Related Experiment Video
Updated: Jun 28, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Ergodicity of ideal Galerkin three-dimensional magnetohydrodynamics and Hall magnetohydrodynamics models
S Servidio1, W H Matthaeus, V Carbone
1Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA.
Abstract:
We explore the problem of the ergodicity of magnetohydrodynamics and Hall magnetohydrodynamics in three-dimensional, ideal Galerkin systems that are truncated to a finite number of Fourier modes. We show how single Fourier modes follow the Gibbs ensemble prediction, and how the ergodicity of the phase space is restored for long-time Galerkin solutions. Running time averages and two-time correlation functions show, at long times, a convergence towards zero of time averaged single Fourier modes. This suggests a delayed approach to, rather than a breaking of, ergodicity. Finally, we present some preliminary ideas concerning the origin of the associated time scales.
Related Concept Videos
Magnetostatic Boundary Conditions
Potential Due to a Magnetized Object
The vector...
The Hall Effect
Maxwell's Equation Of Electromagnetism
Symmetry in Maxwell's Equations
Magnetic Vector Potential
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...