A cluster is a group of identical molecules or atoms loosely bound by inter-atomic forces. The optimal geometry minimizes the potential energy — usually modelled as the Lennard-Jones potential — of the cluster. The minimization of the Lennard-Jones potential is a very difficult global optimization problem with extremely many local minima. In addition to cluster problems, the Lennard-Jones poten...

We have used Monte Carlo simulation and the Gibbs–Duhem integration technique to calculate temperature– composition and pressure–temperature phase diagrams for binary Lennard–Jones mixtures. We systematically explore Lennard–Jones parameter space to demonstrate how the features of these phase diagrams change as a function of diameter ratio, well-depth ratio, binary interaction parameter, and pr...

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We have used a variational approach to calculate some thermodynamic properties of the quasi-one dimensional liquid 3He such as the energy, entropy, free energy, equation of state and heat capacity at finite temperature. We have employed the Lennard-Jones potential as the inter-atomic interaction. We have seen that the total energy increases by increasing both temperature and density....

Thermal transport at the interface between Lennard-Jones crystals is explored via non-equilibrium molecular dynamics simulations. The vibrational properties of each crystal are varied by changing the atomic mass of the crystal. By applying a constant thermal flux across the two-crystal composite system, a steady-state temperature gradient is established and thermal boundary conductance at the i...

We discuss the application of Monte Carlo methods to the self-consistent calculation of a Ginzburg–Landau free energy functional for Lennard-Jones systems in three dimensions. Following this discussion, we demonstrate that the parameters in the coarse-grained free energy can be extracted from a multivariate distribution of energies and particle densities which, when suitably reweighted, permit ...

We use classical molecular dynamics simulations to investigate temperature control of unsupported clusters using a noble gas atmosphere. The simulations are performed using a many-body interaction scheme for the intra-cluster potential, while a pairwise Lennard-Jones potential is used to model the interaction between the noble gas and the clusters. In order to isolate different parameters deter...

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...

A structural order parameter for disordered configurations is defined, based, not on local topologies, but the degree of restraint imposed each atom. This provides a clear distinction between strong liquid (SiO2) and fragile (a binary Lennard-Jones mixture) without reference to dynamics. Where exhibits an abrupt transition from unrestrained restrain below melting point, molten silica highly con...

We continue our study of the degree of the colored Jones polynomial under knot cabling started in [8]. Under certain hypothesis on this degree, we determine how the Jones slopes and the linear term behave under cabling. As an application we verify Garoufalidis’ Slope Conjecture and a conjecture of [8] for cables of a two-parameter family of closed 3-braids called 2-fusion knots. 2010 Mathematic...