Metropolis Prescription

The expense is justified, however, when tackling polymer chains, where reconstruction of an entire chain is expressed as a succession of atomic moves of this kind [121]. The first atom is placed at random the second selected nearby (one bond length away), the third placed near the second, and so on. Each placement of an atom is given a greater chance of success by selecting from multiple locations, as just described. Biasing factors are calculated for the whole multi-atom move, forward and reverse, and used as before in the Metropolis prescription. For fiirther details see [122, 123. 124. 125]. A nice example of this teclmique is the study [126. 127] of the distribution of linear and branched chain alkanes in zeolites. 

The Metropolis prescription dictates that we choose points with a Boltzmann-weighted probability. The typical approach is to begin with some reasonable configuration qj. The value of property A is computed as the first element of the sum in Eq. (3.33), and then qi is randomly perturbed to give a new configuration qa. In the constant particle number, constant... 

We can now take one of two approaches (1) construct a probabilistic CA along lines with the Metropolis Monte Carlo algorithm outlined above (see section 7.1.3.1), or (2) define a deterministic but reversible rule consistent with the microcanonical prescription. As we shall immediately see, however, neither approach yields the expected results. 

In order to satisfy detailed balance, the function A(X Y) must have a specific form. In the prescription of Metropolis et al. [1], moves are accepted with probability... 

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