# Stéphane LabbéSorbonne Université | UPMC · Laboratoire Jacques-Louis Lions (LJLL)

Stéphane Labbé

Professor

## About

58

Publications

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602

Citations

## Publications

Publications (58)

Sea ice is a heterogeneous, evolving mosaic comprised of many individual floes, which vary in spatial scales from meters to tens of kilometers. Both the internal dynamics of the floe mosaic (floe-floe interactions), and the evolution of floes under ocean and atmospheric forcing (floe-flow interactions), determine the exchange of heat, momentum, and...

Weight savings in mobility and transport are mandatory in order to reduce CO2
emissions and energy consumption. The steel industry offers weight saving solutions by
a growing portfolio of Advanced High Strength Steel (AHSS) products. AHSS owe
their strength to their largely refined and complex microstructures, containing multiple
metallurgical phas...

Weight savings in mobility and transport are mandatory in order to reduce CO 2 emissions and energy consumption. The steel industry offers weight saving solutions by a growing portfolio of Advanced High Strength Steel (AHSS) products. AHSS owe their strength to their largely refined and complex microstructures, containing multiple metallurgical pha...

In the current work we present the results of 3D micromagnetic modelling of magnetostrictive strain and magnetic hysteresis under uniaxial stress in ferrite. The simulations are performed on artificial microstructures with different grain orientations that allow to take into account the anisotropy of magnetic and mechanical properties of iron-based...

In this text we propose a model of antennas network. The goal is to understand the challenges encountered in power and cost optimisation in order to enhance the efficiency of the system respecting the maximal prescribed power levels locally.

In this work, 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 a step toward the mathematical understanding of thermal effects on ferromagnets. In a first part, we discuss modelling issues and propose several ways to integrate a random noi...

In this paper, we derive a one-dimensional asymptotic model for the dynamics of the magnetic moment in a twisted ferromagnetic nanowire with arbitrary elliptical cross-section, curvature and torsion.

Although it has been experimentally reported that speed variations is the optimal way of optimizing his pace for achieving a given distance in a minimal time, we still do not know what the optimal speed variations (i.e. accelerations) are. At first, we have to check the hypothesis that human is able to accurately self-pacing its acceleration and th...

Frequency-domain waveform modeling in the acoustic and elastic approximations requires the solution of large ill-conditioned linear systems. In the context of frequency-domain full waveform inversion, the solutions of these systems are required for a large number of sources (i.e. right-hand sides). Because of their tremendous memory requirements, d...

In this paper, we present a model describing the dynamics of a population of ice floes with arbitrary shapes and sizes, which are exposed to atmospheric and oceanic skin drag. The granular model presented is based on simplified momentum equations for ice floe motion between collisions and on the resolution of linear complementarity problems to deal...

When applied to wave propagation modeling in anisotropic media, Perfectly Matched Layers (PML) exhibit instabilities. Incoming waves are amplified instead of being absorbed. Overcoming this difficulty is crucial as in many seismic imaging applications, accounting accurately for the subsurface anisotropy is mandatory. In this study, we present the S...

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...

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 stoch...

Thanks to averaging processes and Gamma-convergence techniques, we are able
to link a microscopic description of ferromagnetic materials based on spin
lattices and their mesoscopic description in the static framework for the three
fundamental contributions: exchange, magnetostatic and external field. The
results are in accordance with the classical...

Inthiswork,wepresentamathematicalstudyofstabilityandcon- trollability of one-dimensional network of ferromagnetic particles. The control is the magnetic field generated by a dipole whose position and whose ampli- tude can be selected. The evolution of the magnetic field in the network of particules is described by the Landau-Lifschitz equation. Fir...

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 c...

We 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-dimens...

We study the magnetic behavior of ferromagnetic bilayers and how the super-exchange energy affects it. To this end, we compute, for several values of the super-exchange parameters, the final magnetiza-tion states of two configurations of bilayered ferromagnetic domains: one made of two stacked thin square plates and the other made of two stacked th...

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite
length. First we justify the model by Γ-convergence arguments.
Furthermore we prove the existence of wall profiles. These walls being unstable, we
stabilize them by the mean of an applied magnetic field.

We study a 2-scale version of the Landau-Lifshitz system of ferromagnetism,
introduced by Starynkevitch to modelize hysteresis: the response of the
magnetization is fast compared to a slowly varying applied magnetic fi eld.
Taking the exchange term into account, in space dimension 3, we prove that,
under some natural stability assumption on the equ...

This paper is devoted to the analysis of flux schemes coupled with the reservoir technique for approximating hyperbolic equations and linear hyperbolic systems of conservation laws [F. Alouges, F. De Vuyst, G. Le Coq, E. Lorin, The reservoir scheme for systems of conservation laws, in: Finite Volumes for Complex Applications, III, Porquerolles, 200...

We address the problem of control of the magnetic moment in a ferromagnetic nanowire by means of a magnetic field. Based on theoretical results for the 1D Landau-Lifschitz equation, we show a robust controllability result.

The high-frequency properties of small 3D ferromagnetic elements are investigated by means of micromagnetic simulations. The dynamic susceptibilty spectra associated with two types of submicrometer-size elements: a cylindrical dot with a vortex state and an eye shape particle with a bidomain state are reported. In these confined structures, the spe...

We present an optimized Schwarz waveform relaxation algorithm for the parallel solution in space-time of the equations of
ferro-magnetics in the micromagnetic model. We use Robin transmission conditions, and observe fast convergence of the discretized
algorithm. We show numerically the existence of an optimal parameter in the Robin condition, and s...

The dynamic susceptibility spectra of ferromagnetic nanodots with a large perpendicular anisotropy exhibiting a two-stripe domain state at remanence are investigated using 3D micromagnetic simulations. Due to the confined geometry, multiple domain wall excitations are revealed within the frequency range 0.1–15 GHz. The size dependence (dot thicknes...

In this Note, we present a Γ-convergence type result for ferromagnetic films. We propose a model of films for which we could ensure the strong convergence of minimizers when the exchange parameter vanishes. In this model, the plate thickness is kept constant and the magnetization stays constant in the thickness of the film. To cite this article: F....

ESAIM Proceedings volume 18 http://www.esaim-proc.org/index.php?option=com_toc&url=/articles/proc/abs/2007/03/contents/contents.html

La mod ́elisation de mat ́eriaux ferromagn ́etiques suit la th ́eorie du micromagn ́etisme propośee par Brown pour les configurations statiques (d' ́equilibre) et les ́equations de Landau-Lifchitz (ou Landau-Lifchitz-Gilbert) pour la dynamique. Dans ce papier, nous d ́ecrivons rapidement les principaux modèles utiliśes et nous concentrons dans les...

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, c...

The aim of this article is to propose a generalization of the finite dif-ference scheme suitable with solutions of Dirac distribution type. This type of solution is for example encountered in earthquake or explosion simulations. In such problems, the difficulty is to catch sharply a moving singular front modeled by a Dirac type distribution. We giv...

In many applications, for instance the simulation of the behaviour of ferromagnetic materials, the demagnetization field, approximation of the Maxwell contribution, has to be computed. One of the applications aimed by this paper is the simulation of ferromagnetic periodic layers. This type of layers could be, for example, structured poly-cristals o...

3D numerical simulations of ferromagnetic materials can be compared with experimental results via microwave susceptibility. In this paper, an optimised computation of this microwave susceptibility for large meshes is proposed. The microwave susceptibility is obtained by linearisation of the Landau and Lifchitz equations near equilibrium states and...

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.

Controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model. In the present paper, under the main assumptions that the discretized semigroup is uniformly analytic, and that the control operator is mildly unbounded, we p...

Dans cet article, nous présentons des travaux récents concernant la simulation de phènomènes ferromagnétiques. Les principaux problèmes rencontrés sont le calcul du champ démagnétisant et de la susceptibilité. En ce qui concerne le calcul du champ démagnétisant, il s'agit de discrétiser un opérateur non-local. Nous nous concentrerons sur le cas pér...

The goal of this article is to analyse the time asymptotic stability of one dimensional Bloch wall in ferromagnetic materials. The equation involved in modelling such materials is the Landau-Lifschitz system which is non-linear and parabolic. We demonstrate that the equilibrium states called Bloch walls are asymptotically stable modulo a rotation t...

In this paper, an efficient method is developed for computing the magnetostatic field for ferromagnetic materials on large structured meshes. The problem,is discretized using a finite volume approximation. The discrete operator is proved to preserve the main properties of the continuous model, and a lower estimate of its lower eigenvalue is given....

The dynamic susceptibility spectra of a soft ferromagnetic nanodot supporting a vortex-type magnetic configuration is studied in the frequency range 0.1–20GHz by means of dynamic micromagnetic simulations. The frequency evolution of the detected magnetic excitations as a function of both dot radius (40⩽R⩽160nm) and dot thickness (5⩽Lz⩽80nm) is repo...

The Benney-Luke equation (BL) is a model for the evolution of three-dimensional weakly nonlinear, long water waves of small amplitude. In this paper we propose a nearly conservative scheme for the numerical resolution of (BL). Moreover, it is known (Paumond, Differential Integral Equations 16 (2003) 1039–1064; Pego and Quintero, Physica D 132 (1999...

The microwave permeability of composites made of ferrite particles in a non-magnetic matrix is affected by particle shape and size. To account for the second effect, we have developed a micromagnetic model for calculating the microwave polarizability of a particle with non-uniform magnetization. This model is described in detail: a generalized dema...

Three-dimensional numerical simulations of ferromagnetic materials can be compared with experimental results using microwave susceptibility. In this Note the computation of this microwave susceptibility is presented for large meshes. The microwave susceptibility is obtained by linearisation of the Landau and Lifchitz equations near equilibrium stat...

Three-dimensional numerical simulations of ferromagnetic materials can be compared with experimental results using microwave susceptibility. In this Note the computation of this microwave susceptibility is presented for large meshes. The microwave susceptibility is obtained by linearisation of the Landau and Lifchitz equations near equilibrium stat...

During the 40's, W.F. Brown introduced the micromagnetism theory to explain the behaviour of non-linear magnetic materials : the ferro and ferrimagnetics.
The model used is based on two main points. The first one is the use of the Landau-Lifchitz partial differential equation, which describes the evolution in time of the magnetisation.The second on...

In order to model ferromagnetic materials in the field of hyperfrequencies, the magnetostatic equations are coupled with the Landau-Lifshitz evolution system (micromagnetism [1]). The demagnetisation term (magnetostatic) involves the whole space domain, making dynamic simulation very expensive, especially when key phenomena such as wall migrations,...

In order to model ferromagnetic materials in the field of hyperfrequencies, the magnetostatic equations are coupled with the Landau-Lifshitz evolution system (micromagnetism [1]). The demagnetisation term (magnetostatic) involves the whole space domain, making dynamic simulation very expensive, especially when key phenomena such as wall migrations,...

A commonly used model for ferromagnetic materials in the quasistatic regime is the Landau-Lifshitz system coupled with the so-called quasistatic Maxwell’s equations. By an appropriate scaling, we justify this approach and we propose a new asymptotic expansion. This suggest a new numerical method.

Le micromagnétisme, théorie élaborée dans les années 40 par W.F.
Brown, a pour but d'expliquer le comportement des matériaux magnétiques non-linéaires : les ferro et ferrimagnétiques.
Le modèle utilisé repose sur l'utilisation d'une équation aux dérivées partielles, introduite par Landau et Lifchitz, décrivant l'évolution de la densité d'aimantatio...