A nonequilibrium Monte Carlo approach to potential refinement in inverse problems

Abstract

The inverse problem for a disordered system involves determining the interparticle interaction parameters consistent with a given set of experimental data. Recently, Rutledge has shown [Phys. Rev. E 63, 021111 (2001)] that such problems can be generally expressed in terms of a grand canonical ensemble of polydisperse particles. Within this framework, one identifies a polydisperse attribute (“pseudospecies”) σ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution ρ̄(σ) measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution μ(σ) which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of μ(σ) for which ρ̄(σ) matches the available experimental data. The difficulty in doing so is that μ(σ) is (in general) an unknown functional of ρ̄(σ) and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between μ(σ) and ρ̄(σ) renders this process computationally problematic and laborious. Here we describe an efficient and robust nonequilibrium simulation scheme for finding the equilibrium form of μ[ρ̄(σ)]. The utility of the method is demonstrated by calculating the chemical potential distribution conjugate to a specific log-normal distribution of particle sizes in a polydisperse fluid.