Corpus ID: 13128182

A generalized Boltzmann equation for "non-classical" particle transport

@inproceedings{Larsen2007AGB,
  title={A generalized Boltzmann equation for "non-classical" particle transport},
  author={Edward W. Larsen},
  year={2007}
}
We are interested in non-standard transport equations where the description of the scattering events involves an additional “memory variable”. We establish the well posedness and investigate the diffusion asymptotics of such models. While the questions we address are quite classical the analysis is original since the usual dissipative properties of collisional transport equations is broken by the introduction of the memory terms. 
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References

SHOWING 1-10 OF 19 REFERENCES
Anisotropic diffusion in model 2-D pebble-bed reactor cores
We describe an analysis of neutron transport in a modeled 2-D (transport in a plane) pebble-bed reactor (PBR) core consisting of fuel discs stochastically piled up in a square box. Specifically, weExpand
On the extinction of radiation by a homogeneous but spatially correlated random medium: comment.
  • A. Borovoi
  • Physics, Medicine
  • Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2002
TLDR
The validity of exponential extinction laws for large observation distances (as compared with the size of inhomogeneities of a medium) is proven and emphasized. Expand
Asymptotic Derivation of the Multigroup P1 and Simplified PN Equations with Anisotropic Scattering
The multigroup and P{sub 1} and Simplified P{sub N} equations are shown to be a family of asymptotic approximation to the multigroup transport equation with anisotropic scattering. The physicalExpand
On the extinction of radiation by a homogeneous but spatially correlated random medium.
  • A. Kostinski
  • Physics, Medicine
  • Journal of the Optical Society of America. A, Optics, image science, and vision
  • 2001
TLDR
It is shown that when a dilute random medium is statistically homogeneous but spatially correlated, the attenuation of incoherent radiation with depth is often slower than exponential, because spatial correlations among obstacles of the medium spread out the probability distribution of photon extinction events. Expand
On the extinction of radiation by a homogeneous but spatially correlated random medium: reply to comment
In response to comments by Borovoi [J. Opt. Soc. Am. A19, 2517 (2002)] on my earlier work [J. Opt. Soc. Am. A18, 1929 (2001)], the kinetic approach to extinction is compared with the traditionalExpand
Super-exponential extinction of radiation in a negatively-correlated random medium
Abstract It was shown in recent work that spatial correlations among obstacles of a random, absorbing medium can lead to slower-than-exponential (sub-exponential) extinction of radiation withExpand
Average time spent by Lévy flights and walks on an interval with absorbing boundaries.
TLDR
It is shown that if x(0) is placed in the vicinity of absorbing boundaries, the average total length has a minimum at alpha=1, corresponding to the Cauchy distribution, and discussed the relevance of this result to the problem of foraging. Expand
Scale-dependent droplet clustering in turbulent clouds
The current understanding of fundamental processes in atmospheric clouds, such as nucleation, droplet growth, and the onset of precipitation (collision–coalescence), is based on the assumption thatExpand
Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions
Beer's law of exponential decay in direct transmission is well-known but its break-down in spatially variable optical media has been discussed only sporadically in the literature. We document hereExpand
First geometrical path length probability density function derivation of the skylight from high-resolution oxygen A-band spectroscopy: 2. Derivation of the Lévy index for the skylight transmitted by midlatitude clouds
For the first time Levy indices (γ) of the solar light transmitted by cloudy skies at mid latitude (50°N, 8.2°E) are reported. The Levy index describes the dependence of the mean geometrical paths (Expand
...
1
2
...