|
ИСТИНА |
Войти в систему Регистрация |
ФНКЦ РР |
||
Non-Linear Stability of Equilibrium Solutions of the Vlasov Equation with a Lennard-Jones type Potentialтезисы доклада
- Автор: Salnikova T.V/
- Сборник: International Conference Topological Methods in Dynamics and Related Topics – IV Book of Abstracts National Research University Higher School of Economics Nizhny Novgorod, 2-5 August 2021
- Тезисы
- Год издания: 2021
- Место издания: National Research University Higher School of Economics Nizhny Novgorod
- Первая страница: 54
- Последняя страница: 55
- Аннотация: We consider the gravitating particles that can collide. Collisions can be described invarious ways. We can use the theory of inelastic interaction of solids with Newton’s recoverycoefficient for the relative velocity of colliding particles. In numerical implementation, themain difficulty of this approach is to track and refine a huge number of time moments ofparticle collisions. Another approach is to add to the gravitational potential the potential ofrepulsive forces, similar to the intermolecular Lennard-Jones forces. Numerical experimentsshow that when the Jacobi stability condition is satisfied, both models lead to a qualitativelyidentical character of evolution with the possible formation of stable configurations.As it is known, when pair collisions of an infinitely large number of gravitating particlesare taken into account, the probability density function evolves in accordance with the Vlasov-Boltzmann-Poisson system of equations.We suggest a research method using the Vlasov equation with the Lennard Jones typepotential. This allows to take into account the size of the interacting particles, and alsotake into account not only paired, but also triple or more collisions of the particles. For thisdynamical system the existence of a large class of nonlinearly stable equilibrium solutions isproved by the Energy-Casimir method.
- Добавил в систему: Сальникова Татьяна Владимировна