Bublik, S. A. Semin, M. A.
Published in
Mathematical Models and Computer Simulations

Abstract—The paper is devoted to the simulation of oil displacement by water and the formation of the Saffman–Taylor instability. The problem is solved in two-dimensional formulation. A circular domain with one injection well and eight production wells located along the contour around the injection well is considered as geometry. To study the patte...

Simonov, V. N. Matison, N. L. Boytsova, O. V. Markova, E. B.
Published in
Mathematical Models and Computer Simulations

AbstractThe results of a study of the oscillations of microcantilevers (MCs) made of nanoporous anodic aluminum oxide and constituting the base of biochemical sensors are described. Finite-element modeling of an MC’s vibrations reveal the sources of resonances in the frequency spectrum that do not correspond to the cantilever’s oscillations and com...

Shestakov, A. A.
Published in
Mathematical Models and Computer Simulations

Abstract—The aim of this work is to study and compare various approximations for the system of radiative heat transfer equations (TEs) in optically dense and transparent media. For this purpose, in optically dense media, asymptotic analysis is used; and in optically transparent media, an approach that allows reducing the solution of diffusion equat...

Freinkman, B. G.
Published in
Mathematical Models and Computer Simulations

AbstractThe era of the development of fundamentally new materials began with the discovery of graphene. Their unique properties already allow us to create many useful products in electronics, biomedicine, and other high-tech industries. However, the study of graphene and its derivatives is continuing. The mechanism of the formation of the graphene ...

Markov, M. B. Parot’kin, S. V.
Published in
Mathematical Models and Computer Simulations

AbstractThe generation of an electromagnetic field in a region with a perfectly conducting boundary by a long duration pulse of ionizing radiation is considered. The problem of calculating the field by numerically solving the complete system of Maxwell equations is posed. The approximations of the large and small radiation conductivity of the mediu...

Gladkikh, A. A. Malinetskii, G. G.
Published in
Mathematical Models and Computer Simulations

AbstractThe possibility of introducing a nonlinear correction to the Dirac equation for graphene in order to adequately describe collective electronic phenomena is considered. In contrast to the other papers on this topic the interaction term includes the sum of the spinor components’ squares instead of their difference. Particular attention is pai...

Chikurov, N. G.
Published in
Mathematical Models and Computer Simulations

AbstractA numerical solution method based on the reduction of systems of ordinary differential equations to the Shannon form is considered. Shannon’s equations differ in that they contain only multiplication and summation operations. The absence of functional transformations makes it possible to simplify and unify the process of numerical integrati...

Meretin, A. C. Savenkov, E. B.
Published in
Mathematical Models and Computer Simulations

Abstract—The issues of the mathematical modeling of a thermoporoelastic medium taking its damage into account are considered. The employed model generalizes the classical Biot model simulating the behavior of a poroelastic medium taking the thermoelastic effects into account. In order to describe the damage of the medium, the approach of continual ...

Blokhin, A. M. Semenko, R. E.
Published in
Mathematical Models and Computer Simulations

Abstract—Steady-state solutions for the problem of magnetohydrodynamic motion of an incompressible polymer fluid over an infinite rotating disk are considered. The representation of the solution used here is similar to the Von Kármán self-similar solution for a viscous fluid. Examples of the numerical steady-state solutions for various values of th...

Polbin, A. V. Fokin, N. D.
Published in
Mathematical Models and Computer Simulations

AbstractThis paper provides a vector autoregression model with an additional regularization problem similar to the Hodrick–Prescott filter problem to model a single, i.e., balanced, growth rate of the structural component of the main macroeconomic indicators of the Russian economy. This model includes the real GDP without government expenditure, th...