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 functions 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 equipment 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 techniques 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 equipment David M. Ferguson and David G. Garrett Monte Carlo tools for Polymeric structures Juan J. de Pablo and Fernando A. Escobedo Thermodynamic-Scaling equipment in Monte Carlo and Their software to section Equilibria John Valleau Semigrand Canonical Monte Carlo Simulation: Integration alongside Coexistence strains David A. Kofke Monte Carlo tools for Simulating part Equilibria of complicated Fluids J. Ilja Siepmann Reactive Canonical Monte Carlo J. Karl Johnson New Monte Carlo Algorithms for Classical Spin structures G. T. Barkema and M.E.J. NewmanContent:

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6). We will now present a very brief description of quasi-random sequences. Those interested in a much more detailed review of the subject are encouraged to consult the recent work of Niederreiter [25]. An example of a onedimensional set of quasi-random numbers is the van der Corput sequence. First we choose a base, b, and write an integer n in base b as n = cp=P;”ai b’. Then we define the van der Corput sequence as x, = zp2g” aib-’-’ . 7) One sees intuitively how this sequence, while not behaving in a random fashion, fills in all the holes in a regular and low-discrepancy way.

R. P. Brent, “Uniform Random Number Generators for Supercomputers,” in Proceedings Fifth Australian Supercomputer Conference, 5ASC Organizing Committee, 1992, pp. 95104. 16. M. Mascagni, “Parallel Linear Congruential Generators with Prime Moduli,” Parallel Computing (in press). 17. M. Mascagni, S. A. Cuccaro, and D. V. Pryor, “Techniques for Testing the Quality of Parallel Pseudorandom Number Generators,” in Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia, Pennsylvania, 1995, pp.

QUASI-RANDOM NUMBERS It is well known that the error estimate from any MC calculations (or in general from a simulation) converges as N - 'Iz,where N is the number of 32 ASHOK SRINIVASAN, DAVID M. CEPERLEY AND MICHAEL MASCAGNI random samples or equivalently the computer time expended. Recently there has been much research into whether nonrandom sequences could result in fast convergence, but still have the advantages of MC in being applicable to high-dimensional problems. Consider the following integral: 1 I = ddxf(x) The Monte Carlo estimate for this integral is where the points xi are to be uniformly distributed in the s-dimensional unit cube.