Validity of molecular dynamics simulations for soft matter: average effects

Abstract

In this work, we focus on the average effects of molecular dynamics trajectories of a particle colliding with a linear potential wall having a slope a. We consider the dynamics and the statistics of the system separately. The inevitable energy change $\Updelta E$ that occurs during the collision with the potential wall is only dependent on α and μ ≡ a τ/p ₀, where α is a fraction of the time step τ immediately after the contact with the potential wall and p ₀ is the momentum before the collision. The average of $\langle|\Updelta E|\rangle_{\alpha}$ over a uniform distribution of α in (0, 1] shows a broken power law behavior $\langle|\Updelta E|\rangle_{\alpha} \propto \mu^\beta$ having two exponents: β ≈ 1.98 at larger μ values and β ≈ 0.99 at smaller μ values. The latter is comparable to the individual values $|\Updelta E|\propto \mu^\beta$ having an exponent β ≈ 1.08. The difference at the larger value of μ originates from cancelation of the error in the energy drift by averaging. The ensemble averages of $\langle|\Updelta E|\rangle_{\mu}$ under a uniform distribution and a Maxwell--Boltzmann distribution of momenta p ₀ are also calculated, but the results show a significantly different behavior with α.