By David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar, Ilya Prigogine, Stuart A. Rice
In Monte Carlo equipment in Chemical Physics: An creation to the Monte Carlo process for Particle Simulations J. Ilja Siepmann Random quantity turbines for Parallel purposes Ashok Srinivasan, David M. Ceperley and Michael Mascagni among Classical and Quantum Monte Carlo tools: "Variational" QMC Dario Bressanini and Peter J. Reynolds Monte Carlo Eigenvalue tools in Quantum Mechanics and Statistical Mechanics M. P. Nightingale and C.J. Umrigar Adaptive Path-Integral Monte Carlo tools for actual Computation of Molecular Thermodynamic houses Robert Q. Topper Monte Carlo Sampling for Classical Trajectory Simulations Gilles H. Peslherbe Haobin Wang and William L. Hase Monte Carlo methods to the Protein Folding challenge Jeffrey Skolnick and Andrzej Kolinski Entropy Sampling Monte Carlo for Polypeptides and Proteins Harold A. Scheraga and Minh-Hong Hao Macrostate Dissection of Thermodynamic Monte Carlo Integrals Bruce W. Church, Alex Ulitsky, and David Shalloway Simulated Annealing-Optimal Histogram tools David M. Ferguson and David G. Garrett Monte Carlo tools for Polymeric platforms Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling equipment in Monte Carlo and Their software to part Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration alongside Coexistence traces David A. Kofke Monte Carlo equipment for Simulating section Equilibria of complicated Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin platforms G. T. Barkema and M.E.J. NewmanContent:
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Extra info for Advances in Chemical Physics: Monte Carlo Methods in Chemical Physics, Volume 105
The actual Monte Carlo methodology used for this is almost identical to the usual classical Monte Carlo methods, particularly those of statistical mechanics. Nevertheless, quantum behavior can be studied with this technique. The key idea, as in classical statistical mechanics, is the ability to write the desired property (0) of a system as an average over an ensemble for some specific probability distribution P(R). In classical equilibrium statistical mechanics this would be the Boltzmann distribution.
It is this fact that has motivated the search for quasi-random points. What goes wrong with this argument as far as most high-dimensional problems in physical science is that the Koksma-Hlwaka bound is extremely poor for large s. Typical integrands become more and more singular the more one differentiates. The worse case is the Metropolis rejection step-the acceptance is itself discontinuous. Even assuming that V ( f )were finite, it is likely to be so large (for large s) that truly astronomical values of N would be required for the bound in Eq.
The LCG (with identical seeds) failed badly as can be seen from the dashed line in Figure 5. We then generalized the statistical tests, interleaving 256 sequences at a time. The LCG again failed, demonstrating the effectiveness of these tests in detecting nonrandom behaviour. The modified LFG passed these tests. In the tests mentioned above, we had started each parameterized LCG with the same seed but used different additive constants. Even when we discarded the first million random numbers from each sequence, the sequences were still correlated.
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