Phase transitions random number generators

Another example is from the numerical study of phase transitions. Renormalization theory has proved accurate for the basic scaling properties of simple transitions. The attention of the research community is now shifting to corrections to scaling, and to more complex models. Very long simulations (also of the MCMC type) are done to investigate this effect, and it has been discovered that the random number generator can influence the results [3-6]. As computers become more powerful, and Monte Carlo methods become more commonly used and more central to scientific progress, the quality of the random number sequence becomes more important. 

Statistical Mechanics Approach In this approach, free energy is considered relatively as a constant. By using Monte Carlo simulation on model proteins, a random-number generator is employed to move molecules at random. Monte Carlo simulation aims at the calculation of the critical point at which the protein molecule collapses. This is basically the smdy of phase transition. 

There exist several possibilities to generate such turbulent fluctuations at the inflow boundary [19]. Batten et al. [3] reformulated on the ideas of Kraichnan [14] and Smirnov et al. [21] for wall bounded flows. The velocity signal is generated by a sum of sines and cosines with random phases and amplitudes. The wave numbers are calculated from a three-dimensional spectrum and are scaled by the values of the Reynolds-stress tensor. A special wall treatment was applied to elongate near-wall structures. A transition length to physical turbulence of about ten channel half heights was obtained at low Reynolds number channel flow. 

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