Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2510.18191

Estimation of a Gas Diffusion Coefficient by Fitting Molecular Dynamics Trajectories to Finite-Difference Simulations

Isaac Viviano
View original source ↗Read source document ↗Export metadata ↓

Abstract

A procedure is presented to estimate the diffusion coefficient of a uniform patch of argon gas in a uniform background of helium gas. Molecular Dynamics (MD) simulations of the two gases interacting through the Lennard-Jones potential are carried out using the LAMMPS software package. In addition, finite-difference (FD) calculations are used to solve the continuum diffusion equation for the argon concentration with a given diffusion coefficient. To contain the computational cost and facilitate data visualization, both MD and FD computations were done in two space dimensions. The MD argon trajectories were binned to the FD grid, and the optimal diffusion coefficient was estimated by minimizing the difference between the binned MD data and the FD solution with a nonlinear least squares procedure (Levenberg-Marquardt algorithm). Numerical results show the effect of the MD binning parameter and FD grid spacing. The estimated diffusion coefficient is compared to an experimental measurement.

Explore related subjects

math.NAcs.NA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Isaac Viviano. 2026-05-10. Estimation of a Gas Diffusion Coefficient by Fitting Molecular Dynamics Trajectories to Finite-Difference Simulations. https://arxiv.org/abs/2510.18191

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fully spectral scheme for the linear BGK equation on the whole space

In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $Φ$, even if the method could be applied to different collision operators. It is based upon the projection on Hermite polynomials in velocity and orthonormal polynomials with respect to the weight $e^{-$Φ$}$ in space. The potential $Φ$ is assumed to be a polynomial. It is, to the author's knowledge, the first scheme which preserves hypocoercive behavior in addition to the conservation laws. These different properties are illustrated numerically on both quadratic and double well potential.

math.NA↗
arXiv2026

Inverse inequalities for kernel-based approximation on bounded domains and Riemannian manifolds

This paper establishes inverse inequalities for kernel-based approximation spaces defined on bounded Lipschitz domains in $\mathbb{R}^d$ and compact Riemannian manifolds. While inverse inequalities are well-studied for polynomial spaces, their extension to kernel-based trial spaces poses significant challenges. For bounded Lipschitz domains, we extend prior Bernstein inequalities, which only apply to a limited range of Sobolev orders, to the full range of lower and upper orders, and derive Nikolskii inequalities that bound $L_\infty$ norms by $L_2$ norms. For compact Riemannian manifolds, we focus on restricted kernels, which are defined as the restriction of positive definite kernels from the ambient Euclidean space to the manifold, and prove their counterparts.

math.NA↗
arXiv2026

Error Estimates for Hyperbolic Scaling Limits of Linear Kinetic Models on Networks

This paper studies linear discrete kinetic models on networks and their asymptotic behavior in the small Knudsen number limit. For coupling conditions at an n-edge junction under a symmetric formulation, we introduce a change of variables that reformulates the system into n independent initial-boundary value problems. The asymptotic expansions are then constructed and rigorously justified by deriving an error estimate based on the energy method.

math.NA↗