Metropolis scheme

The MC method can be implemented by a modification of the classic Metropolis scheme [25,67]. The Markov chain is generated by a three-step sequence. The first step is identical to the classic Metropolis algorithm a randomly selected molecule i is displaced within a small cube of side length 26r centered on its original position... 

The Markov chain Metropolis scheme [11] is by far the most common MC methodology. The system is randomly perturbed and the proposed move from microstate A to B is accepted with probability ... 

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. 

This method provides a much more efficient sampling way for a harmonic system than the usual Metropolis scheme. This is because the distribution of the amplitudes is the Gaussian and each mode is independent of other modes the generated configurations have no correlations. In the case of occupation of nonspherical ethane molecules, the reference system is chosen to be the hydrate of spherical guest molecules. The orientations of the guest ethane molecules in the real system are assigned randomly. 

At a fixed T and for a given value of p, the adsorption process has been simulated by using the grand canonical Monte Carlo method [S]. At any elementary step, a site chosen at random is tested to change its occupancy state according to the Metropolis scheme of probabilities where Hf andtf/ are the hamiltonians... 

Adsorption of k-mers in multilayer regime was simulated following the Metropolis scheme. In this framework, the transition probability from a state i to a new state j, W( i -> j), is defined by W( 1 -> j) min l,exp[-P(AU-fiAN)], where P=l/ltBT and (AN) AU represents the variation in the (number of particles) total energy, when the system changes from the state i to the state j. 

In the following, we employed the effective pair interaction W(r) between two macroions in a Metropolis scheme of MC simulations to study the macroion structuring under plane-parallel and wedge-shaped confinements. 

From the present state of the system (denoted by the symbol o, a trial move is attempted to a trial state n. In the Metropolis scheme, the (stochastic) rule for the generation of these trial moves is such that the probability Oon to attempt a trial move to n, given that the system is initially in o, is equal to the probability a o to generate a trial move to o, given that the system is initially in n. 

To emphasize how the Metropolis scheme works in practice, let us return once more to the hard-disk example. Here the matrix am represents the probability of moving a particle to a new trial positions, which is achieved by the generation of two random numbers for displacements in the x and directions. To make the underlying matrix symmetric, the displacements are calculated from dmlJ2 — 1), where [Pg.6]

Most Monte Carlo simulations of molecular systems are more properly referred to as Metropolis Monte Carlo calculations after Metropolis and his colleagues, who reported the first such calculation. The distinction can be important because there are other ways in which an ensemble of configurations can be generated. As we shall see in Chapter 7, the Metropolis scheme is only one of a number of possibilities, though it is by far the most popular. 

Under such a circumstance, numerical method should often be useful. In the case of statistical mechanics of fluids, we have Monte Carlo (MC) simulation based on the Metropolis scheme. All the static properties can be numerically calculated in principle by the MC method. 

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