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Macroscopic models of collective motion and self-organization

Pierre Degond, Amic Frouvelle, Jian-Guo Liu, Sebastien Motsch, Laurent Navoret (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

In this paper, we review recent developments on the derivation and properties of macroscopic models of collective motion and self-organization. The starting point is a model of self-propelled particles interacting with its neighbors through alignment. We successively derive a mean-field model and its hydrodynamic limit. The resulting macroscopic model is the Self-Organized Hydrodynamics (SOH). We review the available existence results and known properties of the SOH model and discuss it in view...

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

Ayman Kachmar (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2009)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Magnetization switching on small ferromagnetic ellipsoidal samples

François Alouges, Karine Beauchard (2008)

ESAIM: Control, Optimisation and Calculus of Variations

The study of small magnetic particles has become a very important topic, in particular for the development of technological devices such as those used for magnetic recording. In this field, switching the magnetization inside the magnetic sample is of particular relevance. We here investigate mathematically this problem by considering the full partial differential model of Landau-Lifschitz equations triggered by a uniform (in space) external magnetic field.

Many-body aspects of approach to equilibrium

Eric Carlen, M. C. Carvalho, Michael Loss (2000)

Journées équations aux dérivées partielles

Kinetic theory and approach to equilibrium is usually studied in the realm of the Boltzmann equation. With a few notable exceptions not much is known about the solutions of this equation and about its derivation from fundamental principles. In 1956 Mark Kac introduced a probabilistic model of N interacting particles. The velocity distribution is governed by a Markov semi group and the evolution of its single particle marginals is governed (in the infinite particle limit) by a caricature of the spatially...

Marking (1, 2) points of the brownian web and applications

C. M. Newman, K. Ravishankar, E. Schertzer (2010)

Annales de l'I.H.P. Probabilités et statistiques

The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding...

Markovian perturbation, response and fluctuation dissipation theorem

Amir Dembo, Jean-Dominique Deuschel (2010)

Annales de l'I.H.P. Probabilités et statistiques

We consider the Fluctuation Dissipation Theorem (FDT) of statistical physics from a mathematical perspective. We formalize the concept of “linear response function” in the general framework of Markov processes. We show that for processes out of equilibrium it depends not only on the given Markov process X(s) but also on the chosen perturbation of it. We characterize the set of all possible response functions for a given Markov process and show that at equilibrium they all satisfy the FDT. That is,...

Mathematical modeling and simulation of flow in domains separated by leaky semipermeable membrane including osmotic effect

Jaroslav Hron, Maria Neuss-Radu, Petra Pustějovská (2011)

Applications of Mathematics

In this paper, we propose a mathematical model for flow and transport processes of diluted solutions in domains separated by a leaky semipermeable membrane. We formulate transmission conditions for the flow and the solute concentration across the membrane which take into account the property of the membrane to partly reject the solute, the accumulation of rejected solute at the membrane, and the influence of the solute concentration on the volume flow, known as osmotic effect. The model is solved...

Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Jinn-Liang Liu (2012)

Nanoscale Systems: Mathematical Modeling, Theory and Applications

Within the effective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version...

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