Mathematical Modeling to Study the Dynamics of A Diatomic Molecule N2 in Water

TL;DR

This paper develops a mathematical model using Langevin stochastic differential equations to analyze the dynamics of N2 molecules in water, focusing on statistical behaviors like variance and covariance.

Contribution

It introduces a novel Langevin-based stochastic model for diatomic molecules in water, incorporating key physical forces and solving via Euler's method.

Findings

Variance in position and velocity analyzed

Covariance between position and velocity studied

Model provides insights into molecular dynamics in water

Abstract

In the present work an attempt has been made to study the dynamics of a diatomic molecule N2 in water. The proposed model consists of Langevin stochastic differential equation whose solution is obtained through Euler's method. The proposed work has been concluded by studying the behavior of statistical parameters like variance in position, variance in velocity and covariance between position and velocity. This model incorporates the important parameters like acceleration, intermolecular force, frictional force and random force.