Finite Number Of Scatterers Research Articles

Homogenization of composites using full-wave point-dipole model

We propose a full-wave point-dipole-based scheme for accurate material homogenization of composites. Unlike conventional homogenization approaches which employ periodic boundary conditions for the effective permittivity extraction, the proposed technique can efficiently compute the interactions between the scatterers even in inhomogeneous mixtures as well as aperiodic arrangement of a finite number of scatterers. The method utilizes each inclusion as a basis function, and thereby sidesteps the computational burden to discretize each inclusion scatterer. In addition, the supplementary analytical calculations provide closed-form expressions to deal with the field singularities and to calculate the mutual interaction between the scatterers. We demonstrate that the proposed homogenization scheme can precisely extract the composite permittivity profile of a finite size specimen.

Formula omitted] masses on an infinite string and related one-dimensional scattering problems

One-dimensional time-harmonic waves interact with a finite number of scatterers: they could be beads on a long string, for example. If the scatterers are identical and equally spaced, such periodic problems can be solved exactly. One problem solved here arises when one scatterer in a periodic row is forced to oscillate, giving the Green function for the row. Our main interest is with disordered problems, where a periodic configuration is disturbed. Two problems are studied. First, just one scatterer in a finite periodic row is displaced: an exact solution is obtained for the transmission coefficient and its average over all allowable displacements. Second, a similar problem is treated where each scatterer is displaced by a small distance from its position in the periodic row. The main tools used are perturbation theory and transfer matrices.

Formulation for statistics of echoes due to a finite number of scatterers and patches of scatterers in a directional sonar beam.

A general theoretical formulation is developed for echo statistics associated with a finite number of scatterers and patches of scatterers, each being randomly located in a directional sonar beam. This is the case of a direct-path sonar where there are no echoes from the seafloor and sea surface. The formulation is derived by combining the equations of Ehrenberg and colleagues (single scatterer randomly located in sonar beam) and Barakat (sum of finite number of random variables). Each scatterer or patch of scatterers is independent and can have its own echo probability density function (PDF) (before beampattern effects). Examples show that the PDF of the echo (as received by the sonar) is strongly non-Rayleigh due to beampattern effects and finite number of scatterers or patches. Numerical simulations are made for validation. [Work supported by ONR.]

Distributed-system detection in correlated clutter

Distributed sonar systems decide if a target is present through use of a rule that combines information from each individual sensor. The most basic of these are the ‘‘and’’ and ‘‘or’’ data fusion rules. Analysis of these rules has typically been restricted to cases where the target is detected on some number of sensors, and the false alarms are assumed to arise from processes that are statistically independent from sensor to sensor. In active sonar systems operating in clutter‐dominated areas, this assumption may be far from the truth. Active sonar clutter often has its origins in scattering from physical objects (e.g., shipwrecks, fish schools, rock outcroppings, or mud volcanoes). Particularly when the scatterers are small in terms of wavelengths, this leads to false alarms that can be highly correlated from sensor to sensor. In this work, clutter scattering is assumed to arise from a finite number of scatterers with an exponentially‐distributed size, which would lead to a K‐distributed matched‐filter envelope. The performance of the ‘‘and’’ and ‘‘or’’ fusion rules is then evaluated for two sensors with partially overlapping resolution cells. The resulting detection statistics from the two sensors are not independent, necessitating approximation of the joint distribution function.

Investigating the richness of the finite scatterers MIMO wireless channel

The independent Rayleigh fading MIMO channel is compared here with a more realistic channel model; specifically the finite scatterers (FS) channel where a finite number of scatterers are each defined by a path gain and angles of departure and arrival. For the case of quasi-static, flat fading where only the receiver knows the channel, capacity CDFs are converted to plots of outage probability as functions of SNR. The losses of the FS channel owing to a lack in channel richness over the ideal independent Rayleigh case are then assessed. For sufficient scatterers, trends in SNR losses as a function of antenna spacing follow a Bessel function which itself is the predicted average correlation between antennas for the FS channel. For sufficient antenna spacing, SNR and diversity order losses reduce quickly as the number of scatterers increases. In summary, informed choice of antenna spacings along with a reasonable number of scatterers can realise the full independent Rayleigh channel diversity order although a small SNR loss appears unavoidable.

Novel physical interpretations of K-distributed reverberation

Interest in describing and modeling envelope distributions of sea-floor backscatter has increased recently, particularly with regard to high-resolution active sonar systems. Sea-floor scattering that results in heavy-tailed-matched-filter-envelope probability distribution functions (i.e., non-Rayleigh distributions exemplified by the K, Weibull, Rayleigh mixture, or log-normal distributions) is often the limiting factor in the performance of these types of sonar systems and in this context is referred to as reverberation or acoustic clutter analogous to radar clutter. Modeling of reverberation has traditionally entailed fitting various candidate distributions to time samples of the envelope of the scattered sonar (or radar) returns. This type of descriptive analysis and the asymptotic (infinite number of scatterers) analysis defining the K-distribution yield little insight into the environmental mechanisms responsible for heavy-tailed distributions (e.g., distributions and, clustering of discrete scatterers, patchiness in geo-acoustic properties, scattering strength of scatterers, etc.) and do not allow evaluation of the effect of changing sonar system parameters such as bandwidth and beamwidth. In contrast, we derive the envelope distribution for the scattered returns starting from simple physical descriptions of the environment with a finite number of scatterers. It is shown that plausible descriptions of the environment can lead to K-distributed reverberation. This result explains, at least partially, the success of the K-distribution in the modeling of radar clutter and sonar reverberation at a variety of frequencies and scales. The finite-number-of-scatterers model is then used to predict how the shape parameter of the K-distribution will change as the beamwidth of a towed-array receiver is varied. Analysis of reverberation data from a low-frequency (450-700 Hz) active sonar system illustrates that, within our ability to estimate it, the shape parameter of the K-distribution is proportional to the beamwidth of the towed-array receiver, a result important for sonar simulation and performance prediction models. These results should prove useful in developing methods for modeling, predicting and mitigating reverberation on high-resolution sonar systems.

A Numerical Algorithm of the Multiple Scattering from an Ensemble of Arbitrary Scatterers

Sound scattering by a finite number of arbitrary scatterers has remained a complicatedproblems. For this reason, only limited numerical results have been documented in the liter-ature. The main difficulty perhaps has been associated with the lack of efficient numericalalgorithmsandthelimitedcomputingcapability.Amongmanyusefulformalismssuggestedfor describing sound scattering by a finite group of arbitrary scatterers, three approachesappear to be particularly useful, that is, the self-consistent approach [1, 2], theT-matrixmethod [3, 4], and the method of moments [5].The recent expanding capability of digital computers has in principle made it possibleto compute the more complicated problem of multiple scattering from a finite numberof scatterers. Following the self-consistent scheme in Foldy [1], the multiple scatteringprocesses can be represented by a set of coupled linear equations. The solution to theseequations can be obtained by a matrix inversion. Such a procedure has been used previouslyto investigate multiple scattering by isotropic scatterers, especially the acoustic localizationin bubbly liquids in which air-filled bubbles are isotropic scatterers [6]. The purpose ofthis paper is to generalize the numerical matrix method in Ye and Alvarez [6] to morecomplicated cases involving many anisotropic scatterers. It will be clear from the derivationthat the present approach can be used for scattering from many scatterers with arbitraryconfigurations for a wide range of situations.

Configurations with finite numbers of scatterers—A self-consistent T-matrix approach

A self-consistent scheme is developed to analyze the scattering of waves by a configuration containing a finite number of scatterers. The T matrix obtained using the null field equations is used to characterize the response of a single scatterer to arbitrary excitation. Translation theorems for the spherical basis functions are used not only to express the T matrix of individual scatterers with respect to a common coordinate system, but also to take care of multiple scattering between the scatterers. The formulation given is equally applicable for the scattering of acoustic, electromagnetic, or elastic waves. The scatterers may have different shapes and be of different types; e.g., sound soft, sound hard, or permeable in the acoustic case. Numerical results are presented for the case of two elastic cavities in a solid.