Mean free path

About: Mean free path is a research topic. Over the lifetime, 4412 publications have been published within this topic receiving 114418 citations.

Anomalous diffusion limit for kinetic equations with degenerate collision frequency

Abstract: This paper is devoted to hydrodynamic limits for collisional linear kinetic equations. It is a classical result that under certain conditions on the collision operator, the long time/small mean free path asymptotic behavior of the density of particles can be described by diffusion-type equations. We are interested in situations in which the degeneracy of the collision frequency for small velocities causes this limit to break down. We show that the appropriate asymptotic analysis leads to an anomalous diffusion regime.

Method and apparatus for measuring locally and superficially the scattering and absorption properties of turbid media

Abstract: We present a method and apparatus for local and superficial measurement of the optical properties of turbid media. The depth probed is on the order of 1 transport mean free path of the photon. The absorption coefficient, reduced scattering coefficient and the phase function parameter γ=(1−g 2 )/(1−g 1 ) are optical parameters computed from a single measurement of the spatially resolved reflectance close to the source. Images of superficial structures of the medium can be obtained by performing multi-site measurements. An important application of this technique is the characterization of biological tissues, for example for medical diagnostic purposes. Measurements on biological tissues can be achieved using a probe of diameter less than 2 mm, and the average volume probed is on the order of 1 mm 3 . Separate images of absorption and tissue structure can be achieved with a resolution of approximately one transport mean free path of the considered tissue.

Length dependence of thermal conductivity by approach-to-equilibrium molecular dynamics

Abstract: The length dependence of thermal conductivity over more than two orders of magnitude has been systematically studied for a range of materials, interatomic potentials, and temperatures using the atomistic approach-to-equilibrium molecular dynamics (AEMD) method. By comparing the values of conductivity obtained for a given supercell length and maximum phonon mean free path (MFP), we find that such values are strongly correlated, demonstrating that the AEMD calculation with a supercell of finite length actually probes the thermal conductivity corresponding to a maximum phonon MFP. As a consequence, the less pronounced length dependence usually observed for poorer thermal conductors, such as amorphous silica, is physically justified by their shorter average phonon MFP. Finally, we compare different analytical extrapolations of the conductivity to infinite length and demonstrate that the frequently used Matthiessen rule is not applicable in AEMD. An alternative extrapolation more suitable for transient-time, finite-supercell simulations is derived. This approximation scheme can also be used to classify the quality of different interatomic potential models with respect to their capability of predicting the experimental thermal conductivity.

Derivation of the electron inelastic mean free path from the elastic peak intensity

Abstract: Measurements of the elastic peak intensity make possible estimation of the true inelastic mean free path (IMFP). Corresponding experiments are relatively simple and can be performed for any sample. The theoretical models can be used to derive the relation between elastic peak intensity and IMFP for single and multiple elastic scattering. In the present work both models were based on the differential scattering cross-sections calculated within the partial wave expansion method. Examples of calculations of the IMFP using both theoretical models are presented.