The Landau-Lifshitz-Gilbert equation describes dynamics of ferromagnetism, where strong nonlinearity, nonconvexity are hard to tackle: so far, existing schemes to approximate weak solutions suffer from severe time-step restrictions. In this paper, we propose an implicit fully discrete scheme and verify unconditional convergence.

We present an extension of the Gilbert-Pearson theory of subordinacy, which relates dimensional Hausdorff spectral properties of one-dimensional Schrödinger operators to the behavior of solutions of the corresponding Schrödinger equation. We use this theory to analyze these properties for several examples having the singular-continuous spectrum, including sparse barrier potentials, the almost M...

Two-dimensional magnetic skyrmions are particle-like domains in thin films. The kinetic property of at finite temperature is well described by the Thiele equation, including a stochastic field and mass. This study examines validity constant-mass approximation comparing Fourier spectrum Brownian motions equation Landau–Lifshitz–Gilbert equation. Then, expression diffusion flow derived from four-...