Transport mean free path

Alexander, M., Corredig, M., and Dalgleish, D.G. (2006). Diffusing wave spectroscopy of gelling food systems the importance of the photon transport mean free path (I ). Food Hydrocolloids. 20, 325-331. 

In this, Eq is the energy of thermal neutrons, r = ]nE/Eo where E is the neutron energy, D, which may be a function of r, is one-third of the transport mean free path, (r, x,y,z) is the smn of the velocities of those neutrons for which ItiE/Eq is in imit interval at r and which are in unit volume at ar, y, z, 5 = (7 is the slowing down power, a being the scattering cross section per... 

In this Do is one-third of the transport mean free path for thermal neutrons. So the value of the slowing down power S for r = 0, i.e., for thermal neutrons. 

A survey of the literature (Hagen et al. 1993) has indicated that, in general, the anomalous Hall behavior is present among moderately clean superconductors (// 0.5-5, where / is the transport mean free path and is the coherence length), but does not occur in either the very clean (// 1) or dirty (// 1) limits. Colino... 

It is apparent that values for the transport mean free path Atr(E) may also be obtained in a similar way. The crosses in Fi re 1 are 0.71 times the experimental values for Xtr(E) obtained from the ratio of surface to center flux using the values of L already determined namely,... 

The first requirement, then, is that the absorption cross section be small relative to the transport cross section. The second requirement is that the transport mean free path be small in comparison to a, the characteristic dimension (size) of the system. We find therefore that, in order for the results based on the extrapolated boundary condition to match well the results based on the no-return current condition, the absorption cross section must be small as compared with the scattering cross section [note that for most nuclei — 2, by (5.46)]. Moreover, the scattering mean free path (again using b) must be appreciably smaller than the size of the system. This condition is in fact a prerequisite if diffusion theory is to be valid in a given situation. We conclude then that the... 

The multiply scattered light that escapes the sampling volume is called reflectance. The transport mean free path length of a photon is defined as ... 

We independently measured the transmittance of the sample that is directly related to the photon transport mean free path when the diffusing particles are not interacting. From the field autocorrelation function, g (t) = yjg2(t)-l, we were able to deduce the mean square displacement Ar (t) of the diffusing particles. In the case of backscattering geometry, the field autocorrelation function is linked to the mean square displacement of the particles through... 

In the above equations, y is a variable related to the transport mean free path /, which is the length that a photon must travel before its direction is completely randomized, and / is the sample thickness. Eq. 5.39 has a characteristic decay time In neither setup, can Orbe resolved directly unless / is known. 

The diffusion length is an important reactor parameter which determines the amount of thermal-neutron leakage out of a finite medium. Of course, in a chain reacting pile the diffusion length is that of a mixture of materials moderator, fuel, structure, etc. The measurement of L in a nonmultiplying medium is significant in that cross sections can be determined from the measurement. As previously defined, = d/z. The diffusion coefficient equals one-third the transport mean free path, and Z is the inverse of the absorption mean free path. Therefore,... 

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