Continuum thermodynamics of two dimensional liquid crystals.
Christina Papenfuss, Wolfgang Muschik (1996)
Extracta Mathematicae
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Christina Papenfuss, Wolfgang Muschik (1996)
Extracta Mathematicae
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Günay Doğan, Ricardo H. Nochetto (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise...
Andrea Braides, Anneliese Defranceschi, Enrico Vitali (2002)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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As a model for the energy of a brittle elastic body we consider an integral functional consisting of two parts: a volume one (the usual linearly elastic energy) which is quadratic in the strain, and a surface part, which is concentrated along the fractures (i.e. on the discontinuities of the displacement function) and whose density depends on the jump part of the strain. We study the problem of the lower semicontinuous envelope of such a functional under the assumptions that the surface...
Marco Bonacini (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local...
Günay Doğan, Ricardo H. Nochetto (2012)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise...
Phelan, Robert, Weaire, Denis, Brakke, Kenneth (1995)
Experimental Mathematics
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