Abstract Details
Abstracts
Author: Philip J Morrison
Requested Type: Poster
Submitted: 2026-04-04 16:38:11
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Univerinsity of Texas at Aust
2515 Speedway
Austin , TX 78712
United States
Abstract Text:
In a recent work [1] we use the metriplectic formalism [2,3] to obtain equilibrium states. Metriplectic dynamical systems consist of a special combination of a Hamiltonian and a (generalized) entropy-gradient flow, such that the Hamiltonian is conserved and entropy is dissipated. It is natural to expect that, in the long-time limit, the orbit of a metriplectic system should converge to an extremum of entropy restricted to a constant-Hamiltonian surface. In this talk, I will discuss sufficient conditions for this to occur. Then, consider a class of metriplectic systems inspired by the Landau operator for Coulomb collisions in plasmas, which is included as special case. For this class of brackets, checking the conditions for convergence reduces to checking two usually simpler conditions, and we discuss examples in detail. The results have been applied to construct relaxation methods for the solution of equilibrium problems in fluid dynamics and plasma physics.
[1] C. Bressan, M. Kraus, O. Maj, and P. J. Morrison, "Metriplectic Relaxation to Equilibria," arXiv:2506.09787v1 [math-ph] 11 Jun 2025. Invited article by Communications in Nonlinear Science and Numerical Simulation.
[2] P. J. Morrison, "Bracket formulation for irreversible classical fields," Phys. Lett. A 100, 423 (1984); "Some observations regarding brackets and dissipation, Tech. Rep. PAM 228, University of California at Berkeley, available at arXiv:2403.14698v1 [mathph] 15 Mar 2024 (March 1984); "A paradigm for joined Hamiltonian and dissipative systems", Physica D 18, 410 (1986).
[3] P. J. Morrison and M. H. Updike, Inclusive curvature-like framework for describing dissipation: Metriplectic 4-bracket dynamics, Phys. Rev. E 109 (2024) 045202.
Characterization: 4.0
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