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Néel and Cross-Tie wall energies for planar micromagnetic configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2002)

ESAIM: Control, Optimisation and Calculus of Variations

We study a two-dimensional model for micromagnetics, which consists in an energy functional over $S^{2}$ -valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....

Néel and Cross-Tie Wall Energies for Planar Micromagnetic Configurations

François Alouges, Tristan Rivière, Sylvia Serfaty (2010)

ESAIM: Control, Optimisation and Calculus of Variations

 We study a two-dimensional model for micromagnetics, which consists in an energy functional over S2-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which can be described as vortices (Bloch lines in physics). As the characteristic “exchange-length” tends to 0, they converge to planar divergence-free unit norm vector fields which jump along line singularities. We derive lower bounds for the energy, which are explicit functions of the jumps of the limit....

Non uniqueness and uniqueness of capillary surfaces.

Robert Finn (1988)

Manuscripta mathematica

Note on a mixed variational principle in finite elasticity

Gérard A. Maugin, Carmine Trimarco (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present context the variation is performed keeping the deformed configuration fixed while a suitable material stress tensor $S$ and the material coordinates are required to vary independently. The variational principle turns out to be equivalent to an equilibrium problem of placements and tractions prescribed at the boundary of a body of finite extent.

Numerical approaches to rate-independent processes and applications in inelasticity

Alexander Mielke, Tomáš Roubíček (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A conceptual numerical strategy for rate-independent processes in the energetic formulation is proposed and its convergence is proved under various rather mild data qualifications. The novelty is that we obtain convergence of subsequences of space-time discretizations even in case where the limit problem does not have a unique solution and we need no additional assumptions on higher regularity of the limit solution. The variety of general perspectives thus obtained is illustrated on several...