Statistical error in simulations of Poisson processes: Example of diffusion in solids

Abstract

Simulations of diffusion in solids often produce poor statistics of diffusion events. We present an analytical expression for the statistical error in ion conductivity obtained in such simulations. The error expression is not restricted to any computational method in particular, but valid in the context of simulation of Poisson processes in general. This analytical error expression is verified numerically for the case of Gd-doped ceria by running a large number of kinetic Monte Carlo calculations. ; Funding Agencies|Swedish Energy Agency (STEM) [35515-1]; Carl Tryggers Foundation [CTS 14:433]; Swedish Research Council (VR) [2014-5993, 2011-42-59]; LiLi-NFM; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University (Faculty Grant SFO-MatLiU) [2009 00971]