Validity of Molecular Dynamics for the Simulation of Soft Matter
Year: 2014
Type: conference-paper
Abstract: In this work, we analytically examine the validity of molecular dynamics for a soft potential system by considering a simple one-dimensional system with a piecewise continuous linear repulsive potential wall having a constant slope $a$. We derive an explicit analytical expression for an inevitable energy change $ΔE$ due to the discrete process, which is dependent on two parameters: 1) $α$, which is a fraction of time step $τ$ immediately after the collision with the potential wall, and 2) $μ\equiv \frac{a τ}{p_0}$, where $p_0$ is the momentum immediately before the collision. The whole space of parameters $α$ and $μ$ can be divided into an infinite number of regions, where each region creates a positive or negative energy change $ΔE$. On the boundaries of these regions, energy does not change, \textit{i.e}, $ΔE=0$. The envelope of $|ΔE|$ \textit{vs.} $μ$ shows a power law behavior $|ΔE| \propto μ^β$, with the exponent $β\approx 0.95$. This implies that the round-off error in energy introduced by the discreteness is nearly proportional to the discrete time step $τ$.
Author: Sangrak Kim
Language: English
Subfield: Physical and Theoretical Chemistry
Field: Chemistry
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1729326175