Gradient Monte Carlo simulations: Hard spheres in spatially varying temperature and gravitational fields

There are many physical situations where particles experience external fields or are in a nonisothermal environment. Monte Carlo (MC) simulations can be useful to understand such experimental systems at steady state. Within this context, we formulate a general framework to study these systems via inhomogeneous MC simulations incorporating spatially varying temperature and gravitational fields. Using this approach we study granular materials consisting of hard spheres in an external field with either uniform or nonuniform temperature. We present comprehensive results from our MC simulations and compare these with theoretical results based on the Carnahan-Starling equation of state.