Metropolis acceptance rule

Various acceptance rules have been devised for importance sampling, the simplest of which is the so-called Metropolis algorithm [45]. In this case. 

These restrictions ensure that very favorable configurations will be open and very unfavorable configurations will be closed. An obvious choice that obeys these restrictions is the standard Metropolis acceptance/rejection rule [29,31,32]... 

In summary, we have extended the recoil growth scheme for systems with continuous potentials. We find that in a NVT simulation RG is much more efficient thcin CBMC for long chains and high densities. However, in appendix B we have shown that RG is less suitable for parallelization using the parallel algorithm of section 2.3. We found that the standard Metropolis acceptance/rejection rule is a reasonable stochastic rule when a Lennard-Jones potential is used. 

Ef+ 0 from the target function are calculated according to Eq. (10). The proposed configuration ff+l r) is accepted with the probability p given by the Metropolis rule... 

Bond switches are made according to the usual Monte Carlo Metropolis rules. Switches are made at random on a trial basis and the energies of the two structures are compared. If the new structure is of lower energy it is accepted. If it is of higher energy it is accepted with probability... 

The crucial point to note is that the above average combines information about both the accepted and the rejected state of a trial move. Note that the Monte Carlo algorithm used to generate the random walk among the states n need not be the same as the one corresponding to TTnm- For instance, we could use standard Metropolis to generate the random walk, and use the S3Tnmetric rule [4]... 

The most widely used acceptance/rejection rule was proposed by Metropolis et al. [14] almost a half a century ago. It is a rejection scheme based on the principle of reversibility between successive states of an equilibrium system. Consider proposing some arbitrary transition from configuration r N to configuration rN (where r represents the coordinates of the N particles in the system). The Metropolis criterion prescribes that a trial move be accepted with probability... 

In the third step, the updated value(s), , are assigned as with probability equal to the minimum of r and 1 and, otherwise. Thus, the algorithm always accepts steps that increase the density and occasionally those that decrease it. The advantage to the asymmetric jumping rules in the Metropolis-Hastings algorithm is an increase in speed. 

A Metropolis Monte Carlo simulation starts with a collection of molecules in a known configuration. The simulation consists of a large number of steps, each of which is an attempt to introduce an acceptable change in the collection of molecules. This change is either accepted or rejected based on a simple set of rules that ensure consistency of the results with the desired ensemble. If a change is accepted, the new state is used to generate the next step of the simulation otherwise, the unmodified configuration is used. Translational and rotational moves in the canonical ensemble are described below, followed by... 

Any attempted movement consistent with the nonoverlapping restriction is accepted by considering the Metropolis rule [64] y < exp(—Aii(r)/ BT), where y is a random number uniformly distributed between zero and unity. According to this condition, the process evolves until a thermal equilibrium state is reached (see Figure 4.8). 

The simulation is performed on a cubic lattice of dimensions L = 44, with periodic boundary conditions in all directions (5). Reptation (7) and the extended Verdier-Stockmayer moves (5) are used to convert one replica into another, with the Metropolis rules (P) employed for acceptance of new replicas. Each of the 200 diblock copolymers contains Na beads of A and Nb beads of B. Vacant lattice sites are considered to be occupied by solvent, S. 

Insertion of this form of the transition probability into the detailed balance condition provides a condition for the acceptance probability that can be satisfied with the so-called Metropolis rule [174]. The resulting acceptance probability is given by [124] ... 

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