Spatial moments for the nonstationary one-velocity problem of transport theory with isotropic scattering. I. Point instantaneous source
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Equations for the moments of spatial particle distribution in a homogeneous medium with isotropic scattering are derived for the nonstationary one-velocity problem of transport theory. Exact analytical and numerical solutions are found for five even moments (from the second to the tenth one) by the Laplace transform method, and an algorithm for calculating the moments of arbitrary order is described. Convergence to the corresponding moments is investigated in the diffusion approximation for t→∞, and its nonuniform character is established: higher moments differ significantly from the corresponding diffusion moments at any t. The physical causes for such behavior of the moments are discussed.
KeywordsDiffusion Approximation Transport Theory Isotropic Scattering Exact Moment Spatial Moment
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