Related papers: Relaxation to magnetohydrodynamics equilibria via …
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/produced (depending on a sign convention). It is…
The metriplectic framework, which permits to formulate an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The…
We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic…
A new formulation of time-dependent Relaxed Magnetohydrodynamics (RxMHD) is derived variationally from Hamilton's Action Principle using microscopic conservation of mass, and macroscopic conservation of total magnetic helicity, cross…
Metriplectic dynamics couple a Poisson bracket of the Hamiltonian description with a kind of metric bracket, for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is…
The metriplectic formalism couples Poisson brackets of the Hamiltonian description with metric brackets for describing systems with both Hamiltonian and dissipative components. The construction builds in asymptotic convergence to a…
This work generalizes the classical metriplectic formalism to model Hamiltonian systems with nonconservative dissipation. Classical metriplectic representations allow for the description of energy conservation and production of entropy via…
The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of…
We propose a metriplectic reformulation of Lagrangian variational formulations for non-equilibrium thermodynamics. We prove that solutions to these constrained variational principles can be generated by the sum of a classic Poisson bracket…
We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $\Lambda$-convex hull, the latter providing inequalities…
Flows on symplectic, Poisson, contact, and metriplectic manifolds are reviewed in order to describe our main result, which is to associate a natural metriplectic dynamical system on the general one-jet bundle $J^1N=T^*N\times \mathbb{R}$,…
Dissipation can be represented in Hamiltonian mechanics in an extended phase space as a symplectic process. The method uses an auxiliary variable which represents the excitation of unresolved dynamics and a Hamiltonian for the interaction…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
General equations for conservative yet dissipative (entropy producing) extended magnetohydrodynamics are derived from two-fluid theory. Keeping all terms generates unusual cross-effects, such as thermophoresis and a current viscosity that…
An inclusive framework for joined Hamiltonian and dissipative dynamical systems, which preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket, a quantity like the…
We present a novel framework for addressing the nonlinear Landau collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau collision integral and,…
We present the Hamiltonian formalism for the Euler equation of symplectic fluids, introduce symplectic vorticity, and study related invariants. In particular, this allows one to extend D.Ebin's long-time existence result for geodesics on…
This article introduces a new 3D magnetohydrodynamic (MHD) equilibrium solver, based on the concept of admissible variations of B, p that allows for magnetic relaxation of a magnetic field in a perturbed/non-minimum energy state to a lower…
This work presents the first numerical investigation of using Voigt regularization as a method for obtaining magnetohydrodynamic (MHD) equilibria without the assumption of nested magnetic flux surfaces. Voigt regularization modifies the MHD…