Monte Carlo methods criticality problem solution

THE SOLUTION OF CRITICALITY PROBLEMS BY MONTE CARLO METHODS... 

With the widespread acceptance of Monte Carlo methods to solve plant problems, the complexion of the experimental programs has changed. Prior to the early 1960 s, experimental data alone provided the guidance for criticality criteria and, in most cases, the experiments were tailored to the direct solution of specific industrial problems. Today, however, with versatile Monte Carlo codes, fast machines, and improved cross-section data, the previous experimental approach would be wasteful of our resources. Hence, in strial problems are currently solved with the aid of computer codes, and the experimental data are needed principally to check calculationai methods for accuracy and reliability. 

In general, percolation is one of the principal tools to analyze disordered media. It has been used extensively to study, for example, random electrical networks, diffusion in disordered media, or phase transitions. Percolation models usually require approximate solution methods such as Monte Carlo simulations, series expansions, and phenomenological renormalization [16]. While some exact results are known (for the Bethe lattice, for instance), they are very rare because of the complexity of the problem. Monte Carlo simulations are very versatile but lack the accuracy of the other methods. The above solution methods were employed in determining the critical exponents given in the following section. 

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