The phase diagram of a polydisperse hard-sphere system is examined by numerical minimization of a discretized form of the Ramakrishnan-Yussouff free-energy functional. Crystalline and glassy local minima of the free energy are located and the phase diagram in the density-polydispersity plane is mapped out by comparing the free energies of different local minima. The crystalline phase disappears...

This paper demonstrates input-to-state stability (ISS) of the SIR model infectious diseases with respect to disease-free equilibrium and endemic equilibrium. Lyapunov functions are constructed verify that both equilibria individually robust perturbation newborn/immigration rate which determines eventual state populations in epidemics. The construction analysis geome...

Jarzynski and Crooks have recently shown that equilibrium free energy differences can be computed from non-equilibrium thermodynamic path integrals. In the present paper we give a new derivation of this extraordinary relation. Our derivation which is valid for time reversible deterministic systems highlights the close relationship between the non-equilibrium free energy theorems and the fluctua...

We describe an analytical form of the Wulff plot construction procedure and derive a general expression for the surface energy from the three-dimensional equilibrium crystal shape in generalized orthogonal curvilinear coordinates. Particular expressions in Cartesian, spherical polar, and circular cylindrical coordinates are also presented. Corresponding results for a two-dimensional (2D) island...

In this paper, by considering the notion of extended BCK-module, we define the concepts of free extended BCK-module, free object in category of extended BCK-modules and we state and prove some related results. Specially, we define the notion of idempotent extended BCK-module and we get some important results in free extended BCK-modules. In particular, in category of idempotent extended BCK-mod...

Since the first experimental realization of Bose-Einstein condensation in cold atomic gases in 1995 there has been a surge of activity in this field. Ingenious experiments have allowed us to probe matter close to zero temperature and reveal some of the fascinating effects quantum mechanics has bestowed on nature. It is a challenge for mathematical physicists to understand these various phenomen...

We study the large–time asymptotics of reaction–diffusion type systems, which feature a monotone decaying entropy (Lyapunov, free energy) functional. We consider both bounded domains and confining potentials on the whole space for arbitrary space dimensions. Our aim is to derive quantitative expressions for (or estimates of) the rates of convergence towards an (entropy minimising) equilibrium s...

The effect of pressure on the hexagonal close-packed structure of titanium is investigated. The lattice parameters of the equilibrium structure were determined in terms of the Gibbs free energy using the Epitaxial Bain Path method. When this process was repeated for several pressures, the effect of pressure on the lattice parameters was revealed. The calculated lattice parameters were in good a...

Systems undergoing an equilibrium phase transition from a liquid state to an amorphous solid state exhibit certain universal characteristics. Chief among these are the fraction of particles that are randomly localized and the scaling functions that describe the order parameter and ~equivalently! the statistical distribution of localization lengths for these localized particles. The purpose of t...

It has long been known that there is a relation between boundary sineGordon theory and thermodynamics of charge neutral two-component Coulomb plasma on a unit circle. On the other hand, recently it was found that open string worldsheet description of brane decay can be related to a sequence of points of thermodynamic equilibrium of one-component plasma. Here we consider a different decay proces...