Biased Monte Carlo

In summary. Metropolis Monte Carlo biases the generation of configurations toward those that make significant contributions to the integral... 

M Falciom, MW Deem. A biased Monte Carlo scheme for zeolite structure solution. I Chem Phys 110 1754-1766, 1999. 

R Abagyan, M Totrov. Biased probability Monte Carlo conformational searches and electrostatic calculations for peptides and proteins. I Mol Biol 235 983-1002, 1994. 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

For adsorption in zeolites, the biased Monte Carlo method as developed by Smit is an excellent method to determine the free energies of molecules adsorbed on zeolites [9bj. This method can be used to compute the concentration of molecules adsorbed on zeolites, as we discuss below. 

Table 1.1 Configurationally biased Monte Carlo simulations of the adsorption enthalpies of hydrocarbons for two zeolites.

Faldoni, M., and Deem, M.W. (1999) A biased Monte Carlo shceme for zeolite structure solution./. Chan. Phys., 110 (3), 1754-1766. 

Having specified the interactions (i.e., the model of the system), the actual simulation then constructs a sequence of states (or the system trajectory) in some statistical mechanical ensemble. Simulations can be stochastic (Monte Carlo (MC)) or deterministic (MD), or they can combine elements of both, such as force-biased MC, Brownian dynamics, or generalized Lan-gevin dynamics. It is usually assumed that the laws of classical mechanics (i.e., Newton s second law) may adequately describe the atoms and molecules in the physical system. 

Favrin, G., Irback, A., Sjunnesson, F. Monte Carlo update for chain molecules biased Gaussian steps in torsional space. J. Chem. Phys. 2001, 114, 8154 8. 

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. 

When biasing a BJT, we are also interested in the collector to emitter voltage, V g The minimum or maximum value of Vq can also be easily found using the Worst Case analysis. We can use the same setup that was used to find the collector current. All we have to do is modify the Monte CarlO/WorSt Case settings. Fill in the dialog boxes as shown below ... 

CombiSMoG Uses a Monte Carlo ligand growth algorithm and knowledge-based potentials to combine combinatorial and rational strategies for generating biased compound libraries (86)... 

In the literature, some computer models describing the evolution of copolymer sequences have been proposed [26,28]. Most of them are based on a stochastic Monte Carlo optimization principle (Metropolis scheme) and aimed at the problems of protein physics. Such optimization algorithms start with arbitrary sequences and proceed by making random substitutions biased to minimize relative potential energy of the initial sequence and/or to maximize the folding rate of the target structure. 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

Bascle, J., Garel, T., Orland, H. and Velikson, B. (1993). Biasing a Monte Carlo chain growth method with Ramachandran s plot application to twenty-L-alanine. Biopolymers, 33, 1843-1849. 

Lee, B., Kurochkina, N. and Kang, H. S. (1996). Protein folding by a biased Monte Carlo procedure in the dihedral angle space. Faseb J, 10,119-125. 

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