Global weak Solutions for the Landau-Lifschitz equation with magnetostriction

ACLInternational audienceIn this paper we prove the global in time existence for weak solutions to a Landau-Lifschitz system with magnetostriction arising from ferromagnetism theory. We describe also the ω-limit set of a solution

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

Global weak Solutions for the Landau-Lifschitz equation with magnetostriction

ACLInternational audienceIn this paper we prove the global in time existence for weak solutions to a Landau-Lifschitz system with magnetostriction arising from ferromagnetism theory. We describe also the ω-limit set of a solution

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

Walls in notched ferromagnetic nanowires

International audienc

Domain Walls Dynamics for One Dimensional Models of Ferromagnetic Nanowires

International audienceWe give here an overview of several papers concerning the domain walls dynamics in one-dimensional models of ferromagneticnanowires. After justifying the one-dimensional models by asymptotic analysis, we first study configurations with one wall in an infinite wire,and we establish the stability of these configurations. In the second part, we prove that the same model in the case of a finite wire is irrelevant because the solution describing one wall is unstable. In addition, it cannot describe complex distributions of several walls located at arbitrarypositions. In order to describe such situations, we use Carr and Pego's geometric method to obtain a metastability result for approximate solutions in a model taking into account the smallness of the exchange length

Stability of static walls for a three-dimensional model of ferromagnetic material.

ACLInternational audienceIn this paper we consider a three dimensional model of ferromagnetic material. We deal with the static domain wall configuration calculated by Walker. We prove the stability of this configuration for the Landau-Lifschitz equation with a simplified expression of the demagnetizing field. Résumé. Dans cet article, on considère un modèle tridimensionnel de matériau ferromagnétique. OnétudieOnétudie les profils de murs statiques calculés initialement par Walker. On démontre la sta-bilité de ces profils pour l'´ equation de Landau-Lifschitz avec un modèle simplifié pour le champ démagnétisant

Asymptotic study for Stokes-Brinkman model with jump embedded transmission conditions

International audienceIn this paper, one considers the coupling of a Brinkman model and Stokes equations with jump embedded transmission conditions. In this model, one assumes that the viscosity in the porous region is very small. Then we derive a Wentzel–Kramers–Brillouin (WKB) expansion in power series of the square root of this small parameter for the velocity and the pressure which are solution of the transmission problem. This WKB expansion is justified rigorously by proving uniform errors estimates

People’s Conceptions and Valuations of Nature in the Context of Climate Change

This paper investigates how people conceive and evaluate nature through language, in a climate change context. With material consisting of 1,200 answers to open-ended questions in nationally representative surveys in Norway, we explore what semantic roles and values the respondents attribute to nature as well as to how they interact with the public debate about climate change. We observe that different conceptions and valuations of nature are tied to different perspectives on the climate change issue: some address the responsibilities of causing climate change, others its consequences, and others yet its potential solutions. The study provides knowledge about the variety of conceptions of nature that can be mobilised by individuals and suggests that policy measures and public communication could benefit by taking this diversity into account.acceptedVersio