Jump-walking method

Tsai, C.J. Jordan, K.D., Use of the histogram and jump-walking methods for overcoming slow barrier crossing behavior in Monte Carlo simulations applications to the phase transitions in the (Ar)i3 and (FbOjs clusters, J. Chem. Phys. 1993, 99, 6957... 

H and B J Berne 1999. Multicanonical Jump Walking A Method for Efficiently Sampling Rough Energy Landscapes. Journal of Chemical Physics 110 10299-10306. 

Xu, H., Berne, B.J. Multicanonical jump walking a method for efficiently sampling rough energy landscapes. J. Chem. Phys. 1999, 110, 10299-306. 

We tested whether sampling efficiency could be further enhanced by using swapping [44] and jump-walking [45], two improvements on the classical MMC method that combine sampling at two different temperatures to generate search trajectories that can more easily cross barriers. 

Although the number of jumps is tremendously large, the mean displacement of each atom is relatively small - most of the time it moves back and forth. In the diffusion process it is not possible to observe the individual jumps of the atoms, and it is necessary to find a relation between the individual atom jumps for large number of atoms and the diffusion phenomena which may be observed on a macroscopic scale. The problem is to find how far a large number of atoms will move from their original sites after having made a large number of jumps. Such relations may be derived statistically by means of the so-called random walk method. 

The jump-walking procedure" is another effective conformational technique. This method can be implemented in both standard MC" and ESMC" simulations. Taking the application of this method in an ESMC simulation as an example, the basic idea is to break a single long ESMC run into many short runs, each of which starts with an independent new conformation. The new starting conformations of these short runs are not generated completely randomly, but rather are... 

In a previous section reference was made to the random walk problem (Montroll and Schlesinger [1984], Weiss and Rubin [1983]) and its application to diffusion in solids. Implicit in these methods are the assnmptions that particles hop with a fixed jump distance (for example between neighboring sites on a lattice) and, less obviously, that jumps take place at fixed equal intervals of time (discrete time random walks). In addition, the processes are Markovian, that is the particles are without memory the probability of a given jump is independent of the previous history of the particle. These assumptions force normal or Gaussian diffusion. Thus, the diffusion coefficient and conductivity are independent of time. 

In summary, there is a difference between the jump diffusirai coefficient, which reflects the random walk of a particle in the available DOS and geometry, and the chemical diffusion coefficient measured by inducing a gradient by a small step method. The difference is expressed in (87) and cmisists of the thermodynamic factor that accounts for the difference between a gradient in concentration, and a gradient in electrochemical potential, thus generalizing Pick s law [12],... 

Finally, we note that after determining the primary jump rates between different sites of a multicomponent disordered polypeptide, these data can be used as input in a stochastic (random walk) theory of hopping conductivity in random media. Since, however, this theory has not yet been applied to any real polymers, we do not describe this method here but refer to the appropriate papers. ... 

Therefore, from the probability distribution of the random variable N = I (the length of the first walk) in the measure (2.88), we can obtain estimates of the critical exponent 7 by the maximum-hkelihood method (see Section 2.7.3). Since the join-and-cut move can make large jumps in N in a single step, this evades the bound (2.86). 

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