Monte Carlo methods extracting information from simulation

The Boltzmann equation must be solved with appropriate boundary conditions to obtain f and f. The full Boltzmann equation has not been solved analytically or numerically. Current approximate methods for extracting the desired information from the Boltzmann equation are covered in detail in a recent reference [2.84]. In view of this review, discussion of these methods will not be given. It is sufficient to indicate some of the principal methods which have been employed. These are moment or integral methods for specific molecular scattering laws, the use of "models" (of which the BGK model is the simplest) for the collisions term J(fgfg), and direct simulation by Monte Carlo or molecular-dynamics techniques. 

For the case of equilibrium methods, for mesoporous materials gas porosimetry is complemented by Small Angle Neutron Scattering to obtain information on pore size distribution. For microporous membranes the extraction of structural information from the equilibrium sorption measurements can be based on techniques like Grand Canonical Monte Carlo Simulation. 

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