Publisher Summary This chapter discusses the main properties of Γ-convergence, in
particular those that are useful in the actual computation of Γ-limits. For some classes of …

We investigate ground state configurations of atomic systems in two dimensions interacting
via short range pair potentials. As the number of particles tends to infinity, we show that low …

Manufacturing system is the core subsystem of enterprises and the fundamental driving
force for sustainable development of enterprises [1]. Its competitiveness directly determines …

We study the homogenization of lattice energies related to Ising systems of the form with ui a
spin variable indexed on the portion of a cubic lattice Ω∩ εZd, by computing their Γ-limit in …

We introduce and discuss discrete two-dimensional models for XY spin systems and screw
dislocations in crystals. We prove that, as the lattice spacing ε tends to zero, the relevant …

In this paper we consider the XY (N-dimensional possibly anisotropic) spin-type model and,
by comparison with a Ginzburg–Landau-type functional, we perform a variational analysis in …

We introduce a class of n-dimensional (possibly inhomogeneous) spin-like lattice systems
presenting modulated phases with possibly different textures. Such systems can be …

We study the magnetic energy of magnetic polymer composite materials as the average
distance between magnetic particles vanishes. We model the position of these particles in …

We consider the minimization of the repulsive–attractive power-law interaction energies that
occur in many biological and physical situations. We show the existence of global …

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 …