Exterior Dissipation, Proportional Decay, and Integrals of Motion,Physical Review Letters

当前位置： X-MOL 学术 › Phys. Rev. Lett. › 论文详情

Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)

Exterior Dissipation, Proportional Decay, and Integrals of Motion
Physical Review Letters ( IF 8.1 ) Pub Date : 2021-09-22 , DOI: 10.1103/physrevlett.127.134101
M Aureli ₁ , J A Hanna ₁

Affiliation

Given a dynamical system with

m

independent conserved quantities, we construct a multiparameter family of new systems in which these quantities evolve monotonically and proportionally, and are replaced by

m - 1

conserved linear combinations of themselves, with any of the original quantities as limiting cases. The modification of the dynamics employs an exterior product of gradients of the original quantities, and often evolves the system toward asymptotic linear dependence of these gradients in a nontrivial state. The process both generalizes and provides additional structure to existing techniques for selective dissipation in the literature on fluids and plasmas, nonequilibrium thermodynamics, and nonlinear controls. It may be iterated or adapted to obtain any reduction in the degree of integrability. It may enable discovery of extremal states, limit cycles, or solitons, and the construction of new integrable systems from superintegrable systems. We briefly illustrate the approach by its application to the cyclic three-body Toda lattice, driven from an aperiodic orbit toward a limit cycle.

中文翻译：

外部耗散、比例衰减和运动积分

给定一个动态系统

米

独立守恒量，我们构建了一个新系统的多参数族，其中这些量单调和成比例地演化，并被替换为

米 - 1

自身的守恒线性组合，以任何原始数量作为极限情况。动力学的修改使用原始量的梯度的外积，并且经常使系统朝着非平凡状态中这些梯度的渐近线性相关性发展。该过程对现有的流体和等离子体、非平衡热力学和非线性控制文献中的选择性耗散技术进行了概括和提供了额外的结构。它可以被迭代或调整以获得可集成度的任何降低。它可以发现极值状态、极限环或孤子，以及从超级可积系统构建新的可积系统。我们通过将其应用于循环三体 Toda 格子来简要说明该方法，

更新日期：2021-09-22

点击分享查看原文

点击收藏

公开下载

阅读更多本刊最新论文本刊介绍/投稿指南11