Dan Censor

Exact Inverse‐Separation Series for Multiple Scattering in Two Dimensions

We consider configurations of arbitrary scatterers (s = 1, … ,N) in two dimensions, such that the circles circumscribing the scatterers do not intersect. As shown previously [V. Twersky, in Electromagnetic Waves, R. E. Langer, Ed. (University of Wisconsin Press, Madison, 1962), pp. 361–389], the solution can be written in terms of the multiple‐scattered scattering amplitudes Gs, and the Gs are specified by the presumably known farfield isolated scattering amplitudes gs by a set of integral equations G(g) (which can be converted to algebraic equations involving Hankel functions of the separations bst, etc.). Among other applications, the previous paper gave the complete asymptotic series for G(g) in inverse powers of the bs; this was based essentially on Hankels asymptotic expansion for the Hankel functions Hn. The present paper derives the analogous convergent representation of G(g) based on the exact representation of Hn in terms of Lommel polynomials. For N scatterers, we give the multiple‐scattering ...

Scattering of Electromagnetic Waves by a Cylinder Moving Along its Axis

The scattering of a time-harmonic, linearly polarized plane electromagnetic wave by a cylinder uniformly moving along its axis is discussed. The formalism is relativistically exact, and explicit forms are provided for first-order velocity effects. Consideration is given to both a cylinder moving in free space, using the procedure suggested by Einstein, and two refractive media; it is veritied that the first case is a special case of the second one. Thin scatterers are considered and it is shown that no first-order velocity effects are present. For a moving medium, having in its rest frame the same constitutive parameters as the surrounding medium, it is shown that the velocity-independent part vanishes, but scattered fields of the first order in the velocity are still present. Moreover, these waves appear with the opposite polarization (compared to the incident wave).

Scattering by time varying obstacles

Abstract The present paper considers scattering problems involving impenetrable obstacles which deform as a function of time. The method can be applied to practical vibration problems involving machinery with sliding parts or with flexible components changing their form as a function of time. In particular the theory is applied to periodically varying shapes which can be conveniently related to circular cylinders and spheres. Special cases of interest are discussed: e.g., radially and lineally vibrating objects, and rotating ellipses of small eccentricity. Explicit results are given for small deformations and the derivation of higher order effects is delineated. Although the incident wave is monochromatic, the scattered wave has a spectrum of frequencies. The main effect is the production of two sidebands whose spectral and spatial structure might provide a signature for the special mode of motion at hand.

RADIO PROPAGATION IN RURAL RESIDENTIAL AREAS WITH VEGETATION

In this paper we describe radio wave propagation within mixed residential area consisting of vegetation and houses. We assume no specific knowledge of the houses and vegetation location, but only of their statistical parameters. A three-dimensional (3D) stochastic approach, which is based on the statistical description of the terrain features, houses and vegetation, and deterministic description of signal decay is presented. The scattering and diffraction from trees and buildings, as well as the diffused reflection from the rough structures of the obstructions are modeled using the statistical description of an array of non-transparent phase screens randomly distributed on the rough terrain. The model, which accounts for single scattering and diffraction phenomena and a similar model, which accounts for multiple scattering effects without effects of diffraction are compared with measurements carried out in typical rural mixed residential areas with vegetation. The accuracy of the theoretical prediction is analyzed accounting possible variations of the terrain features. The approach presented here is applicable in many cases, where specific topographical information is not available.

Scattering by Weakly Nonlinear Objects

An attempt is made to construct a consistent scattering theory for systems involving nonlinear objects. Weak nonlinearity is assumed, such that harmonic generation is present, but shock wave formation is excluded. Mathematically this is described by constitutive relations in the form of Volterra series. For periodic (as opposed to monochromatic) waves, this procedure facilitates algebraic constitutive relations and dispersion equations in the transform space. Weak nonlinearity, as defined here, implies phase matching, i.e., all harmonics of the fundamental wave possess the same phase velocity (this is the reason that shock waves cannot be formed). Due to this stipulation superposition is allowed in a restricted sense, facilitating the construction of arbitrary wave solutions, e.g., cylindrical and spherical waves, by using sums (integrals) of plane waves.Using wave solutions from the linear theory, various boundary value problems can be discussed. Plane interfaces are considered, displaying well known pro...

APPLICATION-ORIENTED RELATIVISTIC ELECTRODYNAMICS (2)

This article is a revised and upgraded edition of a previous one published in this journal, hence the label (2), see the General Remarks section below. Relativistic Electrodynamics, for many years a purely academic subject from the point of view of the applied physicist and electromagnetic radiation engineer, is nowadays recognized as pertinent to many practical applications. We therefore need to define a syllabus and explore the best methods for educating future generations of such users. Such an attempt is presented here, and is of course biased by personal preferences. What emerges as general guidelines are the facts that Relativistic Electrodynamics should be presented axiomatically, without trying to “explain the physical meaning” of Special Relativity, that four-vectors and their mathematical properties should be emphasized, and that the field tensors, an elegant formalism, albeit of limited practical use, should be avoided. Use of four-fold Fourier transforms not only greatly simplifies the relevant manipulations, it is also of paramount importance for discussion of dispersive media. This approach yields many concepts as mathematical results, e.g., the Relativistic Doppler effect, which therefore do not require a long phenomenological discussion with many “explanations”. Introducing this approach as early as possible opens new vistas for the student and the educator, indeed some of the new results here do not appear in textbooks on Special Relativity. One of the main results shown here is the fact that the generalized Fermat principle states that the ray will propagate in such a manner that the proper time will be minimized (or extremized, in general). It also strips the mystique of this principle, showing that it is in fact equivalent to a modest mathematical condition on the smoothness of the phase function. The presentation is constructed in a way

Acoustical Doppler effect analysis—Is it a valid method?

The Doppler effect approach is a powerful tool used in various areas of physics to analyze motion in a wave field, by observing the frequency shifts of scattered waves. In acoustics, Doppler effect analysis is used for diagnostics in biomedical systems and for industrial applications, e.g., in cases where scatterers are present in moving fluids. The theoretical models used to analyze such systems usually ignore the fact that the moving ambient medium might produce effects of the same order of magnitude as the scatterers themselves. It has even been argued that in certain circumstances such effects should completely cancel the Doppler frequency shifts. A model is developed here that contributes to our understanding of the scattering in the presence of moving objects and space‐ and time‐dependent moving media. The model is restricted to irrotational flows, neglects velocity effects except of the first order in the Mach number v/c, and assumes slow variations in the ambient medium. These restrictions facilit...

Fermat's principle and real space-time rays in absorbing media

Real wave packets and group velocities are considered for linear, dispersive homogeneous (but possibly anisotropic) absorptive media. In inhomogeneous media the rays are determined by the Fermat principle. Coupled with the relevant constraints this yields the Hamilton equations of geometrical optics for real rays in absorbing media.

Waveguide and Cavity Oscillations in the Presence of Nonlinear Media

This paper deals with the problem of waves in metallic structures containing nonlinear media. Problems of this kind are encountered in the analysis of microwave devices operated at high power levels, or when the constitutive parameters of nonlinear materials are investigated by means of microwave measurements. The Volterra series are the functional analog of the well-known Taylor series for functions. This mathematical tool is adequate for a description of constitutive relations in dispersive nonlinear media. For practical purposes, we deal with weak nonlinearity, such that the series can be truncated. Weak nonlinearity also denotes the absence of shock waves, such that all spectral components of a wave are phase matched (i.e., propagate with the same phase velocity). The main effect of nonlinearity are the production of harmonics, and the dependence of the dispersion equation on the field amplitudes. These are incorporated into the present model. The development of the present model involves some heuristic assumptions which facilitate the derivation of an algebraic dispersion equation. Therefore, the range of validity of the present model will have to be determined by experimental results, when these are available. In waveguides, and cavities in particular, the question of the effect of the geometry and boundary conditions arises, too. It is shown here that nonlinearity induces harmonic modes in rectangular structures. In cylindrical and spherical structures, the geometry affects the budget of harmonics and produces mode coupling.

THE MATHEMATICAL ELEMENTS OF RELATIVISTIC FREE-SPACE SCATTERING

This study attempts to summarize and systematize the mathematical tools used in free-space electromagnetic wave scattering problems. The elements of Relativistic Electrodynamics relevant to the subject are reviewed. Then, various two- and three-dimensional representations for waves scattered by objects at rest are summarized. Finally the two aspects are combined into a package of various representations for the scattered wave by moving objects and the associated scattering amplitude.