The field generated by scattering of light from a quasi-homogeneous source on a quasi-homogeneous, random medium is investigated. It is found that, within the accuracy of the first-order Born approximation, the far field satisfies two reciprocity relations (sometimes called uncertainty relations). One of them implies that the spectral density (or spectral intensity) is proportional to the convolution of the spectral density of the source and the spatial Fourier transform of the correlation coefficient of the scattering potential. The other implies that the spectral degree of coherence of the far field is proportional to the convolution of the correlation coefficient of the source and the spatial Fourier transform of the strength of the scattering potential. While the case we consider might seem restrictive, it is actually quite general. For instance, the quasi-homogeneous source model can be used to describe the generation of beams with different coherence properties and different angular spreads. In addition, the quasi-homogeneous scattering model adequately describes a wide class of turbulent media, including a stratified, turbulent atmosphere and confined plasmas.
We investigate the spatial coherence properties in the focal region of a converging, spatially partially coherent wave field. In particular, we find that, depending on the effective coherence length of the field in the aperture, the longitudinal and transverse coherence lengths in the focal region can be either larger or smaller than the corresponding width of the intensity distribution. Also, the correlation function is shown to exhibit phase singularities.
Strongly driven granular media are known to undergo a transition from a gas-like to a cluster regime when the density of particles is increased. However, the main mechanism triggering this transition is not fully understood so far. Here, we investigate experimentally this transition within a 3D cell filled with beads that are driven by two face-to-face vibrating pistons in low gravity during parabolic flight campaigns. By varying large ranges of parameters, we obtain the full phase diagram of the dynamical regimes reached by the out-of-equilibrium system: gas, cluster or bouncing aggregate. The images of the cell recorded by two perpendicular cameras are processed to obtain the profiles of particle density along the vibration axis of the cell. A statistical test is then performed on these distributions to determinate which regime is reached by the system. The experimental results are found in very good agreement with theoretical models for the gas-cluster transition and for the emergence of the bouncing state. The transition is shown to occur when the typical propagation time needed to transmit the kinetic energy from one piston to the other is of the order of the relaxation time due to dissipative collisions.
In the analysis of light scattering on a sphere it is implicitly assumed that the incident field is spatially fully coherent. However, under usual circumstances the field is partially coherent. We generalize the partial waves expansion method to this situation and examine the influence of the degree of coherence of the incident field on the radiant intensity of the scattered field in the far zone. We show that when the coherence length of the incident field is comparable to, or is smaller than, the radius of the sphere, the angular distribution of the radiant intensity depends strongly on the degree of coherence. The results have implications, for example, for scattering in the atmosphere and colloidal suspensions. DOI: 10.1103/PhysRevLett.104.173902 PACS numbers: 42.25.Fx, 42.25.Kb In the usual description of light scattering by a homogeneous sphere (the scalar analogue of the well-known Mie scattering) it is generally assumed that the incident field is spatially fully coherent [1][2][3][4][5]. In practice, this assumption is not always justified. Examples are fields generated by multimode lasers, and fields that have passed through a random medium such as the turbulent atmosphere. Hardly any studies have been devoted to this more general case (see, however, [6]). The extinguished power due to scattering of random fields on a random medium has been analyzed in [7,8], and certain reciprocity relations for cases of this kind were derived in [9]. The extinguished power from scattering a random field on deterministic media was discussed in [10,11]. However, the influence of the state of coherence of the incident field on the angular distribution of the scattered field seems to have been studied only in two publications [12,13].In this Letter we analyze the scattering of a wide class of beams of any state of coherence on a homogeneous spherical scatterer, namely, beams of the well-known Gaussian Schell-model class (see [14], Sec. 5.6.4). We present numerical examples that show how the effective spectral coherence length (i.e., the coherence length at a fixed frequency) of the incident beam affects the angular distribution of the radiant intensity of the scattered field.Let us first consider a plane, monochromatic scalar wave of unit amplitude, propagating in a direction specified by a real unit vector u 0 , incident on a deterministic, spherical scatterer occupying a volume V (see Fig. 1 whereHere r denotes the position vector of a point in space, t the time, and ! the angular frequency. Also, k ¼ !=c ¼ 2 = is the wave number, c being the speed of light in vacuum and denotes the wavelength. The timeindependent part Uðr; !Þ of the total field that results from scattering of the plane wave on a sphere may be expressed as the sum of the incident field U ðiÞ ðr; !Þ and the scattered field U ðsÞ ðr; !Þ, viz., Uðr; !Þ ¼ U ðiÞ ðr; !Þ þ U ðsÞ ðr; !Þ:The scattered field in the far-zone of the scatterer, at an observation point r ¼ ru (u 2 ¼ 1) is given by the asymptotic formula
The segregation of granular mixtures in rotating cylinders into axial bands is not well understood so far. Abnormal diffusion of the grains has been proposed to play an important role in that process. We measure axial diffusion in binary mixtures, completely embedded in water, by means of nuclear magnetic imaging (magnetic resonance imaging). It is found that the small size particles in a radially segregated structure undergo normal (Fickian) axial diffusion, whereas an initial pulse of the large species shows subdiffusive behavior. An interpretation within a model for the particle dynamics is given. The diffusion of small particles occurs in the axial kernel, whereas particles of the large species migrate on the free surface of the granular bed.
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