Optimizing Monte Carlo simulation of the square-well fluid Public

http://ir.library.oregonstate.edu/concern/honors_college_theses/c247dv19v

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  • We identify and develop efficient Monte Carlo methods for determining thermodynamic properties of the square-well fluid in order to test square-well density functional theories near the critical point. Previous works have developed generic so-called histogram methods for collecting statistics on low energy system states, but little or no literature exists on these methods’ systematic com- parison, as well as their application to the square-well fluid. The square-well fluid in particular introduces application challenges not manifest in traditional models for testing and benchmarking such numerical techniques (e.g. the Ising model). We implement our own “simple flat” method, the Wang-Landau method, transition matrix Monte Carlo (TMMC), and a modified version of the optimized ensemble. The performance of each method is measured by low energy sampling rates and maximum errors in computed system properties. We find that Wang-Landau potentially performs better than other histogram methods, but fails catastrophically without a predetermined energy range. The simple flat method and TMMC give results comparable to successful Wang-Landau simulations, but simple flat has some anomalous cases with large errors. Finally, our implementation of the optimized ensemble using a transition matrix results in worse performance over the straightforward TMMC.
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