0
2013
Impact Factor

Andrey Shafarevich

Leninskie Gory, Moscow, 119991, Russia
Lomonosov Moscow State University

Publications:

Chernyshev V. L., Tolchennikov A. A., Shafarevich A. I.
Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory
2016, vol. 21, no. 5, pp.  531-537
Abstract
We review our recent results concerning the propagation of “quasi-particles” in hybrid spaces — topological spaces obtained from graphs via replacing their vertices by Riemannian manifolds. Although the problem is purely classical, it is initiated by the quantum one, namely, by the Cauchy problem for the time-dependent Schrödinger equation with localized initial data.We describe connections between the behavior of quasi-particles with the properties of the corresponding geodesic flows. We also describe connections of our problem with various problems in analytic number theory.
Keywords: hybrid spaces, propagation of quasi-particles, properties of geodesic flows, integral points in polyhedra, theory of abstract primes
Citation: Chernyshev V. L., Tolchennikov A. A., Shafarevich A. I.,  Behavior of Quasi-particles on Hybrid Spaces. Relations to the Geometry of Geodesics and to the Problems of Analytic Number Theory, Regular and Chaotic Dynamics, 2016, vol. 21, no. 5, pp. 531-537
DOI:10.1134/S156035471605004X
Allilueva A. I., Shafarevich A. I.
Asymptotic Solutions for Linear and Nonlinear MHD Systems with a Rapid Jump near a Surface. Dynamics of the Surface of the Jump and Evolution of the Magnetic Field
2015, vol. 20, no. 6, pp.  691-700
Abstract
We review our recent results concerning the asymptotic solutions for both linear and nonlinear MHD equations.We describe the asymptotic structure of the solution with a rapid jump near a 2D-surface. For the linear system we demonstrate the effect of the instantaneous growth of the solution. We also study the weak limit of the solution and the corresponding generalized problem. For the nonlinear system we describe the asymptotic division into different modes, the free boundary problem for the movement of the surface and the equation on the moving surface for the profile of the asymptotic solution. We also study the possibility of the instantaneous growth of the magnetic field. It appears that the growth is possible only in the case of the so-called degenerate Alfvén modes; the latter appear if the main term of the magnetic field is tangent to the surface of the jump.
Keywords: MHD equations, discontinuous solutions, free boundary problems, dynamo theory, growth of the magnetic field
Citation: Allilueva A. I., Shafarevich A. I.,  Asymptotic Solutions for Linear and Nonlinear MHD Systems with a Rapid Jump near a Surface. Dynamics of the Surface of the Jump and Evolution of the Magnetic Field, Regular and Chaotic Dynamics, 2015, vol. 20, no. 6, pp. 691-700
DOI:10.1134/S1560354715060052

Back to the list