folding bands. The goal is to improve the comb frequency characteristic without introducing multipliers. In this paper we present a very simple method to get a flat characteristic in comb passband and an high attenuation in folding bands.The method is compared with some recently proposed methods in literature.
Characterization of corrosion defects in coating – substrate structure
Salim Bennoud, Laboratory of Aircrafts, University of Saad Dahlab (Blida 1)., Algeria, Laboratory of Aircrafts,, Algeria
Abstract: Corrosion is critical problem of in-service aircraft structures and elements which lead to a degradation of structure integrity and fatigue resistance and directly affect the airworthiness of an aircraft and even result in loss of elements and materials. Eddy current testing is one of the non destructive techniques often used to detect defects and ensure total integrity of conducting materials. This technique has been effectively applied in corrosion detection. In this study, a probe is placed near the studied sample which is made up of a substrate of low conductivity on which a fine layer of conducting material is deposited. The control of the physical characteristics of the deposit is carried out by measuring the impedance changes. The principle objective of this study is to simulate eddy current problems by employing the finite element method in order to calculate the probe response due to the presence of corrosion hidden in a multi-layer structure (COATING – SUBSTRATE sample). The simulations enable to more understand this kind of problems typically present in aeronautical structures and to study the influence of different parameters on the impedance responses, which enables to minimize errors of modeling and ameliorate the design performances.
A model of jam formation in congested traffic
Nadezhda Bunzarova, Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics, Russian Federation
Abstract: We study a model of irreversible jam formation in congested vehicular traffic on an open segment of a single-lane road. The vehicles obey a stochastic discrete-time dynamics which is a limiting case of the generalized Totally Asymmetric Simple Exclusion Process. Its characteristic features are: (a) the existing clusters of jammed cars do not break into parts during their motion along the selected segment of the road; (b) with probability p, at each time moment the clusters of cars are translated as a whole entity one site to the right, provided the target site is empty, and (c) any two clusters of cars, occupying consecutive positions on the chain, may become nearest-neighbors and merge irreversibly into a single cluster. The above dynamics has been used in a one-dimensional model of irreversible aggregation by N. Zh. Bunzarova and N. C. Pesheva [Phys. Rev. E 95, 052105 (2017)]. The model was shown to have three stationary non-equilibrium phases, depending on the probabilities of injection (α), ejection (β), and hopping (p) of particles: a many-particle one, MP, when β > α and α < p, a phase with a completely filled with particles configuration, CF, when α > p, and a mixed MP+CF phase when β > α and α < p. Here we present a detailed study, based on a random walk theory, of the stationary gap distribution between neighboring clusters of jammed cars on three different length scales, when the size L of the road segment increases unboundedly. A central concept of the theory is the stationary probability P(1) of completely jammed configuration of the system. An exact expression for P(1) in the mixed MP+CF phase is obtained: P(1) = p (α – β)/α(p – β), β ≤ α < p. In the evolution of the gap size, we take into account that during each configuration update, the left edge of the gap can move one site to the right with probability p, while the right edge belongs to the cluster which extends to the exit site L, and moves one site to the right with the ejection probability β. Therefore, the random width of the gap behaves, in general, as an asymmetric random walk: after each update, the gap width increases by one site with probability pg = β(1– p), decreases by one site with probability qg = p(1– β), and remains the same with probability r = 1 – β – p +2βp. We obtain that, when the injection rate is close to the borderline with the CF phase, there exist three different regimes: (i) many small-size jams divided by growing gaps of size O(L) in the MP phase (pg > qg); (ii) macroscopic jams separated by contracting gaps of size O(1) in the MP+CF phase (pg < qg); and (iii) a critical regime (pg = qg), when the macroscopic jams are divided by gaps of intermediate size O(L1/2). These results are supported by extensive Monte Carlo calculations
Acknowledgements: N.B. acknowledges partial support by a grant of the Representative Plenipotentiary of the Bulgarian Goverment at the Joint Institute for Nuclear Research and the Bogoliubov Laboratory of Theoretical Physics.
The Wang Landau parallel algorithm for the simple grids. Optimizing OpenMPI parallel implementation.
Arman Kussainov, al-Farabi Kazakh National University, National Nanotechnology Laboratory of Open Type, Physics and Technology, Kazakhstan
Abstract: The Wang Landau Monte Carlo algorithm to calculate density of states for the different simple spin lattices was implemented. The energy space was split between the individual threads and balanced according to the expected runtime for the individual processes. Custom spin clustering mechanism, necessary for overcoming of the critical slowdown in the certain energy subspaces, was devised. Stable reconstruction of the density of states was of primary importance. Some data post-processing techniques were involved to produce the expected smooth density of states.
Acknowledgements: This research was supported by grant #3824/GF4 provided by the Science Committee at the Ministry of Science and Education of Republic of Kazakhstan to the principal investigator at the National Nanotechnology Laboratory of Open Type, Physics and Technology Department, al-Farabi Kazakh National University.
Parametric modeling of animate and inanimate nature objects functioning
Ihor Klymenko, National Aerospace University "KhAI", Department of Physics, Ukraine
Valeriy Mygal, National Aerospace University "KhAI", Department of Physics, Ukraine
Galina Mygal, National Aerospace University "KhAI", Department of Vehicles and Transport Infrastructure, Ukraine
Abstract: In the researching of complex dynamic systems of animate and inanimate nature, should be considered a multitude of internal and external factors that are inherently diverse in nature. They determine the subtle features of signals of functioning, for the detection of which different methods of investigating and processing signals are used, as well as different parameters, indicators and criteria. They are not interrelated, that complicates the system analysis of functioning and increases the uncertainty of its modeling. In particular, improving models of functioning often leads to greater ambiguity. This is due to the contradiction between the system nature of the modeling object and the variety of non-correlated methods of obtaining, processing and analyzing the signals of functioning. In the paper, it is shown that the parametric 3D geometrization of the dynamics of the functioning signals allows to solve the contradiction. It is based on the transformation of a signal as a time series of functioning parameters into a parametric cycle of dynamic events that encompasses a subset of possible states. Its power is characterized by the Boltzmann entropy, that makes it possible to statistically analyze the functioning of the object. Geometrization is accompanied by a natural decomposition of the cycle into dynamic and energy components, the character of the relationship of which determines its structure. In its reorganization, usually hidden spatio-temporal correlations of the functioning of the object are appeared. Using the example of sensors and biosensors research, the possibility of transforming the parametric 3-D model of functioning into geometric 1st and 2nd orders models-signatures is shown. Unified tools are proposed that allow us to apply fundamental laws, principles and criteria in system analysis.
Network structures sustained by internal links and distributed lifetime of old nodes in stationary state of number of nodes
Nobutoshi Ikeda, Tohoku Seikatsu Bunka Junior College, Living and Culture, Japan
Abstract: There are some real networks, such as social networks and WWW, in which the deletion of old nodes is inevitable in order to review how their structures developed. In network models that take into account growth properties, however, deletion of old nodes has a serious impact on degree distributions, because old nodes tend to become hub nodes. In this study, we aim to provide a simple explanation for why hubs exist even in conditions where old nodes have been deleted. First, we show that an exponential increase in the degree of nodes is a natural consequence of equivalence between deletion and addition of nodes if the preferential attachment rule is employed. Secondly, we show that the existence of hubs is determined by the magnitude relationship between the time scale of the exponential growth of degrees and lifetime of old nodes. We focus on internal links within networks and variation in the lifetime of old nodes, as factors that affect the rate of exponential growth of degrees and characteristic length of the lifetime of old nodes.
On Lie symmetries application in study of thermal diffusion in binary mixtures
Irina Stepanova, Institute of Computational Modelling SB RAS, Differential equations in Mechanics, Russian Federation
Abstract: The presentation deals with the equations describing heat and mass transfer in a binary mixture under Soret and Dufour effects. Thermal diffusion (Soret effect) is a molecular transport of substance associated with a thermal gradient. The diffusive thermal conductivity (Dufour effect) is the heat flux caused by mass concentration gradient. From the mathematical point of view heat and mass transfer equations taking into account these reciprocal effects have become more complicated. Furthermore, the mathematical model includes dependencies of transport coefficients on temperature and concentration. They are often unknown and should be found also. We apply the Lie symmetry approach which allows finding the forms of transport coefficients and transformations admitted by the governing equations for every form of these coefficients. Obtained transformations help to reduce the governing equations to more simple form and to integrate them. We present the solution of group classification problem with respect to four transport coefficients and some exact solutions describing mass transfer in solutes under the Soret effect action.
Acknowledgements: The work is supported by Russian President Grant (MK-4519.2016.1)
Models of evaluation of public joint-stock property management
Nailya Yakupova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Svetlana Levachkova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Svetlana Absalyamova, Kazan Federal University, Institute of Management, Economics and Finance, Russian Federation
Gulnara Kvon, Kazan National Research Technical University named after A.N.Tupolev, , Afghanistan
Abstract: The paper deals with the models of evaluation of performance of both the management company and the individual subsidiaries on the basis of a combination of elements and multi-parameter and target approaches. The article shows that due to the power of multi-dimensional and multi-directional indicators of financial and economic activity it is necessary to assess the degree of achievement of the objectives with the use of multivariate ordinal model as a set of indicators, ordered by growth so that the maintenance of this order on a long interval of time will ensure the effective functioning of the enterprise in the long term. It is shown that these models can be regarded as the monitoring tools of implementation of strategies and guide the justification effectiveness of implementation of management decisions.
Numerical and approximate calculation of the generalized susceptibility matrix elements of dislocation segment in nondissipative crystal
Viktor Dezhin, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Igor Bataronov, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Abstract: Numerical calculation of the generalized susceptibility and the inverse generalized susceptibility matrix elements of the dislocation segment for edge and screw dislocations, different frequencies and different values of the dislocation segment length is performed. Certain regularities have been established. Based on the graphical results of numerical calculations, an approximate calculation of the generalized susceptibility matrix elements was carried out. Expressions for the diagonal and off-diagonal generalized susceptibility matrix elements of the dislocation segment are obtained.
On the natural small vibrations of dislocation in an isotropic medium
Viktor Dezhin, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Igor Bataronov, Voronezh State Technical University, Higher mathematics and physical and mathematical modeling, Russian Federation
Abstract: The equation for the natural bending vibrations of an infinite dislocation is written. The long-wavelength limit is considered. The orientation dependence of the vibrational spectrum has been studied. Solutions for two cases (the bending wave velocity along the dislocation line is not equal to the speed of sound waves and the bending wave velocity along the dislocation line is close to the speed of sound waves) are obtained. Local and quasilocal branches of edge and screw dislocations vibrations are found.
COMPUTER SIMULATION OF THE POLYMERIZATION PROCESS OF GALVANIZED SHEET PAINTED IN COIL COATING TECHNOLOGY USING NEURO-FUZZY METHODS
Evgeniy Ershov, Cherepovets State University, Department of Mathematic Software of Computing Machines, Russian Federation
Luidmila Vinogradova, Cherepovets State University, Department of Mathematic Software of Computing Machines, Russian Federation
Igor Varfolomeev, Cherepovets State University, Department of Mathematic Software of Computing Machines, Russian Federation
Dmitriy Bogachev, Cherepovets State University, Department of Mathematic Software of Computing Machines, Russian Federation
Abstract: The paper presents thedrying process of thepolymer coatingon the surface of metal sheet, based on the lattice gas model and Langmuir’s adsorption. This report contains the results of computer simulation of the adhesion process. The article also presents the implementation of intelligent control using neuro-fuzzy model. The model allows improving the accuracy of structural and parametric identification. The accuracy of predicting the outlet surface temperature of the strip was improved on 5% comparing with the existing systems. The result of «KOH-I-NOOR pencil» test and undercut test showed that the adhesion quality of all coated strips meets the standards’ requirements. At the same time, the usage of optimization model allowed to reduce gas consumption on 2-3%. The test results of the modified neuro-fuzzy model for controlling polymerization process of galvanized metal sheet are presented at the end of the paper.
Could Universe be a harmonic oscillator?
eric guiot, no institution (independant researcher), Rhone, France
Abstract: We study the possibility that the potential of gravity valuable for large distances is harmonic and not Newtonian, as suggested in the Friedman’s equations. In particular we explore the possibility that this modification explains the curve of rotation of galaxies without dark matter. We give the expression of ratio gravitational/inertial mass we expect and suggest a cosmological model.
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