The paper contains some new results and a review of recent achievements, concerning the multisupport solutions to matrix models. In the leading order of the ’t Hooft expansion for matrix integral, these solutions are described by quasiclassical or generalized Whitham hierarchies and are directly related to the superpotentials of four-dimensional N = 1 SUSY gauge theories. We study the derivativ...

The existence of a deformation and magnetization minimizing the magnetostrictive free energy is given. Mathematical challenges are presented by a free energy that includes elastic contributions defined in the reference configuration and magnetic contributions defined in the spatial frame. The one-to-one a.e. and orientation-preserving property of the deformation is demonstrated, and the satisfa...

The aim of this work is to derive the behavior for an austenitic single crystal from which the overall behavior of polynystalline TRIP steels can be deduced using classical scale transition method. The micromechanical modeling is based on the kinematics, kinetics and continuum-thennodynamics of the martensitic transformation. Plastic strains of product and parent phases as we11 as the volume fr...

Abstract. We consider pairing in a two-component atomic Fermi gas, in a threedimensional optical lattice, when the components have unequal densities, i.e. the gas is polarized. We show that a superfluid where the translational symmetry is broken by a finite Cooper pair momentum, namely an FFLO-type state, minimizes the Helmholtz free energy of the system. We demonstrate that such a state is cle...

The one to one correspondence between the existence of a unique equilibrium state and the differentiability of the free energy density with respect to the external field previously shown for Ising ferromagnets is extendend to higher valued spin systems as well as to continuum systems satisfying the Fortuin, Kasteleyn and Ginibre inequalities. In particular this is shown to hold for a mixture of...

We consider the wetting transition on a planar surface in contact with a semi-infinite fluid. In the classical approach, the surface is assumed to be solid, and when interaction between solid and fluid is sufficiently short-range, the contribution of the fluid can be represented by a surface free energy with a density of the form Φ(ρS), where ρS is the limiting density of the fluid at the surfa...

Thomson’s classical analysis (1851, 1854a, 1854b) of thermoelectricity is cast into a modern form by means of contemporary thermodynamic methods based on the introduction of a free energy depending on strain, electrical charge and temperature. The present analysis identifies the phenomenological coefficients in Thomson’s theory in terms of standard thermodynamic functions derivable from the fre...

The computational Projective Dynamics method is used to analyze simulations of magnetization reversal in nanoscale magnetic pillars. It is shown that this method can be used to determine the magnetizations corresponding to the metastable minimum and saddle point in the free energy, and the free-energy barrier associated with those points. For the nanopillars studied here, entropy is found to pr...

In his recent paper [6] Michel Talagrand gave a rigorous proof of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model. In the present paper we utilize the methodology developed in [6] to compute the thermodynamic limit of the free energy of the set of configurations with the fixed average of spins N−1 ∑ i≤N σi = uN as uN → u ∈ [−1, 1].