scholarly journals Transient effective hydraulic conductivities under slowly and rapidly varying mean gradients in bounded three-dimensional random media

1998 ◽  
Vol 34 (1) ◽  
pp. 21-32 ◽  
Author(s):  
Daniel M. Tartakovsky ◽  
Shlomo P. Neuman
Keyword(s):  
Random Media ◽  
Three Dimensional

scholarly journals Characteristic Length and Time Scales of the Highly Forward Scattering of Photons in Random Media

2019 ◽  
Vol 10 (1) ◽  
pp. 93 ◽  
Author(s):  
Hiroyuki Fujii ◽  
Moegi Ueno ◽  
Kazumichi Kobayashi ◽  
Masao Watanabe
Keyword(s):  
Radiative Transfer ◽  
Time Scales ◽  
Analytical Solutions ◽  
Random Media ◽  
Three Dimensional ◽  
Forward Scattering ◽  
Diffusion Equations ◽  
Transport Models ◽  
Photon Diffusion ◽  
Photon Transport

Background: Elucidation of the highly forward scattering of photons in random media such as biological tissue is crucial for further developments of optical imaging using photon transport models. We evaluated length and time scales of the photon scattering in three-dimensional media. Methods: We employed analytical solutions of the time-dependent radiative transfer, M-th order delta-Eddington, and photon diffusion equations (RTE, dEM, and PDE). We calculated the fluence rates at different source-detector distances and optical properties. Results: We found that the zeroth order dEM and PDE, which approximate the highly forward scattering to the isotropic scattering, are valid in longer length and time scales than approximately 10 / μ t ′ and 40 / μ t ′ v , respectively, where μ t ′ is the reduced transport coefficient and v the speed of light in a medium. The first and second order dEM, which approximate the highly forward-peaked phase function by the first two and three Legendre moments, are valid in the longer scales than approximately 4.0 / μ t ′ and 6.3 / μ t ′ v ; 2.8 / μ t ′ and 3.5 / μ t ′ v , respectively. The boundary conditions less influence the length scales, while they reduce the times scales from those for bulk at the longer length scale than approximately 4.0 / μ t ′ . Conclusion: Our findings are useful for constructions of accurate and efficient photon transport models. We evaluated length and time scales of the highly forward scattering of photons in various kinds of three-dimensional random media by analytical solutions of the radiative transfer, M-th order delta-Eddington, and photon diffusion equations.

LOW ENERGY EXCITATIONS AND NON-ERGODICITY IN THE COULOMB GLASS

1994 ◽  
Vol 08 (07) ◽  
pp. 923-933 ◽  
Author(s):  
M. Ortuño ◽  
M. Pollak ◽  
J. Talamantes
Keyword(s):  
Relaxation Time ◽  
Low Temperatures ◽  
Random Media ◽  
Three Dimensional ◽  
Low Energy ◽  
Zero Temperature ◽  
Correlation Effects ◽  
Interacting Particles ◽  
Coulomb Glass

Recent computational methods permit the determination of the low energy states of fair sized systems of localized interacting particles in random media. Making use of such methods, this paper evaluates the nature of the low-energy excitations of the system, and it’s implications on conductivity and on ergodicity. Two- and three-dimensional systems are examined. It is found that the low energy excitations exhibit strong correlation effects, indicating that one-particle theories for equilibrium and non-equilibrium properties are not justified. Ergodicity is tested by relaxation at zero temperature. It is found that relaxation time can be extremely long, indicating that the system is not ergodic at low temperatures.

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