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. E63, 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 (`pseudo-species) $sigma$ corresponding to some appropriate generalized coordinate of the system to hand. Associated with this attribute is a composition distribution $barrho(sigma)$ measuring the number of particles of each species. Its form is controlled by a conjugate chemical potential distribution $mu(sigma)$ which plays the role of the requisite interparticle interaction potential. Simulation approaches to the inverse problem involve determining the form of $mu(sigma)$ for which $barrho(sigma)$ matches the available experimental data. The difficulty in doing so is that $mu(sigma)$ is (in general) an unknown {em functional} of $barrho(sigma)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $mu(sigma)$ and $barrho(sigma)$ renders this process computationally problematic and laborious. Here we describe an efficient and robust {em non-equilibrium} simulation scheme for finding the equilibrium form of $mu[barrho(sigma)]$. 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.
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