## Conference submissions

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
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.
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).
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.
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
“Hypergeomtric solutions for some nonhomogeneous linear differential equations of fractional order” by Jorge Olivares and Pablo Martin, Universidad de Antofagasta, Chile.
Jorge Olivares Funes, University of Antofagasta, Departament of mathematics, Chile
Abstract: In this paper a study is performed to the solution of the linear nonhomogeneous fractional order differential equation (df^α (x))/(dx^α )=I_0 (x) , where I_0 (x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0< α<1. Caputo definition for the fractional derivatives is considered [1,2] . Fractional derivatives have become important in physical and chemical phenomena as viscoeslasticity and viscoplasticity, anomalous diffusion and electric circuits. In particular in this work the values of α=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transfom is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions. In the case of α=1/2 , this is f(x)=2√(x/π) F( 3/4,5/4;1/2,x^2/4). [1]. Podlubny I., “Fractional differential equations “, ( Academic Press, 1990). [2]. Murio D.A . Computers and Mathematics with Applications 51, 1539-1550 (2006).
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.
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.
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.
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.
A note on controllability property for a special class of matrices (Jorge Olivares and Ronald Manríquez)
Jorge Olivares Funes, University of Antofagasta, Departament of mathematics, Chile
Abstract: As is well know, many authors have discussed the controllability property for bilinear control systems when the state variable lies on the plane, see for instance [1], [6], [7]. However, when the dynamic is described on high dimension there are many unsolved problems, and in that sense the search conditions necessary and/or sufficient to characterize the property of controllability have attracted great attention during the last decades, [2], [3], [9], [12], [15]. In this paper, we have establish a characterization of controllability for the class of bilinear systems whose dynamics is determined by a special class of matrices that belong to the semisimple Lie algebra sl(3,R). References 1. Ayala V, and San Martin, L.A.B. Controllability of two{dimensional bilinear system: restricted controls, discrete{time, Proyecciones, 18, 207-223 (1994). 2. C. Bruni, G. Di Pillo, and G. Koch, Bilinear systems: An appealing class of "nearly linear" systems in theory and applications. IEEE Trans. Autom. Control, AC f19, 334-348 (1974). 3. I. Joo and N.M. Tuan, On controllability of some bilinear systems. Comptes Rendus de I'Academie des Sci,. 315, 1393-1398 (1992). 4. J.P. Gauthier and G. Bornard, Controlabilite des Systemes bilineaires, Siam J. Control and Opt., 20(3), 377{384 (1982). 5. L.A.B San Martin, _Algebras de Lie, Unicamp, Campinas, (1999). 6. Rodriguez J. C., V. Ayala, Optimal trajectories for angular systems on the projective line, Optimal Control Applications & Methods, 33, 199{213 (2012). 7. Rodriguez J. C., V. Ayala, L.A.B. San Martin, Optimality on Homogeneous Spaces, and the Angle System Associated with a Bilinear Control System, SIAM Journal on Control and Optimization, 48(4), 2636{2650 (2009). 8. Rodriguez J. C., Control systems, UNICAMP-UCN, (2010). 9. V. Jurdjevic, I. Kupka, Controllability of right invariant systems on semi-simple Lie groups and their homogeneous spaces, Ann. Inst. Fourier, Grenoble, 31(4), 151-179 (1981). 10. V. Jurdjevic, I. Kupka, Accessibility on semi-simple Lie groups and their homogeneous spaces, a paraitre dans "Annales de l'Institut Fourrier " Nov. 1977. 11. V. Jurdjevic, Geometric control theory. Cambridge University Press, (1997.) 12. W. M. Boothby and E. N. Wilson, Determination of the transitivity of bilinear systems, SIAM J. Control Optim., 17, 212-221 (1979). 13. F. Robert, Matrices non_egatives et normes vectorielles. Cours de 3e cycle, INPG ENSIMAG, (1973). 14. Y. L. Sachkov, Control Theory on Lie groups, SISSA, 15/2006/M. 15. Yu. L. Sachkov, Invariant domains of three-dimensional bilinear systems. (Russian) Vest. Mosk. Univ. Ser. Matem., Mekh. 4, 23-26.(1991) English translation: Mosc. Univ. Math.Bulletin.
Numerical approximation of the modified zero-order Bessel differential equation by means of Lagrange Interpolation and Maple software at various intervals (By Jorge Olivares and Elvis Valero)
Jorge Olivares Funes, University of Antofagasta, Departament of mathematics, Chile
Abstract: In the present paper it is shown how the modified differential equation of Bessel of order zero x^ 2 (d ^ 2 y) / (dx ^ 2) + x dy / dx-x ^ 2 y = 0, y (0) = 1, dy / dx (0) = 0 Is approximated by means of the Lagrange interpolation and with the help of maple software commands in the intervals [0,1], [0,1 / 2] and [0,1 / 4]. Reference [1] G. N. Watson, "A treatise on the theory of Bessel functions ", 2nd. ed., Cambrigde,England: Cambrigde University Press(1966). [2] J. D. Jackson, C_ lasical Electrodynamics",2nd. ed., John Wiley and Sons, Inc.,Ch.3 (1975). [3] P. Martin, E. Castro, J. L. Paz and A.De Freitas, "Multipoint quasi-rational approximants in Quantum Chemistry", Chapter 3 of "New Developments in Quantum Chemistry"(Transworld Research Network,Kerala, India, 2009) pp. 55-78. [4] P. Martin, J. Olivares, L. Cortes Vega and A. Sotomayor,"Multi-point quasirational approximants for the midi_ed Bessel function I1(x)", Journal of Physics: Conference Series 738: 012066 (2016). .
Photon wave function and intrinsic electromagnetic properties
CONSTANTIN MEIS, CEA - Saclay, National Institute for Nuclear Science and Technology, France
Abstract: Constantin Meis(1) and Pierre Richard Dahoo(2) (1) National Institute for Nuclear Science and Technology, CEA - Saclay, Université Paris Saclay, 91191 Gif-sur-Yvette, France. (2) LATMOS /IPSL, UVSQ Université Paris-Saclay, F-78280, Guyancourt, France. 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.
Understanding dynamics of polar vortices on Mars and Saturn with "improved" rotating 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.
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»).
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.
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).
Electrical conductivity of a 2D composite with rod-like fillers
Yuri Tarasevich, Astrakhan State University, Math. Modeling, Russian Federation
Nikolai Lebovka, F.D. Ovcharenko Biocolloidal Chemistry Institute, NAS of Ukraine and Taras Shevchenko Kiev National University, , Ukraine
Valeri Laptev, Astrakhan State University and Astrakhan State Technical University, , Russian Federation
Valeria Goltseva, Astrakhan State University, , Russian Federation
Abstract: We examine electrical conductivity of two-dimensional composites with rod-like fillers by means of computer simulation [1]. A lattice approach is used, i.e., a host matrix (a substrate) is approached as a square lattice, rod-like fillers are represented as linear k-mers (particles occupying k adjacent adsorption sites of the lattice). A monolayer is produced by the random sequential adsorption of the k-mers onto the lattice. Overlapping with predeposited k-mers and detachment from the surface are forbidden. We examine both the isotropic and anisotropic systems and consider two different models, i.e., an insulating host matrix and conducting fillers and a conducting host matrix and insulating fillers. A high electrical contrast between a host matrix and fillers is assumed. To calculate the effective electrical conductivity, the monolayer is treated as a random resistor network. The electrical conductivity of such a monolayer in both the x and y directions for different lengths and concentrations of the k-mers is calculated. Moreover, we examine the effect of defects on the behaviour of electrical conductivity in such a composite [2]. In this study, the defects in the host matrix are distributed randomly and these lattice sites are forbidden for the deposition of k-mers. The k-mers are deposited onto the substrate until a jamming state is reached. The defects of the k-mers are distributed randomly on the deposited k-mers. The sites filled with k-mers have high electrical conductivity, whereas the empty sites, and the sites filled by either types of defect have a low electrical conductivity. The effects of the concentrations of defects on the electrical conductive is studied. 1. Yu. Yu. Tarasevich, V. V. Laptev, V. A. Goltseva, N. I. Lebovka, Influence of defects on the effective electrical conductivity of a monolayer produced by random sequential adsorption of linear k-mers onto a square lattice, Physica A: Statistical Mechanics and its Applications. 2017. Vol. 477. P. 195-203. DOI 10.1016/j.physa.2017.02.084. 2. Yu. Yu. Tarasevich, V. A. Goltseva, V. V. Laptev, N. I. Lebovka, Electrical conductivity of a monolayer produced by random sequential adsorption of linear $k$-mers onto a square lattice, Phys. Rev. E. 2016. Oct. Vol. 94, Iss. 4. P. 042112. DOI 10.1103/PhysRevE.94.042112.
Acknowledgements: We acknowledge the funding from the National Academy of Sciences of Ukraine, Project No. 43/17-H (N.I.L.) and the Ministry of Education and Science of the Russian Federation, Project No. 3.959.2017/4.6 (Yu.Yu.T. and V.A.G.).
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).
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.
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.
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).
RMC refinements of 3D local atomic structures using multiple data sets: achievements and challenges.
Victor Krayzman, NIST, MML, United States
Abstract: MML, National Institute of Standards and Technology, USA 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 106 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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
Gauge invariant integrable systems
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.
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
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.
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.
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).
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.
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.
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.
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.
Finding exact constants in a Markov model of Zipf’s law generation
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.
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.
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.
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.
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.
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.
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" of the Russian Academy of Sciences, Dorodnitsyn Computing Centre, Mathematical Physics and Mathematical Modeling, Russian Federation
Abstract: We study the asymptotic behavior of the solution $u(x, t)$ of the Cauchy problem for a 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.
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.
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.
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.
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.
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 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)
MODEL OF PERSONAL CONSUMPTION UNDER CONDITIONS OF MODERN ECONOMY
Diana Rakhmatullina, Kazan (Volga region) Federal University, Institute of Management, Economics and Finance., 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.
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.
Network structures sustained by internal links and distributed lifetime of old nodes in equivalent 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.
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.
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.
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.
MODELING OF LIGHT SCATTERING BY TEXTURED POLYMER COATINGS OF ROLLED METAL © A.V.Maksimov, Maksimova E.A. Cherepovets State University, Cherepovets, Russia E-mail: a_v_maximov@mail.ru
Andrei Maksimov, Cherepovets State University, 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.
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, 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).
Acknowledgements:
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.
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).
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).
Construction of infinitely many conservation laws for nonlinear integrable (2+1)-dimensional equations
Gaukhar Shaikhova, Eurasian National University, General and Theoretical physics, Kazakhstan
Kuralay Yesmakhanova, Eurasian National University, , Kazakhstan
Guldana Bekova, Eurasian National University, , Kazakhstan
Ratbay Myrzakulov, Eurasian National University, , Kazakhstan
Abstract: In this paper, we construct infinitely many conservation laws for nonlinear integrable (2+1)-dimensional equations with symbolic computation from the Riccati form of the Lax pair. 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.
Darboux transformation and exact solution for the (2+1)-dimensional complex modified Korteweg-de Vries equations
Kuralay Yesmakhanova, Eurasian National University, Department of Higher Mathematics, Kazakhstan
Guldana Bekova, Eurasian National University, , Kazakhstan
Gaukhar Shaikhova, Eurasian National University, General and Theoretical physics, Kazakhstan
Ratbay Myrzakulov, Eurasian National University, , Kazakhstan
Abstract: In this paper, we consider the (2+1)-dimensional complex modified Korteweg-de Vries equations. Using the Lax pair, we construct the Darboux transformation. The exact solutions are obtained from the different”seeds” by using the Darboux transformation.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
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
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.
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.
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)
Helical inward convection in toroidal magnetized plasmas
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.
Determination of velocities of wave propagation in some media through the eigenvalues of the material tensors
Armine Ulukhanyan, Bauman Moscow State Tecnical University, Calculus Mathematics and Mathematical Physics, Russian Federation
Abstract: It is known that the eigenvalues of the tensor and the tensor-block matrix are invariant quantities. That is why the aim of this work was to find the expressions for the velocities of wave propagation of some media through the eigenvalues of the material tensors. In particular, it is considered materials with the anisotropy symbol {1.5} and {5.1}, as well as isotropic materials, and expressions for the velocities of wave propagation for them are given. In addition, the expressions for the velocities of wave propagation for materials of cubic syngony with the anisotropy symbol {1,2,3} (the matrix of the elastic modulus tensor components has three independent components), hexagonal system (transversal isotropy) with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has five independent components), trigonal system with anisotropy symbol {1,1,2,2} (the matrix of the elastic modulus tensor components has six independent components), tetragonal system with anisotropy symbol {1,1,1,2,1} (the matrix of the elastic modulus tensor components has six independent components) are obtained. There are also obtained the expressions for the velocities of wave propagation for a micropolar medium with the anisotropy symbol {1.5.3} and {5.1.3}, as well as for an isotropic micropolar material.
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%.
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.
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).
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
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
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
Noether symmetry approach in F(T) gravity with g-essence
Kairat Myrzakulov, Eurasian National University, General and Theoretical Physics, Kazakhstan
Abstract: In this paper, we consider some cosmological aspects in the theory F(T) gravity that is non-minimal coupled to scalar and fermions field for FRLW space-time. Noether symmetry approach can be used to fix the form of coupling function h(φ,u), the torsion scalar function F(T) and the function of g-essence is K(X,Y,φ,u) . We investigate cosmological solutions of the field equations using these forms obtained by the existent of Noether symmetry. It is shown that for the non-minimal coupling case, the cosmological solutions indicate a late-time acceleration for the universe.
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-PARADE, 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
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.
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.
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 Silva, UFVJM, ICET, 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.
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
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-PARADE, 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.