Boltzmann distribution Carlos

This reptation Monte Carlo algorithm has been incorporated into the NRCC program CLAMPS. Significant chain motions are effectuated by these single moves (17). We have employed this technique to sample the Boltzmann distribution of our polymer systems. 

Another procedure to overcome the inefficiency of Metropolis Monte Carlo is adaptive importance sampling.194-196 In this technique, the partition function (and quantities derived from it, such as the probability of a given conformation) is evaluated by continually upgrading the distribution function (ultimately to the Boltzmann distribution) to concentrate the sampling in the region (s) where the probabilities are highest. 

Dynamical effects can also be defined in terms of the availability of special coherent motions. In this way, the dynamical proposal implies that enzymes activate special types of coherent motions, which are not available in the solution reaction. Now, the difference between the reaction in enzyme and in solution cannot be accounted for by evaluating the corresponding Ag using nondynamical Monte Carlo (MC) methods. In other words, if the results from MC and MD are identical, then we do not have dynamical contributions to catalysis. Careful and systematic studies (e.g., Refs. 4,129) have shown that the reactions in both enzymes and solutions involved large electrostatic fluctuations. However, these fluctuations follow the Boltzmann distribution, and thus, do not provide dynamical contributions to catalysis. 

Implementations of the generation mechanism differ in the way they generate a transition or move from one set of parameters to another which is consistent with the Boltzmann distribution at given temperature. The two most widely used generation mechanisms are Metropolis Monte Carlo [47] and molecular dynamics [48] simulations. Metropolis Monte Carlo can be applied to both discrete and continuous optimization problems, but molecular dynamics is restricted to continuous problems. 

To study protein folding theoretically, simulation methods have proved indispensable. The folding transition is ultimately governed by statistical thermodynamics and hence it is paramount to use sampling methods that are able to reproduce the canonical Boltzmann distribution. Common sampling techniques are molecular dynamics (MD), Langevin or Brownian dynamics (BD) and Monte Carlo (MC). 

In Metropolis Monte Carlo a Markov chain of ionic states S is generated according to the Boltzmann distribution P S) oc here Ebo S) is... 

By increasing pressure and/or decreasing temperature, ionic quantum effects can become relevant. Those effects are important for hydrogen at high pressure [7, 48]. Static properties of quantum systems at finite temperature can be obtained with the Path Integral Monte Carlo method (PIMC) [19]. We need to consider the ionic thermal density matrix rather than the classical Boltzmann distribution ... 

The well-known Metropolis Monte Carlo (MMC) procedure randomly samples conformational space according to the Boltzmann distribution of (distinguishable) conformations [34] ... 

RCMC moves can also be applied within the hybrid Monte Carlo (HMC) framework. HMC is a method for using molecular dynamics to guide MC moves [32,33], and has been shown to be more efficient and ergodic than molecular dynamics or Monte Carlo for some classes of problems [34,35]. When implementing RCMC steps within the HMC algorithm, the velocities of the product molecules must be drawn at random from a Maxwell-Boltzmann distribution centered at the appropriate temperature. 

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