The Lennard-Jones (LJ) Potential Energy Problem is to construct the most stable form of N atoms of a molecule with the minimal LJ potential energy. This problem has a simple mathematical form

A mixing rule for the mixtures of hard-spheres is presented which can be reduced to the standard van der Waals mixing rule at low densities. The effectiveness of the mixing rule for the size and energy parameters of lennard-Jones fluid are examined by combining them with an equation of state to calculate thermodynamic properties. The results of calculation are compared with the molecular dy...

We describe a new stochastic global optimization algorithm, and its application to a class of problems in molecular chemistry. The global optimization problem we consider is to find the lowest minimizer of a nonlinear function f that may contain multiple local minimizers, restricted to a bounded domain where f is assumed to be twice continuously differentiable. The two applications described in...

Search for different links with the same Jones' type polynomials: Ideas from graph theory and statistical mechanics. ABSTRACT. We describe, in this talk, 1 three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, tak...

An extension of the simulation tempering algorithm is proposed. It is shown to be particularly suited to the exploration of first-order phase transition systems characterized by the backbending or S-loop in the statistical temperature or a microcanonical caloric curve. A guided Markov process in an auxiliary parameter space systematically combines a set of parametrized Tsallis-weight ensemble s...

The free energy of a 600-atom Lennard-Jones cluster is calculated as a function of surface and bulk crystallinity in order to study the structural transformations that occur in the core of medium sized clusters. Within the order parameter range studied, we find the existence of two free energy minima at temperatures near freezing. One minimum, at low values of both bulk and surface order, belon...

We perform simulations to investigate how the energy carried by a molecule transfers to others in an equilibrium gas model. For this purpose we consider a microcanonical ensemble of equilibrium gas systems; each of them contains a tagged molecule located at the same position initially. The ensuing transfer process of the energy initially carried by the tagged molecule is then exposed in terms o...

A saddle point variational (SPV ) method was applied to the Dirac equation as an example of a fully relativistic equation with both negative and positive energy solutions. The effect of the negative energy states was mitigated by maximizing the energy with respect to a relevant parameter while at the same time minimizing it with respect to another parameter in the wave function. The Cornell pot...

X iv :q -a lg /9 50 60 02 v2 3 1 Ju l 1 99 5 Abstract. The Jones polynomial and the Kauffman bracket are constructed, and their relation with knot and link theory is described. The quantum groups and tangle functor formalisms for understanding these invariants and their descendents are given. The quantum group Uq(sl2), which gives rise to the Jones polynomial, is constructed explicitly. The 3-m...