Published Paper

Inserted: 3 aug 2012
Last Updated: 9 sep 2014

Journal: Math. Mod. Meth. Appl. Sci. (M3AS)
Volume: 24
Pages: 1957-2008
Year: 2014

Abstract:

We consider a variational model which describes a complex system composed, in its reference conguration, of a periodic distribution of `small' interacting particles immersed in a continuous medium. We describe its macroscopic limit via Gamma-convergence, highlighting different regimes. In particular, we show how the interplay between the particles and the continuum leads, for a critical size of the particles, to a capacitary term. Eventually, we discuss how the presence of a continuum affects the properties of the ground states of the system of particles in terms of the validity or not of the so called `Cauchy-Born' rule.

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