Gaussian mean-field probability

The book by Hamley [65] is a good general resource for self-consistent mean field theory. This formalism is based on the assumptions that (a) every chain in the system obeys Gaussian statistics, (b) the fluid is incompressible, and (c) the interactions between different structural units are local so that they depend only on the chemical nature but not on the positions of the units along their respective chains. As a result, the equations describe an ensemble of ideal chains in an external field which, in turn, is determined self-consistently from the structural unit probability distributions. As illustrated by Matsen and Schick [66], solving the exact equations requires a significant amount of computational effort to determine the equilibrium... 

Calculate the thermodynamic average of the surface-averaged mean curvature, H, the mean-square curvature, and the Gaussian curvature, K, of the surface if the Fourier transform of the random" field, rjr(q) is described by a Gaussian probability distribution, P [ (5) ]- Perform the calculation for the case where the different wavevectors, q, are uncoupled so that one can write the probability distribution for a single mode as... 

For this purpose we make the following assumption. The bivariant probability P E t), E t + r)) that the electric field of scattered light at the detector has a given value of E(t) at time t and a given value of E(< -I- r) at time t -t- r is Gaussian. This means that... 

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