Related papers: MHD Equilibrium Equation in Symmetric Systems
We discuss hybrid master equations of composite systems which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested, its consistency is derived from the consistency of Lindblad…
Numerical computation of the ideal Magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated Partial Differential Equations (PDEs) like…
We formulate axion-electrodynamics and magnetohydrodynamics (MHD) in the cosmological context assuming weak gravity. The two formulations are made for a general scalar field with general $f(\phi)$-coupling, and an axion as a massive scalar…
We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincar\'e variational principle. The new stochastic Hall MHD theory has potential applications for uncertainty quantification…
A Hamiltonian formulation of generic many-particle systems with space-dependent balanced loss and gain coefficients is presented. It is shown that the balancing of loss and gain necessarily occurs in a pair-wise fashion. Further, using a…
We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We…
Equations of ideal magnetohydrodynamics (MHD) play an important role in the studies of turbulence, astrophysics, and plasma physics. These equations possess remarkable geometric structures and symmetries. Indeed, they admit a geodesic…
Magnetic fields play a crucial role in many astrophysical scenarios and, in particular, are of paramount importance in the emission mechanism and evolution of Neutron Stars (NSs). To understand the role of the magnetic field in compact…
We compute the optimal constant for a generalized Hardy-Sobolev inequality, and using the product of two symmetrizations we present an elementary proof of the symmetries of some optimal functions. This inequality was motivated by a…
Existence of mild solutions for the 3D MHD system in bounded Lipschitz domains is established in critical spaces with the absolute boundary conditions.
We establish a variational framework for nonlinear instabilities in a setting of the ideal magnetohydrodynamic (MHD) equations. We apply a variational method to various kind of smooth steady states which are shown to be nonlinearly unstable…
Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…
The structure of weighting coefficient matrices of Harmonic Differential Quadrature (HDQ) is found to be either centrosymmetric or skew centrosymmetric depending on the order of the corresponding derivatives. The properties of both matrices…
Symmetry properties of the evolution equation and the state to be controlled are shown to determine the basic features of the linear control of unstable orbits. In particular, the selection of control parameters and their minimal number are…
The formal stability analysis of Eulerian extended magnetohydrodynamics (XMHD) equilibria is considered within the noncanonical Hamiltonian framework by means of the energy-Casimir variational principle and the dynamically accessible…
Harmonic functions of two variables are exactly those that admit a conjugate, namely a function whose gradient has the same length and is everywhere orthogonal to the gradient of the original function. We show that there are also partial…
Self-consistent, one-dimensional quasineutral screw-pinch equilibria are constructed within a hybrid model that couples fluid electrons with kinetic ions governed by the Vlasov equation. The equilibria depend on the radial coordinate…
We study the well-posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl type equations that are derived from the incompressible MHD system with non-slip boundary condition on the velocity and…
Obtaining a stable magnetohydrodynamical (MHD) formalism in SPH - i.e. smoothed particle magnetohydrodynamics (SPMHD) - has proven remarkably difficult. To implement MHD requires two steps: a modification to the momentum equation and an…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…