Related papers: Recent results for the Landau-Lifshitz equation
The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative space-dependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a…
The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…
The present paper concerns the well-posedness of the Cauchy problem for microlocally symmetrizable hyperbolic systems whose coefficients and symmetrizer are log-Lipschitz continuous, uniformly in time and space variables. For the global in…
Starting from the Dirac-Kohn-Sham equation we derive the relativistic equation of motion of spin angular momentum in a magnetic solid under an external electromagnetic field. This equation of motion can be written in the form of the…
We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these…
We study the dynamics of solitons in a Landau-Lifshitz equation describing the magnetization of a three-dimensional ferromagnet with an easy axis anisotropy. We numerically compute the energy dispersion relation and the structure of moving…
We investigate the Cauchy problem to the compressible planar non-resistive magnetohydrodynamic equations with zero heat conduction. The global existence of strong solutions to such a model has been established by Li and Li (J. Differential…
An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for…
The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume…
We report a numerical implementation of the Landau-Lifshitz-Baryakhtar theory, which dictates that the micromagnetic relaxation term obeys the symmetry of the magnetic crystal, i. e. replacing the single intrinsic damping constant with a…
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a…
We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension $n \ge 3$, valid under a smallness condition of initial gradients in the $L^n$ norm. The argument is based on…
The solutions of the Landau-Lifshitz equation with finite-gap behavior at infinity are considered. By means of the inverse scattering method the large-time asymptotics is obtained.
The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fast magnetization dynamics in ferromagnetic materials. Recently, the inertial LLG equation, which contains an inertial term, has been proposed to capture the ultra-fast…
We consider the numerical approximation of the inertial Landau-Lifshitz-Gilbert equation (iLLG), which describes the dynamics of the magnetization in ferromagnetic materials at subpicosecond time scales. We propose and analyze two fully…
Stationary structures in a classical isotropic two-dimensional continuous Heisenberg ferromagnetic spin system are studied in the framework of the (2+1)-dimensional Landau-Lifshitz model. It is established that in the case of \vec S (\vec…
A modeling approach for standing spin-wave resonances based on a finite-difference formulation of the Landau-Lifshitz-Gilbert equation is presented. In contrast to a previous study [Bihler et al., Phys. Rev. B 79, 045205 (2009)], this…
We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this…
We propose and implement a third-order accurate numerical scheme for the Landau-Lifshitz-Gilbert equation, which describes magnetization dynamics in ferromagnetic materials under large damping parameters. This method offers two key…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…