Exterior Dissipation, Proportional Decay, and Integrals of Motion

M. Aureli and J. A. Hanna
Phys. Rev. Lett. 127, 134101 – Published 22 September 2021

Abstract

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 m1 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.

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  • Received 13 April 2021
  • Revised 1 July 2021
  • Accepted 5 August 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.134101

© 2021 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsGeneral PhysicsCondensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Authors & Affiliations

M. Aureli* and J. A. Hanna

  • Department of Mechanical Engineering, University of Nevada, Reno, Nevada 89557, USA

  • *maureli@unr.edu
  • jhanna@unr.edu

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Issue

Vol. 127, Iss. 13 — 24 September 2021

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