Monte Carlo technique simulation

Fig. 5. To generate an ensemble using Molecular Dynamics or Monte-Carlo simulation techniques the interaction between all pairs of atoms within a given cutoff radius must be considered. In contrast, to estimate changes in free energy using a stored trajectory only those interactions which are perturbed need be determined making the approach highly efficient.

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

The partition function Z is given in the large-P limit, Z = limp co Zp, and expectation values of an observable are given as averages of corresponding estimators with the canonical measure in Eq. (19). The variables and R ( ) can be used as classical variables and classical Monte Carlo simulation techniques can be applied for the computation of averages. Note that if we formally put P = 1 in Eq. (19) we recover classical statistical mechanics, of course. 

Toufar H, Baekelandt BG, Janssens GOA, Mortier WJ, Schoonheydt RA (1995) Investigation of supramolecular systems by a combination of the electronegativity equalization method and a Monte-Carlo simulation technique. J Phys Chem 99(38) 13876—13885... 

In the case of classic chemical kinetics equations, one can get in a few cases analytical solution for the set of differential equations in the form of explicit expressions for the number or weight fractions of i-mcrs (cf. also treatment of distribution of an ideal hyperbranched polymer). Alternatively, the distribution is stored in the form of generating functions from which the moments of the distribution can be extracted. In the latter case, when the rate constant is not directly proportional to number of unreacted functional groups, or the mass action law are not obeyed, Monte-Carlo simulation techniques can be used (cf. e.g. [2,3,47-52]). This technique was also used for simulation of distribution of hyperbranched polymers [21, 51, 52],... 

Pollock et al.(12) have also exploited the fact that poly dispersity index is a function of C2 only in a study utilizing a Monte-Carlo simulation technique to compare error propagation in the method of Balke and Hamielec to a revised method (GPCV2) proposed by Yau et al. (13) which incorporated correction for axial dispersion. 

SABRE Method. Acronym for Simulated Approach to Bayesian Reliability Evaluation. An advanced approach to designing a reliability test program developed at PicArsn, the objective of which was to design a test program of minimum sample size for artillery fired atomic projectiles. Called the SABRE method, the program uses mathematical modeling, Monte Carlo simulation techniques, and Bayesian statistics. It is a sophisticated system devised to test items that cannot be tested because of their atomic nature. The aim is to determine the risk factor and to predict what will happen when the projectile is fired... 

Xing and Mattice (1998) applied Monte Carlo simulation techniques to study the models of BAB triblock copolymeric micelles with solubilizates in a selected solvent. They focused on a microscopic picture regarding the locus of solubilizates in BAB triblock copolymer micelles when the... 

Monte Carlo simulation techniques are used for calculating the distribution coefficients of benzene between supercritical C02 and slitpores at infinite dilution. The Lennard-Jones potential model is used for representing the pair interactions between C02, benzene, and graphite carbon. The effects of temperature, slitwidth, and benzene-surface interaction potential on the distribution coefficients are explored at constant density and constant pressure. 

The long-time balance between recombination and drift of carriers as expressed by the y/n ratio has been analyzed using a Monte Carlo simulation technique and shown to be independent of disorder [40]. Consequently, the Langevin formalism would be expected to obey recombination in disordered molecular systems as well. However, the time evolution of y is of crucial importance if the ultimate recombination event proceeds on the time scale comparable with that of carrier pair dissociation (Tc/Td l). The recombination rate constant becomes then capture—rather than diffusion-con-trolled, so that Thomson-like model would be more adequate than Langevin-type formalism for the description of the recombination process (cf. Sec. 5.4). 

J. Phys. Chem., 99, 13876-13885 (1995). Investigation of Supramolecular Systems by a Combination of the Electronegativity Equalization Method and a Monte Carlo Simulation Technique. 

The present Monte Carlo Simulation technique operates employing micro scale properties such as diffusion coefficient of Lithium ions... 

The Grand Ensemble Monte-Carlo simulation technique as applied to adsorption... 

Coalescence and redispersion models applied to these reaction systems include population balance equations, Monte Carlo simulation techniques, and a combination of macromixing and micromixing concepts with Monte Carlo simulations. Most of the last two types of models were developed to... 

The advantage of the proposed modification is that is it much more efficient to attempt to increase the size of an existing molecule, than to attempt to place a molecule at a completely random position. In this respect the proposed modification is similar to the semigrand ensemble Monte Carlo simulation technique (2). 

However, if exact results are very difficult to obtain, it is possible to use numerical simulations. The main difficulty is that every simulation is feasible only for finite lattice sizes. The percolation phenomenon is a statistical phenomenon and only mean values are relevant. Thus the simulations should ideally be done over all possible lattice configurations. This is not possible for large lattices. Monte Carlo simulation techniques are generally used to overcome this difficulty. Some sample algorithms can be found in the textbook by Stauffer and Aharony [101]. 

To address these problems, this paper presents a mass balance technique specifically developed for evaluating the resource-in-place potential of basin-centred gas prospects. This paper begins with a general overview of basin-centred gas systems (BCGS), including a summary of common attributes identified from a literature survey. A derivation of the mass balance technique and an explanation of its elements foUow this summary. Application of the technique is illustrated with an example from the Bossier tight gas sand play in the East Texas Basin located in eastern Texas, USA. Uncertainty in resource-in-place estimates are quantified by incorporating a Monte Carlo simulation technique with the mass balance computations. 

This section illustrates application of the mass balance technique for two exploration prospects in the East Texas Basin. Gas volumes were computed using both the conventional reservoir engineering and mass balance approaches. Furthermore, uncertainty was incorporated into the calculations with a Monte Carlo simulation technique that generates probabilistic distributions of gas volumes. 

Rather than estimating reservoir trapping efficiency from seal capacity measurements, gas volumes expelled from the source rock (equation (13)) were compared with gas volumes computed from conventional reservoir engineering approach (equation (14)). These comparisons provide an indication of the range of possible trapping efficiencies in each prospect area. Additionally, the distribution of source rock expulsion efficiency was computed using a Monte Carlo simulation technique and equation... 

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