Increasingly, it is recognized that new automated forms of analysis are required to understand the high-dimensional output obtained from atomistic simulations. Recently, we introduced a new dimensionality reduction algorithm, sketch-map, that was designed specifically to work with data from molecular dynamics trajectories. In what follows, we provide more details on how this algorithm works and...

In this paper we derive a lower bound, independent from the number of atoms N , for the minimal interatomic distances between atoms in a cluster whose total energy is modelled by means of the so called Morse potential. A similar result was previously proven for Lennard-Jones clusters but the proof can not be extended to Morse clusters. Besides the theoretical interest, the derivation of this lo...

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map M → N of topological manifolds naturally induces a map S(M) → S(N) of their structure sets. We extend the fact to the isovariant structure set SG(M, rel Ms) of G-equivariant topological manifolds isovariantly homotopy equivalent to M and restricts to homormorphism on the...

The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enh...

An investigation of collision dynamics of nanoparticles for a broad range of impact factors and collision speeds is presented. The investigation is based on molecular dynamics simulations in conjunction with the Lennard-Jones interaction potential thus making the results applicable for a broad range of material properties. Identification criteria are used to classify the collision dynamics into...

To learn about basic aspects of nano-scale spherical molecular shells during their formation, spherically curved two-dimensional N-particle Lennard-Jones systems are simulated, studying curvature evolution paths at zero-temperature. For many N-values (N < 800) equilibrium configurations are traced as a function of the curvature radius R. Sharp jumps for tiny changes in R between trajectories wi...

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...

We apply Gamma calculus to the hypoelliptic and non-symmetric setting of Langevin dynamics under general conditions on potential. This extension allows us provide explicit estimates convergence rate (which is exponential) equilibrium for in a weighted $$H^1(\mu )$$ sense, $$\mu $$ denoting unique invariant probability measure system. The result holds singular potentials, such as well-known Lenn...

in this study, the radial distribution and gravimetric storage capacities of hydrogen on coronene (c24h12) and its si substituted forms, c24h12, c24-nsinh12 (n= 4-24), have been investigated at 298 k and 0.1 mpa (standard situation) using (n,v,t) monte carlo simulation by lennard-jones (lj) 12-6 potential. the results show that the increase of number of silicon substitution doesn’t have any eff...