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).
Back to Top