Monte Carlo methods methods

Yu. A. Shreider, Monte Carlo Method Method of Statistical Trials, Pergamon,... 

The problem is solved by Monte-Carlo method, method of moment, and the fast integration described above. For threshold d = 0.35, considering only the uncertainties contained in duration D and damping ratio f, using Eq. (41), the reliability index obtained as = 2.372. 

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion... 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Mbiler-Krumbhaar H and Binder K 1973 Dynamic properties of the Monte-Carlo method in statistical mechanics J. Stat. Phys. 8 1-24... 

Binder K (ed) 1995 The Monte Carlo Method in Condensed Matter Physics vol 71 Topics in Applied Physics 2nd edn (Berlin Springer)... 

Newman M E J and Barkema G T 1999 Monte Carlo Methods in Statistical Physics (Oxford Clarendon)... 

Salsburg Z W, Jacobson J D, Fickett W and Wood W W 1959 Application of the Monte Carlo method to the lattice gas model. Two dimensional triangular lattice J. Chem. Phys. 30 65-72... 

McDonald I R and Singer K 1967 Calculation of thermodynamic properties of liquid argon from Lennard-Jones parameters by a Monte Carlo method Discuss. Faraday Soc. 43 40-9... 

Heermann D W and Burkitt A N 1995 Parallel algorithms for statistical physics problems The Monte Carlo Method In Condensed Matter Physios vol 71 Toplos In Applied Physios ed K Binder (Berlin Springer) pp 53-74... 

Bruce A D, Wilding N B and Ackland G J 1997 Free energies of crystalline solids a lattice-switch Monte-Carlo method Phys. Rev. Lett. 79 3002-5... 

Demidov A A 1999 Use of Monte-Carlo method in the problem of energy migration in molecular complexes Resonance Energy Transfer e6 D L Andrews and A A Demidov (New York Wiley) pp 435-65... 

Agranovich V M, Efremov N A and Kirsanov V V 1980 Computer simulation of kinetics of excitation bimolecular quenching by Monte-Carlo method Fiz. Tverd. Tela 22 2118-27... 

The basic scheme of this algorithm is similar to cell-to-cell mapping techniques [14] but differs substantially In one important aspect If applied to larger problems, a direct cell-to-cell approach quickly leads to tremendous computational effort. Only a proper exploitation of the multi-level structure of the subdivision algorithm (also for the eigenvalue problem) may allow for application to molecules of real chemical interest. But even this more sophisticated approach suffers from combinatorial explosion already for moderate size molecules. In a next stage of development [19] this restriction will be circumvented using certain hybrid Monte-Carlo methods. 

Ch. Schiitte, A. Fischer, W. Huisinga, P. Deuflhard. A Hybrid Monte-Carlo Method for Essential Molecular Dynamics. Preprint, Preprint SC 98-04, Konrad Zuse Zentrum, Berlin (1998)... 

Treatment of Multiple Ionizations by a Monte Carlo Method... 

Monte Carlo Methods for Pure Tsallis Statistics... 

Alternatively, one may use a phase space Monte Carlo method with uniform random trial moves and an acceptance probability... 

A similar algorithm has been used to sample the equilibrium distribution [p,(r )] in the conformational optimization of a tetrapeptide[5] and atomic clusters at low temperature.[6] It was found that when g > 1 the search of conformational space was greatly enhanced over standard Metropolis Monte Carlo methods. In this form, the velocity distribution can be thought to be Maxwellian. 

B. Mehlig, D. W. Heermann, and B. M. Forrest. Hybrid Monte Carlo method for condensed-matter systems. Phys. Rev. B, 45 679-685, 1992. 

In this chapter we shall discuss some of the general principles involved in the two most common simulation techniques used in molecular modelling the molecular dynamics and the Monte Carlo methods. We shall also discuss several concepts that are common to both of these methods. A more detailed discussion of the two simulation methods can be found in Chapters 7 and 8. 

Differences Between the Molecular Dynamics and Monte Carlo Methods... 

---