Related papers: Plasma dynamics in thin domains
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preserving the fundamental advective transport properties of ideal…
We prove the existence of global in time, finite energy, weak solutions to a quantum magnetohydrodynamic system (QMHD) with large data, modeling a charged quantum fluid interacting with a self-generated electromagnetic field. The analysis…
I present a review of incompressible magnetohydrodynamic (MHD) turbulence in a strongly magnetised plasma. The approach is phenomenological even where a more rigorous theory is available, so that a reader armed with paper, pencil and some…
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric…
We consider the equations of relativistic magnetohydrodynamics (RMHD) in the case of special relativity. For the fluid rest frame a nonconservative reformulation of the RMHD equations gives a symmetric system for the vector of primitive…
This paper explores plasma wave modes using the extended magnetohydrodynamics (XMHD) model, incorporating Hall drift and electron inertia effects. We utilize the geometric optics ansatz to study perturbed quantities, with a focus on…
We consider some differential geometric classes of local and nonlocal Poisson and symplectic structures on loop spaces of smooth manifolds which give natural Hamiltonian and multihamiltonian representations for some important nonlinear…
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of…
Magnetohydrodynamics (MHD) couples the Navier--Stokes and Maxwell equations into a nonlinear system of partial differential equations governing stellar interiors, astrophysical jets, fusion plasmas, and space weather. Numerical advances,…
The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO…
We derived one-fluid equations based on a relativistic two-fluid approximation of e$^\pm$ pair plasma and electron-ion plasma to reveal the specific relativistic nature of their behavior. Assuming simple condition on the relativistic…
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits.…
This study derives geometric, variational discretizations of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric…
Parker's formulation of isotopological plasma relaxation process toward minimum magnetics energy states in magnetohydrodynamics (MHD) is extended to electron MHD (EMHD). The lower bound on magnetic energy in EMHD is determined by both the…
We derive a number of solution for one-dimensional dynamics of relativistic magnetized plasma that can be used as benchmark estimates in relativistic hydrodynamic and magnetohydrodynamic numerical codes. First, we analyze the properties of…
The two-dimensional shallow water equations in Eulerian and Lagrangain coordinates are considered. Lagrangian and Hamiltonian formalism of the equations is given. The transformations mapping the two-dimensional shallow water equations with…
Drift-reduced MHD models are widely used to study magnetised plasma phenomena, in particular for magnetically confined fusion applications, as well as in solar and astrophysical research. This letter discusses the choice of Ohm's law in…
Originally introduced to describe a transition region in stars, the magnetic rotating shallow water (MRSW) model is now used in many solar physics and geophysical applications. Derived from the 3-D incompressible magnetohydrodynamic system,…
We consider two elliptic coupled systems of relevance in the fluid dynamics. These systems are posed on the whole three-dimensional space and they consider the action of external forces. The first system deals with the simplified…
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified…