We analyze the variational limit of one-dimensional next-to-nearest neighbours (NNN) discrete systems as the lattice size tends to zero when the energy densities are of multiwell or Lennard-Jones type. Properly scaling the energies, we study several phenomena as the formation of boundary layers and phase transitions. We also study the presence of local patterns and of anti-phase transitions in the asymptotic behaviour of the ground states of NNN model subject to Dirichlet boundary conditions. We use this information to prove a localization of fracture result in the case of Lennard-Jones type potentials.
Braides, A., Cicalese, M. (2007). Surface energies in nonconvex discrete systems. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 17(7), 985-1037 [10.1142/S0218202507002182].
Surface energies in nonconvex discrete systems
BRAIDES, ANDREA;
2007-01-01
Abstract
We analyze the variational limit of one-dimensional next-to-nearest neighbours (NNN) discrete systems as the lattice size tends to zero when the energy densities are of multiwell or Lennard-Jones type. Properly scaling the energies, we study several phenomena as the formation of boundary layers and phase transitions. We also study the presence of local patterns and of anti-phase transitions in the asymptotic behaviour of the ground states of NNN model subject to Dirichlet boundary conditions. We use this information to prove a localization of fracture result in the case of Lennard-Jones type potentials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.