Linear kinetic theory and particle transport in stochastic mixtures. Progress report, June 15, 1993--March 21, 1994
Association folr +0_+ymn a tAiv°nuae'nsd +tm _lg0 Maryland mane, gement _ '+++_" + +__ k ._'_' Spectrose. Radiat. Transfer, in press. We consider the problem of radiation transport through a stochastic background material described by arbitrary statistics. A variational principle is developed to estimate the ensemble average of a general linear functional of the solution. Numerical results based upon this principle are compared with exact benchmark results using a variety of trial functions.
... trial functions. The test problem employed is a source-free rod, in a monochromatic, time independent setting. The variational formalism is used to estimate reflection, transmission, absorption, and the intensity at the rod center for a binary background mixture of immiscible fluids. The numeric;alcalculations employ I various renewal statistics, including Markovian, to describe the mixing of the two fluid components. 3. B. Su and G.C. Pomraning, "A Stochastic Description of a Broken Cloud Field," J. Atmos. Sci., in press. _" We consider the chord length distributions within a cloud and between clouds. Such information is needed as input to certain statistical models of cloud-radiation interaction. Modeling the clouds as azimuthally symmetric ellipsoids, we find that the chord length distribution through a cloud of fixed size is proportional to the chord length. The proportionality constant depends upon the semi-axes of the ellipse as .well as the angle of incidence of the radiation. This linear behavior is easily convolved over an arbi',rarysize distribution of the clouds to obtain the chord length distribution through a statistical mixture of different cloud sizes. The chord length distribution between clouds is also considered for an atmospheric layer of finite thickness. In this case, both analytic and numerical methods are needed to obtain results. In the limit of an infinite thickness atmospheric layer described by homogeneous statistics and fixed cloud chord lengths, our considerations reduce to a Markovian (exponentially distributed chord lengths) model for the inter-cloud spacing. 4. A.K. Prinja and G.C. Pomraning, "On the Propagation of a Charged Particle Beam in a Random Medium. I: Gaussian Statistics," Trattsport Th. Statis. Phys., in press. A model is presented for the transport of energetic charged particles in a medium whose density is a continuous random function of position. Using the straight-aheadcontinuous slowing down approximation and assuming Crafissianstatistics for the density fluctuations, exact solutions for the ensemble-averaged flux and dose are obtained. It is demonstrated that the ensemble-