A discussion on Equation of State modeling/generation leveraging practical approaches.

A demonstration on how to model a complex Equation of State (Bismuth) starting from a simplified approach will be presented. The work was inspired from the works of Johnson, Hayes, and Asay(1). Although the models used here for our EOS are slightly more complex than in the past, we are able to leverage optimization methods which aid in producing a reasonable approximation to the EOS similar to that of Cox(2). We will be leveraging recent data and ab initio calculations for the parameterization of the models. As we further enable our modeling framework with analysis methods such as Markov chain Monte Carlo (MCMC) and Particle Swarm Optimization (PSO), accounting for systematic error in theoretical or experimental data becomes vitally important. For most EOS, the standard models are often under constrained or over fitted and require expert judgement. Yet, quantifying expert judgement remains a mystery as to how best to capture said uncertainty.

(1) Phys. Chrn. Solids. 1974. Vol. 35. pp. 501-J 15.

(2) AIP Conference Proceedings 955, 151 (2007);