Statistical mechanics variational Monte Carlo

Variational Monte Carlo (or VMC, as it is now commonly called) is a method that allows one to calculate quantum expectation values given a trial wavefunction [1,2]. The actual Monte Carlo methodology used for this is almost identical to the usual classical Monte Carlo methods, particularly those of statistical mechanics. Nevertheless, quantum behavior can be studied with this technique. The key idea, as in classical statistical mechanics, is the ability to write the desired property <0> of a system as an average over an ensemble... 

It is also possible to carry out a probabilistic analysis for subsea pipelines in relation to the requirements of fitness for service or life extension. This approach is supported by Hopkins et al. (2001) where the uncertainty values in relation to the inspection data, material strength, and so forth are accounted for The statistics of the input parameters and the engineering models then determine, by probabilistic analysis, the failure probability for each failure mode or mechanism and the variation of the failure probability over time. Once the uncertainty of each input value has been described statistically, a Monte Carlo simulation can be used to predict the growth rate of known defects over time. 

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