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We examine the response of a soft ferromagnetic lm to an in-plane applied magnetic eld by means of both theory and experiment. In the thin-lm limit, we uncover a separation of scales in the rough energy landscape of micromagnetics: leading order terms generate constraints which eliminate degrees of freedom , terms of second order in the lm thickness lead to… (More)
Micromagnetics is a nonlocal, nonconvex variational problem. Its minimizer represents the ground-state magnetization pattern of a ferromagnetic body under a specified external field. This paper identifies a physically relevant thin-film limit and shows that the limiting behavior is described by a certain " reduced " variational problem. Our main result is… (More)
5 A two-dimensional model for large soft films and comparison with experiment 27 5.1 Statement of the limit problem and the convergence result. . 27
We discuss several elastic energies for nematic elastomers and their small strain expansions both in the regime of large director rotations, and in the case that director changes are small. We propose two fully non-linear model anisotropic energies and compare the behavior they predict with the currently available experimental evidence.
The contact angle of a drop in equilibrium on a solid is strongly affected by the roughness of the surface on which it rests. We study the roughness-induced enhancement of the hydrophobic or hydrophilic properties of a solid surface through homogenization theory. By relying on a variational formulation of the problem, we show that the macroscopic contact… (More)
We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An… (More)