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.

Transport properties of random media: An energy-density CPA approach

Abstract: We present an approach for efficient, accurate calculations of the transport properties of random media. It is based on the principle that the wave energy density should be uniform when averaged over length scales larger than the size of the scatterers. This method captures the effects of the resonant scattering of the individual scatterer exactly, and by using a coated sphere as the basic scattering unit, multiple scattering contributions may be incorporated in a mean-field sense. Its application to both ``scalar'' and ``vector'' classical waves gives exact results in the long-wavelength limit as well as excellent agreement with experiment for the mean free path, transport velocity, and the diffusion coefficient for finite frequencies. Furthermore, it qualitatively and quantitatively agrees with experiment for all densities of scatterers and contains no adjustable parameter. This approach is of general use and can be easily extended to treat different types of wave propagation in random media. \textcopyright{} 1996 The American Physical Society.

Diffusion of seismic waves in a thick layer: Theory and application to Vesuvius volcano

Abstract: [1] Multiple scattering of seismic waves in an inhomogeneous layer over a homogeneous half-space is studied. A new model using an analytical solution of the diffusion equation with absorbing boundary condition is presented and compared to existing models with radiation boundary condition and to numerical solutions of the radiative transfer equation. A thick layer condition for the validity of the approach is derived showing that the thickness of the layer must be much larger than the transport mean free path times an averaged reflection coefficient. The theory is much simpler than existing ones and especially useful at volcanoes, where the thick layer condition is generally met. With this model the data set of the TomoVes active seismic experiment at Vesuvius volcano is analyzed, where strong multiple scattering occurs within the heterogeneous shallow material and no scattering is assumed within the less heterogeneous underlying crust. The analytical expression for the coda decay rate includes a trade-off between intrinsic attenuation and leakage of energy from the scattering layer to the homogeneous half-space. As a consequence of this trade-off problem, only an upper bound for intrinsic attenuation and a lower bound for the thickness of the layer can be derived. The thickness of the strongly heterogeneous region is estimated to be larger than 1.5 km. Therefore, as a physical model it is suggested that the observed multiple scattering is caused by the whole inhomogeneous edifice of the stratovolcano above the basement rocks. The value for the diffusivity D is independent of the trade-off between intrinsic attenuation and leakage loss and takes values of around D = 0.1 km2 s−1. This corresponds to a transport mean free path for S waves as low as l ≈ 200 m, which is about 3 orders of magnitude smaller than for usual Earth's crust.

Electrical conductivity of polypropylene

Abstract: The steady-state (d.c.) electrical conductivity of polypropylene has been measured as a function of temperature (25–150°C.) and field strength (0–94 kv./cm.). The temperature coefficient of the conductivity is 34.6 kcal./mole expressed as an activation energy. This is much larger than the activation energy for diffusion of small molecules in the same polymer. Thus, ionization rather than diffusion appears to be the primary activation process. The conductivity is nonohmic; the conductance quotient is a linear function of field strength but is larger than predicted by Onsager's theory. The ion “jump distance” as evaluated from the isothermal field dependence, is the same order of magnitude as the diffusional mean free path estimated from diffusion studies in other polymers. The conductivity, conduction activation energy, and field dependence appear to be relatively insensitive to polymer crystallinity.

Absence of Casimir regime in two-dimensional nanoribbon phonon conduction

Abstract: In stark contrast with three-dimensional (3D) nanostructures, we show that boundary scattering in two-dimensional (2D) nanoribbons alone does not lead to a finite phonon mean free path. If combined with an intrinsic scattering mechanism, 2D boundary scattering does reduce the overall mean free path; however, the latter does not scale proportionally to the ribbon width, unlike the well known Casimir regime occurring in 3D nanowires. We show that boundary scattering can be accounted for by a simple Mathiessen-type approach for many different 3D nanowire cross sectional shapes; however, this is not possible in the 2D nanoribbon case, where a complete solution of the Boltzmann transport equation is required. These facts have strong implications for the thermal conductivity of suspended nanostructures.