Q-tensor continuum energies as limits of head-to-tail-symmetric spin systems
Analysis of PDEs
2013-10-16 v1
Abstract
We consider a class of spin-type discrete systems and analyze their continuum limit as the lattice spacing goes to zero. Under standard coerciveness and growth assumptions together with an additional head-to-tail symmetry condition, we observe that this limit can be conveniently written as a functional in the space of -tensors. We further characterize the limit energy density in several cases (both in 2 and 3 dimensions). In the planar case we also develop a second-order theory and we derive gradient or concentration-type models according to the chosen scaling.
Keywords
Cite
@article{arxiv.1310.4084,
title = {Q-tensor continuum energies as limits of head-to-tail-symmetric spin systems},
author = {Andrea Braides and Marco Cicalese and Francesco Solombrino},
journal= {arXiv preprint arXiv:1310.4084},
year = {2013}
}