Renormalized cluster expansion for multiple scattering in disordered systems

We study wave propagation in a disordered system of scatterers and derive a renormalized cluster expansion for the optical potential or self-energy of the average wave. We show that in the problem of multiple scattering a repetitive structure of Ornstein-Zernike type may be detected. We derive exact expressions for two elementary constituents of the renormalized scattering series, called the reaction field operator and the short-range connector. These expressions involve sums of integrals of a product of a chain correlation function and a nodal connector. We expect that approximate calculation of the reaction field operator and the short-range connector allows one to find a good approximation to the self-energy, even for high density of scatterers. The theory applies to a wide variety of systems.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

A successive scattering methodology with application to two cylinders in the Fresnel region of each other

We present an efficient approach to compute the second-order scattering of an electromagnetic wave by two discrete scatterers in proximity to each other. Such a two-body system represents the simplest canonical arrangement to address near-field volume scattering phenomena in microwave remote sensing models of vegetation. Using an analytical wave-based approach, a successive scattering methodology is employed to derive the first interaction term in multiple scattering by two arbitrary scatterers in terms of their transition operators. The general formulation is applied to find the second-order bistatic scattering amplitude for a pair of finite length thin cylinders at arbitrary interaction distances using the exact Green's function. To improve computational efficiency, the solution is then specialized to the Fresnel region. These second-order bistatic scattering amplitude results are in agreement with the exact Green's function model when the scatterers are in the Fresnel region of each other. Additionally, it is demonstrated that using the far field approximation in the Fresnel region can yield significant deviations from the exact results. The Fresnel model, unlike the far field approximation, accurately predicts the scattering amplitude peak values and null locations, and is suited to fast solutions in realistic canopy simulations.     

Contributions to the self-energy of a wave propagating in a disordered array

We study the self-energy of a scalar wave propagating in a disordered static array of spherical scatterers. We employ the cluster expansion developed in a preceding article and provide detailed expressions for many contributions to the self-energy. The two-body term is covered completely. The three-body term is treated only in part, but we believe that those contributions which are important at not too high density are accounted for. Through resummation some of the contributions to the self-energy involve a large number of scatterers.     

Hot Scatterers and Tracers for the Transfer of Heat in Collisional Dynamics

We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes. We study their ergodic properties in details and provide a useful formula for the cumulant generating function of the time integrated energy current. We observe that out of thermal equilibrium, the generating function is not analytic. When the set of temperatures of the scatterers is fixed by the condition that in average no energy is exchanged between the scatterers and the system, different behaviours may arise. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, the thermal conductivity is interpreted as a frequency of collision between tracers and scatterers.     

Effect of pulse entrapping on diffuse reflection from a resonant random medium: exact solution to the scalar albedo problem

A recently derived radiative transfer equation with three Lorentzian delay kernels is applied to an albedo problem of the scalar wave field produced by the diffuse reflection of a quasi-monochromatic pulse from a semi-infinite random medium consisting of resonant point-like scatterers. The albedo problem is solved exactly in terms of the Chandrasekhar H-function H(μλ), extended analytically into the complex single-scattering albedo λ plane. The resulting analytic solution for the time evolution of a diffusely reflected short pulse is used to study on the whole time axis the effect of the redistribution of the energy of the propagated pulse from the front to the rear of the pulse in cases where the pulse may for most of the propagation time through the medium be 'entrapped' inside resonant scatterers. By considering the power flux through unit area of the boundary of the medium and unit solid angle, it is shown that the relative shift of an 'energy centroid' ('centre of mass') of the pulse diffusely reflected from the resonant random medium (compared with the pulse energy centriod in the non-resonant case) is equal to the parameter describing the energy accumulation inside the scatterers. This result may be used for experimental study of resonant random media with the aid of a short-pulse technique.     

Diffusion in lattices with anisotropic scatterers

We study diffusion in lattices with periodic and random arrangements of anisotropic scatterers. We show, using both analytical techniques based upon our previous work on asymptotic properties of multistate random walks and computer calculation, that the diffusion constant for the random arrangement of scatterers is bounded above and below at an arbitrary density by the diffusion constant for an appropriately chosen periodic arrangement of scatterers at the same density. We also investigate the accuracy of the low-density expansion for the diffusion constant up to second order in the density for a lattice with randomly distributed anisotropic scatterers. Comparison of the analytical results with numerical calculations shows that the accuracy of the density expansion depends crucially on the degree of anisotropy of the scatterers. Finally, we discuss a monotonicity law for the diffusion constant with respect to variation of the transition rates, in analogy with the Rayleigh monotonicity law for the effective resistance of electric networks. As an immediate corollary we obtain that the diffusion constant, averaged over all realizations of the random arrangement of anisotropic scatterers at density, is a monotone function of the density.     

Determination of Tiny Scatterer#x0027;s Shape by Light Scattering Tomography

We have developed a new method of recognizing the shape of tiny light scatterers by matrix calculation (conjugate gradient method) using the wave field on the objective lens. We describe simulation results for scatterers of about 100 nm and show that they accurately produce the scatterer shape.     

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure–time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.     

Asymptotic properties of multistate random walks. II. Applications to inhomogeneous periodic and random lattices

The previously developed formalism for the calculation of asymptotic properties of multistate random walks is used to study random walks on several inhomogeneous periodic lattices, where the periodically repeated unit cell contains a number of inequivalent sites, as well as on lattices with a random distribution of inequivalent sites. We concentrate on the question whether the random walk properties depend on the spatial arrangement of the sites in the unit cell, or only on the number density of the different types of sites. Specifically we consider lattices with periodic and random arrangements of columns and lattices with periodic and random arrangements of anisotropic scatterers.     

Acoustic radiation force due to incident plane-progressive waves on coated spheres immersed in ideal fluids

In this study, the acoustic radiation force resulting from the interaction of a plane progressive wave with a coated sphere was examined. The linear acoustic scattering problem was obtained first by solving the classical boundary conditions to obtain the required coefficients. The radiation force was then determined by averaging the momentum flux tensor expressed in terms of the total scattering pressure or velocity potential in an ideal fluid. Numerical calculations of the radiation force function Yp , which is the radiation force per unit energy density and unit cross-section, were displayed versus the dimensionless size parameter x=k1 b (k1 is the wave number in the exterior fluid and b the radius of the uncoated sphere) over a large range of frequencies. Particular emphasis has been focused on the coating thickness and the absorption of sound inside the outer covering layer. The fluid-loading effect on the radiation force function curves was also analysed.     

Analyzing the coda from correlating scattered surface waves

The accuracy of scattered Rayleigh waves estimated using an interferometric method is investigated. Summing the cross correlations of the wave fields measured all around the scatterers yields the Green's function between two excitation points. This accounts for the direct wave and the scattered field (coda). The correlations themselves provide insights into the location of the scatterers, as well as which scatterer is responsible for particular parts of the coda. Furthermore, these measurements confirm a constant-time arrival in the correlations, not part of the Green's function, but which has previously been derived as a result of the generalized optical theorem.     

Environment-induced decoherence I. The Stern-Gerlach measurement

A dynamical model for the collapse of the wave function in a quantum measurement process is proposed by considering the interaction of a quantum system (spin -1/2) with a macroscopic quantum apparatus interacting with an environment in a dissipative manner. The dissipative interaction leads to decoherence in the superposition states of the apparatus, making its behaviour classical in the sense that the density matrix becomes diagonal with time. Since the apparatus is also interacting with the system, the probabilities of the diagonal density matrix are determined by the state vector of the system. We consider a Stern-Gerlach type model, where a spin-1/2 particle is in an inhomogeneous magnetic field, the whole set up being in contact with a large environment. Here we find that the density matrix of the combined system and apparatus becomes diagonal and the momentum of the particle becomes correlated with a spin operator, selected by the choice of the system-apparatus interaction. This allows for a measurement of spin via a momentum measurement on the particle with associated probabilities in accordance with quantum principles.     

Scattering of longitudinal waves (sound) by defects in fluids. Rough surface

The classical theory of scattering of longitudinal waves (sound) by small inhomogeneities (scatterers) in an ideal fluid is generalized to a distribution of scatterers and such as to include the effect of the inhomogeneities on the elastic properties of the fluid. The results are obtained by a new method of solving the wave equation with spatial restrictions (caused by the presence of the scatterers), which can also be applied to other types of inhomogeneities (like surface roughness, for instance). A coherent forward scattering is identified for a uniform distribution of scatterers (practically equivalent with a mean-field approach), which is due to the fact that our treatment does not include multiple scattering. The reflected wave is obtained for a half-space (semi-infinite fluid) of uniformly distributed scatterers, as well as the field diffracted by a perfect lattice of scatterers. The same method is applied to a (inhomogeneous) rough surface of a semi-infinite ideal fluid. A perturbation-theoretical scheme is devised, with the roughness function as a perturbation parameter, for computing the waves scattered by the surface roughness. The waves scattered by the rough surface are both waves localized (and propagating only) on the surface (two-dimensional waves) and waves reflected back in the fluid. They exhibit directional effects, slowness, attenuation or resonance phenomena, depending on the spatial characteristics of the roughness function. The reflection coefficients and the energy carried on by these waves are calculated both for fixed and free surfaces. In some cases, the surface roughness may generate waves confined to the surface (damped, rough-surface waves).     

Effects of nearest and next-nearest neighbour interaction parameters on atomic correlation functions of stepped surfaces

We extend the range of the interaction between the surface scatterers to the next-nearest neighbours and thus treat the stepped surface as a second-order Markov chain. We employ two interaction parameters to describe the behaviour of the atomic pair correlation function for a two-level system and derive an exact expression for this function. This expression is then used to calculate the profile of the diffracted intensity. The effects of the interaction parameters on the intensity profiles as well as on the terrace width distributions are investigated in detail and compared to the molecular beam epitaxy measurement of Si on a Si(111) surface. The physical meaning of the interaction parameters is also interpreted in terms of the Ising model.     

One-dimensional stochastic Levy-lorentz gas

We introduce a Levy-Lorentz gas in which a light particle is scattered by static point scatterers arranged on a line. We investigate the case where the intervals between scatterers xi(i) are independent random variables identically distributed according to the probability density function &mgr;(xi) approximately xi(-(1+gamma)). We show that under certain conditions the mean square displacement of the particle obeys /=Ct3-gamma for 1相似文献   

Wave propagation in a disordered array of monopole scatterers

We study scalar wave propagation in a disordered static array of spherical scatterers. Due to a hard core repulsion the scatterers do not overlap. The wave is scattered by a δ-function potential at the center of each of the spheres. To this monopole model we apply the previously developed cluster expansion for the self-energy. We find the root of the dispersion equation for the coherent wave for a range of volume fraction⁵. It turns out that the monopole model develops an instability when the scattering is too strong.     

New Theory of Periodic Systems by Supersymmetric Quantum Mechanics on Finite Interval

We show that the mechanism of gap formation has a resonance nature. The special real solutions were discovered which have knot distribution with a period coinciding with that of potential at all energies of the whole gap interval. In terms of these solutions resonance gap appearance gets the most direct explanation: ever repeating influence of the potential upon wave function results in exponential increase (decrease) of the wave amplitudes in the forbidden zones. Periodical continuation of exactly solvable models of SUSY QM on finite interval gives rise to algorithms of fixing zone properties - shifting chosen boundaries of spectral bands.