In this paper we establish rigorously a one dimensional model of a junction of several ferromagnetic nanowires. Such structures appear in nano electronics or in new memory devices. We present also a numerical scheme adapted to this configuration and we compare our results with the 3d simulation obtained with the code EMicroM.

Abstract Sea ice is a heterogeneous, evolving mosaic of individual floes, varying 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 tracers between the lower atmosphere and upper ocean. Climate models do not represent either of these highly variable interactions. We use a novel, high‐resolution, discrete element modeling framework to examine ice‐ocean boundary layer (IOBL) turbulence within a domain approximately the size of a climate model grid. We show floe‐scale effects could cause a marked increase in the production of fine‐scale three‐dimensional turbulence in the IOBL relative to continuum model approaches, and provide a method of representing that turbulence using bulk parameters related to the spatial variance of the ice and ocean: the floe size distribution and the ocean kinetic energy spectrum.

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 noise in the deterministic model. Then, among all these approaches, we focus on the more natural one and study its long time behaviour. We prove that the system converges to the unique stable equilibrium of the deterministic model and determine the $$L^p$$ rate of the convergence. Finally, we illustrate the theoretical results by numerical simulations.

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 this even in a state of fatigue during exhaustive self-pacing ramp runs. For that purpose, 3 males and 2 females middle-aged, recreational runners ran, in random order, three exhaustive acceleration trials. We instructed the five runners to perform three self-paced acceleration trials based on three acceleration intensity levels: "soft", "medium" and "hard". We chose a descriptive modelling approach to analyse the behaviour of the runners. Once we knew that the runners were able to perceive three acceleration intensity levels, we proposed a mean reverting process (Ornstein-Uhlenbeck) to describe those accelerations: da(t) = -theta(a(t) - a)dt + sigma dW(t) where a is the mean acceleration, a(t) is the measured acceleration at each time interval t, theta the ability of the runner to correct the variations around a mean acceleration and sigma the human induced variations. The goodness-of-fit of the Ornstein-Uhlenbeck process highlights the fact that humans are able to maintain a constant acceleration and are able to precisely regulate their acceleration (regardless of its intensity) in a run leading to exhaustion in the range from 1 min 36 s to 20 min. (C) 2018 Elsevier B.V. All rights reserved.

Although the critical dimension (CD) is getting smaller following the ITRS roadmap, the scanning electron microscope (CD-SEM) is still the most general purpose tool used for non-destructive metrology in the semiconductor industry. However, we are now dealing with patterns whose dimensions are of the same order of magnitude as the electron interaction volume and therefore, the usual edge-based metrology methods fail.Like scatterometry has extended the resolution of optical imaging metrology through complex modeling of light-matter interaction, some electrons-matter simulation models have been proposed. They could be used to improve accuracy and precision of CD-SEM metrology. However, these model-based approaches also face to fundamental limits mainly due to probe size with respect to the considered structure and noise. This paper analyses these limits assuming the model is perfect and the microscope has no systematic defect.In this simulation study, we have used the model proposed by D. Nyyssonen, assuming to perfectly represent the SEM effects in the image. The feature of interest is limited to isolated trapezoidal lines with various CD, sidewall angles (SWA) and heights. We have carried out the study with several beam energies, tilts and probe sizes.Surprisingly enough, sensitivity analysis shows that with typical noise amplitude, sidewall angle can be determined with a reasonable precision using SEM images. Single tilted beam SEM images can also bring advantage to measure patterns height. Since these precision figures depend on the geometries, we provide useful graphs giving the ultimate precision for various dimensions (CD, height, SWA).

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Stability for Walls in Ferromagnetic Nanowire Gilles Carbou, Stéphane Labbé

Ferromagnetic materials are very important in industry and modern technology and are essential for many electronic devices (electric motors, magnetic shields, magnetic storage devices). Ferromagnetism is the basic mechanism which models the behavior of permanent magnets. The thermodynamical theoretical study of ferromagnetism has been first initiated by Weiss [7], following previous works of Landau and Lifshitz on the dynamic behavior of single magnets [6]. A further modeling step has been developed by Brown through it’s micromagnetism model [3]. An open challenge in the study of ferromagnetism is to describe the magnetic moment μt under heat fluctuations. The heat fluctuations in ferromagnetic materials are essential in order to understand their behaviour under critical temperatures (such as Curie temperature), where the Joule effect induces high heat fluxes. The mathematical development of a complete stochastic ferromagnetic theory for understanding such phenomena is important in order to enhance simulations of ferromagnetic devices (such as electronic circuits). These heating effects on the microstructure dynamics in ferromagnetic materials is commonly modeled by the introduction of a noise term at microscopic scale (the scale between the macroscopic and the quantum regime) on the magnetic moment direction [4]. For example, at the mesoscale (continuous scale), the Landau-Lifshitz equation can be modified into a stochastic differential equation (SDE) form [2] in order to incorporate the random fluctuations of the magnetic field H(m(t)) into the dynamic of the magnetization m(t). In our work we introduce a mathematical model for an assembly of ellipsoidal particles [1] under the Heisenberg interaction and the disorder induced by the heating. Furthermore, we provide several numerical simulation results illustrative the stability and the long time behaviour of these systems.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2015Preconditioning and multiple-right hand sides strategies for the solution of the frequency-domain wave propagation problem using the CGMN methodAuthors: Okba HamitouLudovic MétivierStéphane LabbéRomain BrossierJean VirieuxOkba HamitouSpeaker and ISTerre, University Grenoble Alpes and LJK, University Grenoble AlpesSearch for more papers by this author, Ludovic MétivierISTerre, University Grenoble Alpes and LJK, University Grenoble AlpesSearch for more papers by this author, Stéphane LabbéLJK, University Grenoble AlpesSearch for more papers by this author, Romain BrossierISTerre, University Grenoble AlpesSearch for more papers by this author, and Jean VirieuxISTerre, University Grenoble AlpesSearch for more papers by this authorhttps://doi.org/10.1190/segam2015-5889724.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract 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, direct solvers are not yet adapted to the solution of 3D elastodynamics equations. We are thus interested in the use of efficient iterative solvers adapted to the solution of these systems. The CGMN method has shown robust convergence properties for 2D and 3D elastic problems in highly heterogeneous media, compared to standard Krylov methods, but still requires a large number of iterations to reach sufficient accuracy. In this study, the design of an efficient preconditioning strategy adapted to this method is investigated. This preconditioner is computed as a sparse approximate inverse of a heavily damped wave propagation operator. In addition, the single seed method is used to increase the efficiency of the solver for multiple right-hand sides. The efficiency of these two combined strategies is evaluated on the 2D BP2004 model in the visco-acoustic approximation, up to 40 Hz. An overall time speed-up equal to 3 and a reduction of the number of iterations by a factor 10 are observed. Keywords: algorithm, wave propagation, sparse, modeling, frequency-domainPermalink: https://doi.org/10.1190/segam2015-5889724.1FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 2015ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2015 Pages: 5634 publication data© 2015 Published in electronic format with permission by the Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 19 Aug 2015 CITATION INFORMATION Okba Hamitou, Ludovic Métivier, Stéphane Labbé, Romain Brossier, and Jean Virieux, (2015), "Preconditioning and multiple-right hand sides strategies for the solution of the frequency-domain wave propagation problem using the CGMN method," SEG Technical Program Expanded Abstracts : 3612-3616. https://doi.org/10.1190/segam2015-5889724.1 Plain-Language Summary Keywordsalgorithmwave propagationsparsemodelingfrequency-domainPDF DownloadLoading ...

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 with ice floe collisions. Between collisions, the motion of an individual ice floe satisfies the linear and angular momentum conservation equations, with classical formula applied to account for atmospheric and oceanic skin drag. To deal with collisions, before they lead to interpenetration, we included a linear complementarity problem based on the Signorini condition and Coulombs law. The nature of the contact is described through a constant coefficient of friction , as well as a coefficient of restitution (0 epsilon 1) describing the loss of kinetic energy during the collision. In the present version of our model, this coefficient is fixed. The model was validated using data obtained from the motion of interacting artificial wood floes in a test basin. The results of simulations comprising few hundreds of ice floes of various shapes and sizes, exposed to different forcing scenarios, and under different configurations, are also discussed. They show that the progressive clustering of ice floes as the result of kinetic energy dissipation during collisions is well captured, and suggest a collisional regimes of floe dispersion at small scales, different from a large-scale regime essentially driven by wind forcing.

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 continuous description of ferromagnetic phenomena and justifies it. This work is a seed towards a dynamic description of ferromagnetic materials.

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.

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).

We consider the limit of some barotropic compressible fluid model with Korteweg forcing term, studied in [1], as the exponent of the barotropic law goes to infinity. This provides a free boundary problem model, with capillary effects, and therefore generalizes the free boundary model obtained by Lions and Masmoudi [5]. Our interest for such free boundary problem stems from a study of the Leidenfrost effect.

We study a two-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 field. Taking the exchange term into account, in space dimension 3, we prove that, under some natural stability assumption on the equilibria of the system, the strong solutions follow the dynamics of these equilibria. We also give explicit examples of relevant equilibria and exterior magnetic fields, when the ferromagnetic medium occupies some ellipsoidal domain.

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-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. (C) 2012 Elsevier Inc. All rights reserved.

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.

In this work, we present a mathematical study of stability and controllability of one-dimensional network of ferromagnetic particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particles is described by the Landau-Lifschitz equation. First, we model a network of ellipsoidal shape ferromagnetic particles. Then, we prove the stability of relevant configurations and discuss the controllability by the means of the external magnetic field induced by the magnetic dipole. Finally some numerical results illustrate the stability and the controllability results.