We consider 2D discrete systems, described by scalar functions and governed by periodic interaction potentials. We focus on anisotropic nearest neighbors interactions in the hexagonal lattice and on isotropic long range interactions in the square lattice. In both these cases, we perform a complete Γ-convergence analysis of the energy induced by a configuration of discrete topological singularities. This analysis allows to prove the existence of many metastable configurations of singularities in the hexagonal lattice.

Γ-convergence analysis for discrete topological singularities: The anisotropic triangular lattice and the long range interaction energy

De Luca, Lucia
2016

Abstract

We consider 2D discrete systems, described by scalar functions and governed by periodic interaction potentials. We focus on anisotropic nearest neighbors interactions in the hexagonal lattice and on isotropic long range interactions in the square lattice. In both these cases, we perform a complete Γ-convergence analysis of the energy induced by a configuration of discrete topological singularities. This analysis allows to prove the existence of many metastable configurations of singularities in the hexagonal lattice.
File in questo prodotto:
File Dimensione Formato  
De-Luca-AA-rivista.pdf

solo utenti autorizzati

Tipologia: Versione finale editoriale
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 280.38 kB
Formato Adobe PDF
280.38 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/934886
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? 8
social impact