Metropolis Monte Carlo applications

In general, Monte Carlo simulations are such calculations in which the values of some parameters are determined by the average of some randomly generated individuals.45-54 In chemistry applications, the most prevalent methods are the so called Metropolis Monte Carlo (MMC)55 and Reverse Monte Carlo (RMC) ones. The most important quantities in these methods are some kinds of U energy-type potentials (e.g. internal energy, enthalpy,... 

Card and Valleau. application of the Metropolis Monte Carlo method, 320 Center, for electrochemistry, at Texas A M University, 26... 

The best-known physically robust method for calculating the conformational properties of polymer chains is Rory s rotational isomeric state (RIS) theory. RIS has been applied to many polymers over several decades. See Honeycutt [12] for a concise recent review. However, there are technical difficulties preventing the routine and easy application of RIS in a reliable manner to polymers with complex repeat unit structures, and especially to polymers containing rings along the chain backbone. As techniques for the atomistic simulation of polymers have evolved, the calculation of conformational properties by atomistic simulations has become an attractive and increasingly feasible alternative. The RIS Metropolis Monte Carlo method of Honeycutt [13] (see Bicerano et al [14,15] for some applications) enables the direct estimation of Coo, lp and Rg via atomistic simulations. It also calculates a value for [r ] indirectly, as a "derived" property, in terms of the properties which it estimates directly. These calculated values are useful as semi-quantitative predictors of the actual [rj] of a polymer, subject to the limitation that they only take the effects of intrinsic chain stiffness into account but neglect the possible (and often relatively secondary) effects of the polymer-solvent interactions. 

The article has briefly considered the role of Monte Carlo and kinetic Monte Carlo simulations in understanding dissolution and selective dissolution processes that can occur spontaneously in the natural environment and under directed control in laboratories. Algorithms for both Metropolis Monte Carlo and KMC models were discussed, and some results from an implementation of the KMC algorithm were shown as examples. Last, the article surveyed several areas where KMC models have been used to study corrosion processes and where they can contribute in engineering applications. 

Molecular dynamics (MD) methods are nearly as old as the Metropolis Monte Carlo method. The first applications of MD techniques for molecular simulation were made to simple fluids. Simulations for complex liquids such as water followed, and the first MD simulation of a biomacromolecule was performed over 10 years ago. Since then, the MD technique has been used extensively in the study of biomolecules, and the increased utility of this technique parallels closely the development of computer resources. 

Molecular dynamics can be coupled to a heat bath (see below) so that the resulting ensemble asymptotically approaches that generated by the Metropolis Monte Carlo acceptance criterion (equation 6). Thus, molecular dynamics and Monte Carlo are equivalent for the purpose of simulated annealing, although in practice one implementation may be more efficient than the other. Recent comparative work on applications to crystallographic refinement (Adams, Rice, and BrUnger, unpublished) has shown that the molecular dynamics implementation of simulated annealing is more efficient than the Monte Carlo one. 

Monte Carlo Studies in Polyelectrolyte Solutions Structure and Thermodynamics on Monte Carlo studies in polyelectrolyte solutions structure and thermodynamics, this chapter discussing about, Monte Carlo studies of polyelectrolytes, theoretical approach of Monte Carlo studies, application level of Monte Carlo in polyelectrolyte, authors of this chapter are also trying to discuss more with many topics, such as coarse-grain model for poly electrolyte and small ions, ideal gas and excess contribution to the partition function of the system, metropolis Monte Carlo method, Monte Carlo trial moves, conformational and persistence length of a single polyelectrolyte chain, counterions condensation and end-chain effects and morphology of polyelectrolyte complex. 

Monte Carlo search methods are stochastic techniques based on the use of random numbers and probability statistics to sample conformational space. The name Monte Carlo was originally coined by Metropolis and Ulam [4] during the Manhattan Project of World War II because of the similarity of this simulation technique to games of chance. Today a variety of Monte Carlo (MC) simulation methods are routinely used in diverse fields such as atmospheric studies, nuclear physics, traffic flow, and, of course, biochemistry and biophysics. In this section we focus on the application of the Monte Carlo method for... 

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