Development of a program for mathematical modeling of molecular dynamics processes

Abstract

The paper presents the results of developing a program for mathematical modeling of molecular dynamics processes in crystal structures using the MatLab software package. The theoretical part describes the differential equations for simulation, their initial and boundary conditions, and the difference approximation. A method was chosen based on the principle of modeling molecular dynamics using one of the pair potentials, namely the Lennard-Jones potential. In the practical part, the chaotic motion (migration) of atoms in 2D and 3D crystal lattices has been simulated. The distribution over the computational cell and the migration of atoms beyond its limits are shown. The dependence between the bound energies in real metals and the computational model has been determined. The potential of interaction has been determined, which turns out to be positive. The developed program showed high accuracy of simulation results, as well as higher speed compared to other similar programs for molecular dynamics simulation.

Simulation and analysis of transition processes in linear electrical circuits using MatLab software package

“…This package is designed for analytical and numerical solutions of various mathematical problems and the study of dynamical systems, including discrete, continuous, and hybrid models. The system includes the Maple computer algebra core and the Simulink extension package as well as dozens of other extension packages [21]. The Simulink mathematical simulating system is currently one of the most popular numerical calculation tools and used in various fields of knowledge [22].…”