Monte-Carlo procedure

Chesnut D A and Salsburg Z W 1963 Monte Carlo procedure for statistical mechanical calculation in a grand canonical ensemble of lattice systems J. Chem. Phys. 38 2861-75... 

A particular advantage of the low-mode search is that it can be applied to botli cyclic ajic acyclic molecules without any need for special ring closure treatments. As the low-mod> search proceeds a series of conformations is generated which themselves can act as starting points for normal mode analysis and deformation. In a sense, the approach is a system ati( one, bounded by the number of low-frequency modes that are selected. An extension of th( technique involves searching random mixtures of the low-frequency eigenvectors using Monte Carlo procedure. 

But a computer simulation is more than a few clever data structures. We need algorithms to manipulate our system. In some way, we have to invent ways to let the big computer in our hands do things with the model that is useful for our needs. There are a number of ways for such a time evolution of the system the most prominent is the Monte Carlo procedure that follows an appropriate random path through configuration space in order to investigate equilibrium properties. Then there is molecular dynamics, which follows classical mechanical trajectories. There is a variety of dissipative dynamical methods, such as Brownian dynamics. All these techniques operate on the fundamental degrees of freedom of what we define to be our model. This is the common feature of computer simulations as opposed to other numerical approaches. 

In Equation 1, t is a thermal vibration frequency, U and P are, respectively activation energy and volume whereas c is a local stress. The physical significance and values for these parameters are discussed in Reference 1. Processes (a)-(c) are performed with the help of a Monte-Carlo procedure which, at regular short time intervals, also relaxes the entanglement network to its minimum energy configuration (for more details, see Reference 1). 

For nonequilibrium statistical mechanics, the present development of a phase space probability distribution that properly accounts for exchange with a reservoir, thermal or otherwise, is a significant advance. In the linear limit the probability distribution yielded the Green-Kubo theory. From the computational point of view, the nonequilibrium phase space probability distribution provided the basis for the first nonequilibrium Monte Carlo algorithm, and this proved to be not just feasible but actually efficient. Monte Carlo procedures are inherently more mathematically flexible than molecular dynamics, and the development of such a nonequilibrium algorithm opens up many, previously intractable, systems for study. The transition probabilities that form part of the theory likewise include the influence of the reservoir, and they should provide a fecund basis for future theoretical research. The application of the theory to molecular-level problems answers one of the two questions posed in the first paragraph of this conclusion the nonequilibrium Second Law does indeed provide a quantitative basis for the detailed analysis of nonequilibrium problems. 

This detailed balance condition makes sure that the path ensemble sg[z )] is stationary under the action of the Monte Carlo procedure and that therefore the correct path distribution is sampled [23, 25]. The specific form of the transition matrix tt[z(° 2 ) -> z(n, 9-) depends on how the Monte Carlo procedure is carried out. In general, each Monte Carlo step consists of two stages in the first stage a new path is generated from an old one with a certain generation probability... 

We have investigated another procedure for reducing the computational expense of the AIMS method, which capitalizes on the temporal nonlocality of the Schrodinger equation and the deterministic aspect of the AIMS method. Recall that apart from the Monte Carlo procedure that we employ for selecting initial conditions, the prescription for basis set propagation and expansion is deterministic. We emphasize the deterministic aspect because the time-displaced procedure relies on this property. 

Figure 8. Li + H2 Ground-state population as a function of time for a representative initial basis function (solid line) and the average over 25 (different) initial basis functions sampled (using a quasi-classical Monte Carlo procedure) from the Lit2/j) + H2(v — 0, j — 0) initial state at an impact parameter of 2 bohr. Individual nonadiabatic events for each basis function are completed in less than a femtosecond (solid line) and due to the sloped nature of the conical intersection (see Fig. 7), there is considerable up-funneling (i.e., back-transfer) of population from the ground to the excited electronic state. (Figure adapted from Ref. 140.)...

Mach-Zehnder interferometer, 144 Medical applications, 153 Metal-insulator transitions, 52 Monte Carlo procedure, 135 Multi-energy X-ray imaging, 131 Multilayer targets, 131 Multiphoton absorption, 85 Multiphoton ionization, 82 Multiple filamentation, 91, 92 Multipulse techniques, 152... 

A rapid increase in the FPA decay rate with increasing ethidium was attributed to dye clustering and consequent excitation transfer. These data were analyzed using the (invalid) anisotropy expression, r(t) = rB(t) rE(t), wherein rE(t) is calculated via the (valid) Monte Carlo procedure described above/157 158) Satisfactory agreement with the observations was obtained by assuming that ethidium can bind only to a 28-bp stretch of DNA, which is believed to comprise about half the linker DNA. 

The characteristic ratios of stereoirregular 1,4-poiybutadiene and 1,4-polyisoprene chains are theoretically investigated by the Monte Carlo procedure in accordance with the model proposed by Mark (V 001 and V 003). It is pointed out that the presence of discrete cis units in frans-rich chains significantly reduces the characteristic ratio while that of discrete trans units in c/is-rich chains has little effect on the characteristic ratio. The characteristic ratio and its dependence on both the trans and cis contents and their sequence distribution is calculated for stereoirregular polymers in accordance with the interdependent RIS model proposed by Mark (V 001 and V 003), and Ishikawa and Nagai V 005 and V 007 . 

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