Related papers: Landau-Lifshitz Equation with Affine Control
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
As of now, the phenomenological classical Landau-Lifshitz (LL) damping of magnetic order is not conceptually linked to the quantum theory of dissipation of the Lindbladian formalism which is unsatisfactory for the booming research on…
We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown,…
Landau theory is used to investigate the behaviour of a metallic magnet driven towards a quantum critical point by the application of pressure. The observed dependence of the transition temperature with pressure is used to show that the…
Numerical integration of the Landau-Lifshitz-Gilbert equation with thermal fluctuations is used to study the dynamic response of single-domain nanomagnets to rapid changes in the applied magnetic field. The simulation can resolve…
We show that recently reported precessing solution of Landau-Lifshitz-Gilbert equations in ferromagnetic nanowires is stable under small perturbations of initial data, applied field and anisotropy constant. Linear stability is established…
Recently, Kim & Wilkening (Convergence of a mass-lumped finite element method for the Landau-Lifshitz equation, Quart. Appl. Math., 76, 383-405, 2018) proposed two novel predictor-corrector methods for the Landau-Lifshitz-Gilbert equation…
In this paper, we present a finite difference heterogeneous multiscale method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient. The approach combines a higher order discretization and artificial damping in…
We formulate a Landau theory for altermagnets, a class of colinear compensated magnets with spin-split bands. Starting from the non-relativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space…
Metallic ferromagnets subjected to a temperature gradient exhibit a magnonic drag of the electric current. We address this problem by solving a stochastic Landau-Lifshitz equation to calculate the magnon-drag thermopower. The…
We analyse various properties of stochastic Markov processes with multiplicative white noise. We take a single-variable problem as a simple example, and we later extend the analysis to the Landau-Lifshitz-Gilbert equation for the stochastic…
The classical Landau-Lifshitz-Gilbert (LLG) equation has long served as a cornerstone for modeling magnetization dynamics in magnetic systems, yet its classical nature limits its applicability to inherently quantum phenomena such as…
Recent studies have found that fluctuations of magnetization transfer in integrable spin chains violate the central limit property. Here we revisit the problem of anomalous counting statistics in the Landau-Lifshitz field theory by…
Based on lowest-order finite elements in space, we consider the numerical integration of the Landau-Lifschitz-Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange…
A keen interest towards technological implications of spin-orbit driven magnetization dynamics requests a proper theoretical description, especially in the context of a microscopic framework, to be developed. Indeed, magnetization dynamics…
The Landau--Lifshitz--Bloch (LLB) equation is a well-established micromagnetic model for describing magnetisation dynamics in ferromagnets at elevated temperatures. In this paper, we propose and analyse two fully discrete, conforming finite…
In this paper, we consider the Landau-Lifshitz equation of the ferromagnetic spin chain from $\R^2$ to the unit sphere $S^2$ under the general Oseen-Frank energy. We obtain global existence and uniqueness of weak solutions for large energy…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
We prove the existence and uniqueness of non-trivial stable solutions to Landau-Lifshitz-Maxwell equations with Dirichlet boundary condition for large anisotropies and small domains, where the domains are non-simply connected.
Problem of time-optimal control of linear systems with fractional dynamics is treated in the paper from the convex-analytic standpoint. A linear system of fractional differential equations involving Riemann--Liouville derivatives is…