# Advances in Chemical Physics: Monte Carlo Methods in by David M. Ferguson, J. Ilja Siepmann, Donald G. Truhlar, Ilya

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 approach 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 tools for actual Computation of Molecular Thermodynamic homes 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 equipment 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 equipment for Simulating part Equilibria of advanced 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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As an example, consider the simulation of a branching process. Suppose the generation of “neutron” paths is based on the outcome of various interactions between the neutrons and a medium. During a neutron flight, the neutron may collide with an atom and produce new neutrons (fission) or be absorbed (fusion). Efficient utilization of the processors requires good load RANDOM NUMBER GENERATORS FOR PARALLEL APPLICATIONS 23 balancing, and so one can move the computation of the statistics for new neutrons to different processors in order to keep the work evenly balanced.

As with all total energy methods, whether Monte Carlo or not, one needs to consider scaling. That is, as the systems being treated increase in size, how does the computational cost rise? Large-power polynomial scaling offers a severe roadblock to the treatment of many physically interesting systems. With such scaling, even significantly faster computers would leave large classes of interesting problems untouchable. This is the motivation behind the so-called order-N methods in, for instance, density functional theory, where in that case N is the number of electrons in the system.

B. Shift-Register Generators Shift-register generators (SRGs) [21,22] are of the form &+k = k- 1 aixn+i(mod i=O 2, where the x, and a, values are either 0 or 1. The maximal period of 2k - 1 and can be achieved using as few as two nonzero values of a,. This leads to a very fast random number generator. There are two ways to make pseudo-random integers out of the bits produced by Eq. (3). The first, called the digital multistep method, takes n successive bits from Eq. (3) to form an integer of n bits.