We present an internally consistent, iterative solution to the systematically truncated BBGKY hierarchy for a specific transport process, selfhyphen;diffusion. Our method is an elaboration of one proposed by Stillinger and Suplinskas. We consider the decay of a particular nonequilibrium displacementmdash;a single Fourier component corresponding to selfhyphen;diffusion. Then, using the hierarchy, we obtain particularly simple forms for the equations which govern the behavior of the nonequilibrium contributions to the low order reduced distribution functions. We show that closure, by means of the physically plausible ``dynamical superposition'' approximation, is consistent with the general form of the equations. We develop truncation procedures which lead to less complicated equations which are also internally consistent. We then develop the complete, formal, systematic solution to the most highly truncated problem which yields an expression for the selfhyphen;diffusion coefficient. The method we use seems applicable to the untruncated problem as well. We find that a direct momentum expansion of the perturbation functions which describe the nonequilibrium correlations is inconsistent with our form of the closed, truncated hierarchy equations. Instead, in a first approximation, we find thatflpar;1rpar;lpar;Pz,r;thinsp;trpar;equals;explpar;minus;12Pz2rpar;lsqb;1plus;sgr; lpar;trpar;explpar;minus;12agr; Pz2rpar;sinkzrsqb;sol;lsqb;lpar;2pgr;rpar;1sol;2Vrsqb;describes the onehyphen;particle reduced distribution function averaged over thexandymomenta. The parameter agr; varies with the density. We outline some approaches which seem fruitful for further study.
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