de Buyl Pierre, Gaspard Pierre
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, BE-1050 Brussels, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Dec;84(6 Pt 1):061139. doi: 10.1103/PhysRevE.84.061139. Epub 2011 Dec 22.
Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas, and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasistationary states (QSS), i.e., long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation." The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behavior in phase space as the Vlasov system.
无碰撞动力学中的弛豫过程会在具有长程相互作用的系统中导致特殊行为，例如自引力系统、非中性等离子体和波粒系统。这些由弗拉索夫方程充分描述的系统呈现出准稳态（QSS），即动力学的持久中间阶段，这些阶段出现在被称为“剧烈弛豫”的短暂显著演化之后。在没有碰撞的情况下，弛豫的本质尚未被完全理解。我们在本文中展示了弗拉索夫方程数值模拟中拉伸和折叠行为的出现，提供了一种合理的弛豫机制，该机制将系统从其初始条件带入准稳态 regime。发现具有平均场耦合项的保面积离散时间映射在相空间中表现出与弗拉索夫系统类似的行为。
