Monte Carlo methods conventional

The main difference between the force-bias and the smart Monte Carlo methods is that the latter does not impose any limit on the displacement that m atom may undergo. The displacement in the force-bias method is limited to a cube of the appropriate size centred on the atom. However, in practice the two methods are very similar and there is often little to choose between them. In suitable cases they can be much more efficient at covering phase space and are better able to avoid bottlenecks in phase space than the conventional Metropolis Monte Carlo algorithm. The methods significantly enhance the acceptance rate of trial moves, thereby enabling Icirger moves to be made as well as simultaneous moves of more than one particle. However, the need to calculate the forces makes the methods much more elaborate, and comparable in complexity to molecular dynamics. 

It is therefore unsurprising that the MD and TST methods used to characterize diffusion processes are also used to simulate sorption. In the theoretical methodologies section that follows, these methods are not mentioned further as they were summarized in the preceding section. Monte Carlo methods are discussed in detail, including a recently developed technique to simulate the location and adsorption of longer chain molecules than would normally be possible by using conventional methods. Furthermore, we present the methodology of a combined MD/Monte Carlo/EM tech-... 

Let us now consider how the configurational bias Monte Carlo method would deal with this problem. Again, the first site (S) is chosen at random. We next consider where to place the second unit. The sites adjacent to S are examined to see which are free. In this case, only two of the four sites are free. One of these free sites is chosen at random. Note that the conventional Monte Carlo procedure selected from all four adjoining sites at random, irrespective of whether it is occupied or not. A Rosenbluth weight for the move is then calculated. The Rosenbluth weight for each step i is given by ... 

The configurational bias Monte Carlo method involves three types of move. Two of these are translational or rotational moves of the entire molecule, which are performed in the conventional way. The third type of move is a conformational change. A chain is selected at random and one of the segments within it is also randomly chosen. That part of the chain that lies above or below the segment (chosen with equal probability) is discarded and an... 

The basic techniques of the conventional Monte Carlo methods applied to fluid problems have changed little since their invention. Recently, however, there has been a good deal of experimentation seeking to tinker with the technique in order to get new kinds of information. This chapter examined a (no doubt biased) sample of such attempts. 

The local features are essential whenever we want to choose an optimal polymer for a given practical application. If we want to improve the fabrication of rubbers, we need a good understanding of the local motions of a rubber chain—i.e., how they depend on temperature, the influence of steric constraints between neighboring monomers, and so forth. The experimental methods for local probing of a polymer chain are not very different from those used for small molecules (such as infrared and Raman measurements). Similarly, the theoretical methods are (or will become) related to those which are used for conventional liquids molecular dynamics, Monte Carlo methods, etc. 

As opposed to a conventional numerical solution approach, which would start with the derivation of differential equations describing the mathematical model of the physical system, and then discretising the differential equations to solve a set of algebraic equations for the unknown state of the system, the Monte Carlo methods use random sampling techniques to arrive at a solution of the physical problem. Sometimes it is necessary to use other algebraic methods to manipulate the outcomes of Monte Carlo simulations. 

The variational method VQMC is fundamentally the same as the conventional analytic variational method except that the required integrals are evaluated using special Monte Carlo methods. The method has its roots in a numerical method reported by Frost ° in 1942. In Frost s own words ... 

Af/ads is the heat of adsorption from the gas phase, which takes into account the dispersion interaction of hexene with the oxygen atoms in the wall of the zeolite pores. This energy depends both on the size of the reactant (hexene in this case) and the size o .the pores in the zeolite (Figure 8a and 8b) and is estimated with the configurational-bias Monte Carlo method (CB-MC). - The CB-MC method differs from conventional Monte Carlo (see Monte Carlo Simulations for Polymers) in so far as.ti guest species is grown atom by atom inside the host rather than inserted as a complete molecule. ... 

A trick to accelerate the simulation is to impose order parameters relevant to the description of the crystalline state to drive the system towards nucleation. This method was applied to the study of water nucleation and carbon dioxide hydrate formation using a conventional Monte Carlo method. ° ° Stein-hardt s bond-orientational order parameters Q and W , based on quadratic and third-order invariants formed from bond spherical harmonics (Y/ ,(0, (p)), were employed. These order parameters allow quantitative measures of the local symmetry in liquids and glasses. The rotationally invariant orientational order parameters are defined as ... 

Conventional, generalized-ensemble Monte Carlo methods can also be employed, of course, but require sophisticated Monte Carlo updates to be efiScient [306,309],... 

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