相关论文: Control of the Landau-Lifshitz Equation
The Landau-Lifshitz equation is a coupled set of nonlinear partial differential equations that describes the dynamics of magnetization in a ferromagnet. This equation has an infinite number of stable equilibria. Steering the system from one…
The optimal control of magnetization dynamics in a ferromagnetic sample at a microscopic scale is studied. The dynamics of this model is governed by the Landau-Lifshitz-Gilbert equation on a two-dimensional bounded domain with the external…
The Landau-Lifshitz equation describes the behaviour of magnetization inside a ferromagnetic object. It is known that the Landau-Lifshitz equation has an infinite number of stable equilibrium points. The existence of multiple stable…
The Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this.…
This paper investigates the time-optimal control problem for the Landau-Lifshitz-Bloch (LLB) equation, a macroscopic model that characterizes magnetization dynamics in ferromagnetic materials across a wide temperature range, including near…
The Landau-Lifshitz equation for the magnetization dynamics of a single-domain magnetic system is solved using the methods of self-organization. The description takes into account the torque due to spin transfer. The potential energy of the…
We introduce a new approach to understand magnetization dynamics in ferromagnets based on the holographic realization of ferromagnets. A Landau-Lifshitz equation describing the magnetization dynamics is derived from a Yang-Mills equation in…
We derive a continuum equation for the magnetization of a conducting ferromagnet in the presence of a spin-polarized current. Current effects enter in the form of a topological term in the Landau-Lifshitz equation . In the stationary…
Non-damped oscillations of the magnetization vector of a ferromagnetic system subject to a spin polarized current and an external magnetic field are studied theoretically by solving the Landau-Lifshitz-Gilbert equation. It is shown that the…
The Landau-Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which pose…
Using the invariant operator method for an effective Hamiltonian including the radiation-spin interaction, we describe the quantum theory for magnetization dynamics when the spin system evolves nonadiabatically and out of equilibrium, $d…
The stochastic Landau--Lifshitz--Gilbert (LLG) equation describes the behaviour of the magnetization under the influence of the effective field consisting of random fluctuations. We first reformulate the equation into an equation the…
We consider deterministic and stochastic perturbations of dynamical systems with conservation laws in $\R^3$. The Landau-Lifshitz equation for the magnetization dynamics in ferromagnetics is a special case of our system. The averaging…
The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is derived using a two-continuum model constructed by H.F. Tiersten for elastic and saturated ferromagnets. The relevant basic laws of physics are applied…
The dynamics of the magnetic distribution in a ferromagnetic material is governed by the Landau-Lifshitz equation, which is a nonlinear geometric dispersive equation with a nonconvex constraint that requires the magnetization to remain of…
In this study, we investigate the optimal control of the Landau-Lifshitz-Bloch equation within confined domains in $\mathbb R^n$ for $n= 2, 3.$ We establish the existence of strong solutions for dimensions $n=1, 2, 3$ under suitable growth…
The dynamics of an individual magnetic moment is studied through the Landau-Lifshitz equation with a periodic driving in the direction perpendicular to the applied field. For fields lower than the anisotropy field and small values of the…
We consider the Landau-Lifshitz equation for the spin torque oscillator - a uniaxial ferromagnet in an external magnetic field with polarised spin current driven through it. In the absence of the Gilbert damping, the equation turns out to…
In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into Landau-Lifshitz (LL) equation, which describes the…
The dynamical equation of the magnetization has been reconsidered with enlarging the phase space of the ferromagnetic degrees of freedom to the angular momentum. The generalized Landau-Lifshitz-Gilbert equation that includes inertial terms,…