Related papers: An alternative formulation of the magnetostatic bo…
This work is concerned with establishing the existence and uniqueness of the solution to a mixed-type degenerate boundary value problem for a relativistic magnetohydrodynamics system. We first consider a full relativistic…
This paper is concerned with the Laplace boundary-value problem with the directional derivative, corresponding to the specific nature of measurements of the longitudinal component of the photospheric magnetic field. Boundary conditions are…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
In this paper, we consider the steady MHD equations with inhomogeneous boundary conditions for the velocity and the tangential component of the magnetic field. Using a new construction of the magnetic lifting, we obtain existence of weak…
We have proposed a method to calculate the relative magnetic helicity in a finite volume as given the magnetic field in the former paper (Yang et al. {\it Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic flux to…
We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on…
The finite-element analysis of three-dimensional magnetostatic problems in terms of magnetic vector potential has proven to be one of the most efficient tools capable of providing the excellent quality results but becoming computationally…
In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system…
A formula for the magnetostatic energy of a finite magnet is proven. In contrast to common approaches, the new energy identity does not rely on evaluation of a nonlocal boundary integral inside the magnet or the solution of an equivalent…
The numerical solution of problems in nonlinear magnetostatics is typically based on a variational formulation in terms of magnetic potentials, the discretization by finite elements, and iterative solvers like the Newton method. The vector…
In a region free of currents, magnetostatics can be described by the Laplace equation of a scalar magnetic potential, and one can apply the same methods commonly used in electrostatics. Here we show how to calculate the general vector field…
There is not a unique solution to the electro- or magnetostatic problem where the "boundary condition" is merely a specification of the fields along a line. As a practical example, we consider the case where it is desired to have a magnetic…
Starting with a mathematical boundary value problem for the magnetic vector potential in an axisymmetric cylindrical coordinate system, we derive a general solution for any arbitrary current distribution using the method of Green's…
The nonlinear magnetic induction equation with Hall effect can be used to model magnetic fields, e.g. in astrophysical plasma environments. In order to give reliable results, numerical simulations should be carried out using effective and…
A solution is proposed for finding the vector potential and magnetic field of any distribution of currents with axial symmetry. In this approach, the magnetic field and the vector potential are looked for not by solving a differential…
When a (frequency-domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the…
We derive an exact, time-dependent analytical magnetic field solution for the inner heliosheath, which satisfies both the induction equation of ideal magnetohydrodynamics in the limit of infinite electric conductivity and the magnetic…
We present a numerical method for the solution of linear magnetostatic problems in domains with a symmetry direction, including axial and translational symmetry. The approach uses a Fourier series decomposition of the vector potential…
We propose a new concept for determining the interior magnetic field vector components in neutron electric dipole moment experiments. If a closed three-dimensional boundary surface surrounding the fiducial volume of an experiment can be…
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the…