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A non-equilibrium Monte Carlo approach to potential refinement in inverse problems | | N.B. Wilding
; | | Date: |
24 Jul 2003 | | Subject: | Statistical Mechanics; Disordered Systems and Neural Networks | cond-mat.stat-mech cond-mat.dis-nn | | 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. 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 $ar
ho(sigma)$ 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 $ar
ho(sigma)$ matches the available experimental data. The difficulty in doing so is that $mu(sigma)$ is (in general) an unknown {em functional} of $ar
ho(sigma)$ and must therefore be found by iteration. At high particle densities and for high degrees of polydispersity, strong cross coupling between $mu(sigma)$ and $ar
ho(sigma)$ 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 $mu[ar
ho(sigma)]$. 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. | | Source: | arXiv, cond-mat/0307613 | | Services: | Forum | Review | PDF | Favorites | |
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