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 Q-tensors. We further characterize the limit energy density in several cases (both in two and three 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.

Q-tensor continuum energies as limits of head-to-tail symmetric spin systems / Braides, A.; Cicalese, M.; Solombrino, F.. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 47:4(2015), pp. 2832-2867. [10.1137/130941341]

Q-tensor continuum energies as limits of head-to-tail symmetric spin systems

Braides A.;Cicalese M.;Solombrino F.
2015-01-01

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 Q-tensors. We further characterize the limit energy density in several cases (both in two and three 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.
2015
47
4
2832
2867
https://arxiv.org/abs/1310.4084
Braides, A.; Cicalese, M.; Solombrino, F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/139465
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