(281b) Modified-Laguerre Polynomials for Distribution Reconstruction from Moments

It has been shown in an earlier paper that the 8 possible combinations of accretional growth, collisional growth and breakage are attracted to either stationary states or similarity solutions at long times given that the rate kernels are power-law and the fragment distributions are self-similar. A complete mapping of the collisional growth (aggregation) solution space has also been given in terms of modified-gamma distribution parameters as approximate solutions. In this paper, a set of modified-Laguerre orthogonal polynomials is derived expressly for the purpose of reconstructing these stationary or similarity solutions from their moments. This paper discusses the derivation and illustrates the application to similarity solutions for aggregation including an assessment of how well the modified-gamma approximation captures the system behavior.