Stability for Walls in Ferromagnetic Nanowire

We study the stability of travelling wall profiles for a one dimensional model of ferromagnetic nanowire submitted to an exterior magnetic field. We prove that these profiles are asymptotically stable modulo a translation-rotation for small applied magnetic fields

Long time behaviour of a stochastic nano particle

In this article, we are interested in the behaviour of a single ferromagnetic mono-domain particle submitted to an external field with a stochastic perturbation. This model is the first step toward the mathematical understanding of thermal effects on a ferromagnet. In a first part, we present the stochastic model and prove that the associated stochastic differential equation is well defined. The second part is dedicated to the study of the long time behaviour of the magnetic moment and in the third part we prove that the stochastic perturbation induces a non reversibility phenomenon. Last, we illustrate these results through numerical simulations of our stochastic model. The main results presented in this article are the rate of convergence of the magnetization toward the unique stable equilibrium of the deterministic model. The second result is a sharp estimate of the hysteresis phenomenon induced by the stochastic perturbation (remember that with no perturbation, the magnetic moment remains constant)

Control of travelling walls in a ferromagnetic nanowire

We investigate the problem of controlling the magnetic moment in a ferromagnetic nanowire submitted to an external magnetic field in the direction of the nanowire. The system is modeled with the one dimensional Landau-Lifschitz equation. In the absence of control, there exist particular solutions, which happen to be relevant for practical issues, called travelling walls. In this paper, we prove that it is possible to move from a given travelling wall profile to any other one, by acting on the external magnetic field. The control laws are simple and explicit, and the resulting trajectories are shown to be stable

Numerical simulation of a class of models that combine several mechanisms of dissipation: fracture, plasticity, viscous dissipation

We study a class of time evolution models that contain dissipation mech- anisms exhibited by geophysical materials during deformation: plasticity, viscous dissipation and fracture. We formally prove that they satisfy a Clausius-Duhem type inequality. We describe a semi-discrete time evolu- tion associated with these models, and report numerical 1D and 2D traction experiments, that illustrate that several dissipation regimes can indeed take place during the deformation. Finally, we report 2D numerical simulation of an experiment by Peltzer and Tapponnier, who studied the indentation of a layer of plasticine as an analogue model for geological materials

Stability properties of steady-states for a network of ferromagnetic nanowires

International audienceWe investigate the problem of describing the possible stationary configurations of the magnetic moment in a network of ferromagnetic nanowires with length $L$ connected by semiconductor devices, or equivalently, of its possible $L$-periodic stationary configurations in an infinite nanowire. The dynamical model that we use is based on the one-dimensional Landau-Lifshitz equation of micromagnetism. We compute all $L$-periodic steady-states of that system, define an associated energy functional, and these steady-states share a quantification property in the sense that their energy can only take some precise discrete values. Then, based on a precise spectral study of the linearized system, we investigate the stability properties of the steady-states

Axisymmetric Level Set model of Leidenfrost effect

We propose a level-set model of phase change and apply it to the study of the Leidenfrost effect. The new ingredients used in this model are twofold: first we enforce by penalization the droplet temperature to the saturation temperature in order to ensure a correct mass transfer at interface, and second we propose a careful differentiation of the capillary interface with respect to a moving interface with phase change. We perform some numerical tests in the axisymmetric case and show that our numerical method, while not avoiding well known numerical caveats of diffuse interface methods, behave quite well in the limit of numerical interface width going to zero in comparison to an analytical formula

Convergence of a ferromagnetic film model

International audienceDans cette note, nous présentons un résultat de Gamma-convergence pour les films de matériaux ferromagnétiques. Nous proposons un modèle pour lequel il est possible d'assurer une convergence forte des minimiseurs quand le paramètre d'échange tend vers zéro. Dans ce modèle, l'épaisseur du film est considérée comme constante et l'aimantation est contrainte à rester constante dans l'épaisseur du film