Propagation multiple scattering

Fig. 22. The diagrams contributing to electrophoresis and the definition of lithe box. The reason why we only retain this class of terms is that we want to allow long-range propagation by the fluid— as shown in Fig. 21—which is clearly impossible if ions a and fi overlap in the box, because this would correspond to multiple scattering processes on particles a and fi.

All samples in this chapter are assumed to consist of multiple scattering and fluorescent planar layers of arbitrary thickness d. One surface of the layer is irradiated monochromatically at A with parallel light ofintensity /o (per unit area perpendicular to the direction of propagation) under the angle ao relative to the normal of the surface... 

The propagation of light in multiple scattering media is quantified usually on the level of radiative transfer or particle diffusion. Scattering, absorption, and emission are considered as independent statistical processes, and the consequences of wave character are either ignored, like polarization, or added as an additional parameter, like the phase function P(ji n) that describes the angular distribution of scattered... 

Lloyd, P., Berry, M.V. 1967. Wave propagation through an assembly of spheres. IV. Relations between different multiple scattering theories. Proc. Phys. Soc. 91, 678-688. 

The interstitial region between these spheres is represented by a constant potential valve (the muffin-tin constant or muffin-tin zero). This is the region of unscattered electron propagation, in which simple plane-wave or spherical-wave behavior describes the electron wave-field. The plane-wave description is computationally advantageous when dealing with multiple scattering by periodic lattices, since such lattices diffract any plane wave into other well-defined plane waves. This approach is often useful even with non-periodic overlayers adsorbed on an otherwise periodic substrate. 

Here P( R ) is the scattering potential for the ensemble of scatters at locations R G is the free-space electron propagator and T0 the f-matrix for multiple scattering of the electron by the surface. 

For a viscoelastic material both K and G are complex quantities. When the material sample has finite dimensions other modes of wave propagation may occur as a result of multiple scattering from the material boundaries. Mode conversion from longitudinal wave to shear wave, and vice versa, occurs on reflection at a solid boundary. For material samples in the form of thin rods or plates the modes of wave propagation are extenional waves (with speed determined by the Young s modulus, or the plate modulus), and flexural (bending) waves [8]. 

In concentrated systems, multiple scattering is important (I.e. a significant proportion of the energy scattered from one particle is incident upon neighbouring particles). If one considers multiple scattering in the derivation of the complex propagation constant [49], then Eq. 9.13 becomes ... 

Abstract. Propagation of capillary waves along the surface of water covered by a homogeneous insoluble film has been a subject of numerous experimental and theoretical studies. However, it has been shown only recently that real surface films contain two-dimensional aggregates, which influence the characteristics of surface waves. The problem of multiple scattering of surface waves by two dimensional viscoelastic particles is considered briefly below. The results can be compared with the experimental data for condensed films with two-dimensional bubbles of gaseous phase. 

Articles by Miyano and Tamada (1992, 1993), and Wang et al. (1994) also contain some experimental results indicating the influence of surface film heterogeneity on the propagation of capillary waves. The authors noticed that the lack of elaborate theory restrains further progress in this field. The influence of the effects of multiple scattering on the propagation velocity of surface waves is the main subject of this work. 

Multiple Scattering Theory was first formulated by Lord Rayleigh [17] in a paper published in 1892 dealing with the propagation of heat or electricity through an inhomogeneous media. However, for most people the application to optics known as Huygens principle [36], is probably better known. It states that ... 

The second exception is if we are interested in the propagation of a collimated light source (i.e., a laser). In this case, since only one incident direction is to be considered, the problem can be modeled by direct simulation, even for multiple scattering media up to intermediate optical thicknesses (t = 1). In general, the direct simulation of the radiative transfer equation is to be chosen if a fundamental understanding of radiation-combustion or radiation-turbulence interactions is required. 

In dealing with dilute systems and not too intense light sources one can eliminate, from the current density operator, the term with the vector potential A f). This eliminates from consideration multiple scattering processes and inelastic processes. The propagator ((Jx k ), jx(,k)))E is then approximated with its counterpart derived from the equations of motion of matter (electrons). 

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