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Application of Stochastic Differential Equation to Study the Dynamics and Statistical Aspects of a Diatomic Molecule

Nitin Sharma, Madhvi Shakya

Abstract



Molecular dynamics simulation computes the motions of individual molecules in models of solids, liquids and gases, which describe how positions, velocities, and orientations change with time. In molecular dynamics study, if the objective is to study the dynamics of individual molecules, rather than studying the properties of complete system, then Langevin and Brownian dynamics are useful alternatives to molecular dynamics. Sometimes, in molecular dynamics, the extraction of physically meaningful essential dynamics of a molecule becomes very important by incorporating the solvent effects and by studying the effect of viscous force due to the solvent. In this paper we have made an attempt to study the statistical and dynamical behavior of a diatomic molecule O2 in water by using mathematical model of stochastic differential equation. This model incorporates the important parameters like acceleration, intermolecular force, frictional force and random force. Here we have used forward Euler method to solve the given model.

Keywords


Stochastic differential equation, Weiner process, White noise, Potential energy function.

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