On the solution of a nonlocal transport equation by the wiener-hopf method

A one-dimensional transport model for free molecular flow in ducts, developed earlier, is generalized to allow migration of particles in the duct walls before reemission at distinct spatial locations. The resulting transport equation is nonlocal in space, with the scattering kernel displaying spatial memory. For an exponential memory kernel of displacement type and a semi-infinite duct, the transport equation is solved exactly by the Laplace transform Wiener-Hopf technique, and numerical results are given for the albedo as a function of incident particle direction, absorption probability in the duct walls, and severity of nonlocal re-emission. The effect of nonlocal transport is to make the system nonconservative even for zero absorption as a result of particle migration in the duct walls and out of the edges before re-emission into the duct can occur