Sampling Monte Carlo

P = /k T). After an initial relaxation period consisting of many Monte Carlo 

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Ferrenberg A M, Landau D P and Binder K 1991 Statistical and systematic errors in Monte-Carlo sampling J. Stat. Phys. 63 867-82... 

Monte Carlo Sampling from Different Ensembles... 

In performing a Monte Carlo sampling procedure we let the dice decide, again and again, how to proceed with the search process. In general, a Monte Carlo search consists of two steps (1) generating a new trial conformation and (2) deciding whether the new confonnation will be accepted or rejected. 

WK Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 97-109, 1970. 

The expectation values on the right hand side of this equation depend only on the ensemble averages of position and momentum operators, which can be evaluated using the VQRS Monte-Carlo sampling scheme outlined above. 

Figure 5. Molecular dynamics simulation of the decay forward and backward in time of the fluctuation of the first energy moment of a Lennard-Jones fluid (the central curve is the average moment, the enveloping curves are estimated standard error, and the lines are best fits). The starting positions of the adiabatic trajectories are obtained from Monte Carlo sampling of the static probability distribution, Eq. (246). The density is 0.80, the temperature is Tq — 2, and the initial imposed thermal gradient is pj — 0.02. (From Ref. 2.)...

The MD/QM methodology [18] is likely the simplest approach for explicit consideration of quantum effects, and is related to the combination of classical Monte Carlo sampling with quantum mechanics used previously by Coutinho et al. [27] for the treatment of solvent effects in electronic spectra, but with the variation that the MD/QM method applies QM calculations to frames extracted from a classical MD trajectory according to their relative weights. 

Tapia, O., Colonna, F. and Angyan, J. G. Generalized self-consistent reaction field theory in multicenter-multipole ab initio LCGO framework. I. Electronic properties of the water molecule in a Monte Carlo sample of liquid water molecules studied with standard basis sets, J.ChimPhys., (1990), 875-903... 

Monte Carlo sampling, 26 999, 1001—1004 in control systems, 26 1046 future trends in, 26 1047-1048 HSGA algorithm and, 26 1032 in process scheduling, 26 1042-1043 in process synthesis and design, 26 1041 quasi-Monte Carlo sampling and, 26 1011-1016 for risk analysis, 26 1045 in supply chain management, 26 1043-1044... 

Quasi-Fermi levels, 9 728-729, 730 Quasifullerenes, 12 232-233 Quasi-iso tropic laminates, 26 754 26 782 Quasi-Monte Carlo sampling methods, 26 1005, 1011-1015, 1024 parallelization with Monte Carlo sampling, 26 1016... 

Monte Carlo Sampling of Tunneling Paths The Path Integral Instanton Method... 

Immediately when the dynamic interpretation of Monte Carlo sampling in terms of the master equation, Eq. (31), was realized an application to study the critical divergence of the relaxation time in the two-dimensional Ising nearest-neighbor ferromagnet was attempted . For kinetic Ising and Potts models without any conservation laws, the consideration of dynamic universality classespredicts where z is the dynamic exponent , but the... 

In order to study the origin of the deviations observed, we first consider the statistical convergence of the QCL data. As a representative example. Fig. 14 shows the absolute error of the adiabatic population as a function of the number of iterations N—that is, the number of initially starting random walkers. The data clearly reveal the well-known 1/Vn convergence expected for Monte Carlo sampling. We also note the occurrence of the sign problem mentioned above. It manifests itself in the fact that the number of iterations increases almost exponentially with propagation time While at time t = 10 fs only 200 iterations are sufficient to obtain an accuracy of 2%, one needs N = 10 000 at t = 50 fs. 

As the appropriate Boltzmann weights are included in the Metropolis Monte Carlo sampling technique, the average value of the polarizability, or any other property calculated from the MC data, is given as a simple average over all the values calculated for each configuration. 

Figure 7. A "snapshot" of a typical cellulosic chain trajectory taken from a Monte Carlo sample of cellulosic chains, all based on die conformational energy map of Fig. 6. Filled circles representing glycosidic oxygens, linked by virtud bonds spanning the sugar residues (not shown), allow one to trace the instantaneous chain trajectory in a coordinate system that is rigidly fixed to the residue at one end of the chain. Projections of the chain into three mutually orthogonal planes assist in visualization of the trajectory in three dimensions.

Nilmeier, J., Jacobson, M. Multiscale Monte Carlo sampling of protein sidechains application to binding pocket flexibility. J. Chem. Theory Comput. 2008, 4, 835-46. 

Podtelezhnikov, A.A., Wild, D.L. Exhaustive Metropolis Monte Carlo sampling and analysis of polyalanine conformations adopted under the influence of hydrogen bonds. Protein. Struct. Funct. Genet. 2005, 61, 94—104. 

Mezei, M. Efficient Monte Carlo sampling for long molecular chains using local moves, tested on a solvated lipid bilayer. J. Chem. Phys. 2003, 118, 3874 9. 

Laso, M., Karayiannis, N.C., Muller, M. Min-map bias Monte Carlo for chain molecules biased Monte Carlo sampling based on bijective minimum-to-minimum mapping. J. Chem. Phys. 2006, 125,164108. 

Brown, S., Head-Cordon, T. Cool walking a new Markov chain Monte Carlo sampling method. J. Comput. Chem. 2003, 24, 68-76. 

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