In this paper, two finite difference numerical schemes are proposed and analyzed for the droplet liquid film model with a singular Lennard--Jones energy potential involved. Both first second or...

Smit and Frenkel’ have shown that the phase diagram of the two-dimensional Lennard-Jones fluid depends largely on the details of the truncation of the potential. In this Note, Gibbs-ensemble calculations are reported for the three-dimensional Lennard-Jones fluid. As expected, the phase diagram for this system also depends significantly on the details of the truncation. The Lennard-Jones potenti...

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of ...

We give an analysis of a continuation algorithm for the numerical solution of the forcebased quasicontinuum equations. The approximate solution of the force-based quasicontinuum equations is computed by an iterative method using an energy-based quasicontinuum approximation as the preconditioner. The analysis presented in this paper is used to determine an efficient strategy for the parameter st...

The Lennard-Jones(12-6) and the Exponential-6 potential functions are commonly used in computational softwares for describing the van der Waals interaction energy. Some softwares allow switching between these two potentials under prescribed condition(s) that attempt to connect the parameter relationship between the two functions. Here we propose a technique by which the parameter relationship b...

The calculation of free energy from computer simulation is of current interest [1-3]. Two major issues have arisen: the search for an adequate representation of the intermolecular energy (i.e. choice of potential form and its parameters) and the choice of the numerical technique that gives reliable result with the minimum computational effort. It is important to stress that the two issues are e...

Strategies involving smoothing of the objective function have been used to help solve difficult global optimization problems arising in molecular chemistry. This paper proposes a new smoothing approach and examines some basic issues in smoothing for molecular configuration problems. We first propose a new, simple algebraic way of smoothing the Lennard-Jones energy function, which is an importan...

Molecular dynamics and other molecular simulation methods rely on a potential energy function, based only on the relative coordinates of the atomic nuclei. Such a function, called a force field, approximately represents the electronic structure interactions of a condensed matter system. Developing such approximate functions and fitting their parameters remains an arduous, time-consuming process...

In the current research, a three-dimensional finite element model was considered to predict the mechanical behavior of Single Wall (SWCNTs) and Multi Wall Carbon Nanotubes (MWCNTs). Assuming the nonlinear elastic behavior of C-C bond in large strains, hyperelastic models were considered. Literature review revealed that the material parameters of the hyperelastic models have been determined from...