Parallel Monte Carlo simulations

This article reviews some of the progress made in using parallel processor systems to study macromolecules. After an initial introduction to the key concepts required to understand parallelisation, the main part of the article focuses on molecular dynamics. It is shown that simple replicated data methods can be used to carry out molecular dynamics effectively, without the need for major changes from the approach used in scalar codes. Domain decomposition methods are then introduced as a path toward reducing inter-processor communication costs further to produce truly scalable simulation algorithms. Finally, some of the methods available for carrying out parallel Monte Carlo simulations are discussed. 

Monte Carlo simulation shows [8] that at a given instance the interface is rough on a molecular scale (see Fig. 2) this agrees well with results from molecular-dynamics studies performed with more realistic models [2,3]. When the particle densities are averaged parallel to the interface, i.e., over n and m, and over time, one obtains one-dimensional particle profiles/](/) and/2(l) = 1 — /](/) for the two solvents Si and S2, which are conveniently normalized to unity for a lattice that is completely filled with one species. Figure 3 shows two examples for such profiles. Note that the two solvents are to some extent soluble in each other, so that there is always a finite concentration of solvent 1 in the phase... 

Predescu, C. Predescu, M. Ciobanu, C.V., On the efficiency of exchange in parallel tempering Monte Carlo simulations, J. Phys. Chem. B 2005,109, 4189-4196... 

Atomistic Monte Carlo Simulation of cis-1,4 Polyisoprene Melts. II. Parallel Tempering End-Bridging Monte Carlo Simulations. 

Shim, Y., Amar, J.G. Semirigorous synchronous sublattice algorithm for parallel kinetic Monte Carlo simulations of thin film growth. Phys. Rev. B 2005, 71, 1254321-1-14. 

In the Monte Carlo simulation, a few hundreds (100-2000) of scans are calculated, and the Fourier transform of their sum gives the simulated spectrum. The trajectories of spin sets are individual which makes their scans different providing the variety of the samples necessary for the simulation, similar to the case of the single spin interpretation. The calculation of the scans remains independent of each other thus the calculation can be parallelised in the case of coupled spin systems as well.101 The density matrix introduced because of the coupling and the increased amount of calculations on the matrix elements emphasise the use of modern architectures in parallel computation.104... 

As a final example in this subsection we mention the recent study of Zillich and Whaley who examined LiH solvated in He clusters with up to 100 atoms. The authors used a path integral Monte Carlo simulation approach, whose details shall not be discussed further here. The LiH-He interaction potential was found to be highly anisotropic with attractions for He approaching the molecule in a direction parallel to the molecular axis, but with strong repulsions for He approaching the molecule in a direction perpendicular to the molecular bond. Despite these repulsions, the authors found that LiH prefers to occupy central regions of the LiH He clusters for n larger than 10-15. 

Kushner, M.J. Monte-carlo simulation of electron properties in RF parallel plate capacitively coupled discharges. J. Appl. Phys. 1983, 54, 4958 965. 

Fig. 2. Schematic of the Monte Carlo library design and redesign strategy (from Falcioni and Deem, 2000). (a) One Monte Carlo round with 10 samples an initial set of samples, modification of the samples, measurement of the new figures of merit, and the Metropolis criterion for acceptance or rejection of the new samples, (b) One parallel tempering round with five samples at and five samples at f>2- In parallel tempering, several Monte Carlo simulations are performed at different temperatures, with the additional possibility of sample exchange between the simulations at different temperatures.

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