Abstract.Plane harmonic waves in a rotating elastic medium are considered. The inclusion of centripetal and Coriolis accelerations in the equations of motion with respect to a rotating frame of reference leads to the result that the medium behaves as if it were dispersive and anisotropic. The general techniques of treating anistropic media are used with some necessary modifications. Results concerning slowness surfaces, energy flux and mode shapes are derived. These concepts are applied in a discussion of the behavior of harmonic waves at a free surface.Introduction. In this paper plane wave propagation in a linear, homogeneous, isotropic elastic medium will be considered, with the assumption that the entire elastic medium is rotating with a uniform angular velocity. If the coordinate system is taken as fixed in the rotating medium, this introduces additional terms in the equations of motion: a centripetal and a Coriolis acceleration. We consider small-amplitude waves propagating in the medium and exclude any discussion of the time-independent stresses and displacements that are caused by centrifugal forces and other possible body forces.In the following section the equations governing plane-wave solutions in an infinite rotating medium are formulated and it is shown that there are three real slowness surfaces, each corresponding to the root of a cubic characteristic equation. It is shown that the phase speed in all cases depends on the ratio of the wave frequency to the rotational frequency, thus making it clear that the rotation causes the material to be dispersive. The actual slowness surfaces are given for various values of Poisson's ratio and the frequency ratio.In the next section the energy flux for plane waves is discussed and it is proved, for any admissible plane wave, to be perpendicular to the slowness surface at the point indicated by the slowness vector (essentially the wave number vector) of the wave.Actual displacements that occur are discussed qualitatively in the subsequent section. It is seen that, in general, the various modes are neither shear nor compressional, but combinations of both. All exceptional cases of pure shear or pure compressional modes are discussed.In the last section free surface phenomena are discussed. To describe the reflection of plane waves from a plane free surface, use is made of the slowness surfaces. Much qualitative information on types of reflected waves can be brought out even without the use of the explicit expressions for the slowness vector, such as under what circumstances one or two of the reflected waves will be surface waves, i.e. have a complex *

In this work, we continue the analysis of a probabilistic approach and the corresponding stochastic multi-parametric model of wave propagation in built-up areas with randomly distributed buildings. We Concentrate on the influence of buildings' overlay profiles on signal spatial decay, and on path-loss dependence in the frequency domain within UHFIX-band urban propagation channels. Using different buildings' overlay profiles, the field-intensity attenuation along radio paths is examined, taking into account single-scattering and multiple-scattering phenomena, and diffraction from buildings' corners and rooftops, for various positions of receiver and transmitter antennas with respect to surrounding obstacles. The comparison between experimental and theoretical predictions was motivated by the proposed stochastic multi-parametric model and the experimental data obtained for actual areas in Jerusalem (Israel) and Lisbon (Portugal), as well as by other models of multiple diffraction. The discussion is presented for realistic elevations of both terminal antennas to assess the accuracy and limits of the proposed stochastic model. A sensitivity analysis of the influence on the path loss of built-up terrain parameters and the elevation of antennas relative to the buildings surrounding them is presented.

Abstract-It is an accepted fact that transverse Doppler effects of the first order in v/c are nonexistent for all physical wave phenomena, including acoustics, i.e., the Doppler effect is zero for radiation normal to the direction of motion. However, this statement assumes that the incident field is a plane wave, which is not true in general for finite aperture sources. Consequently, the probing of flows transverse to the axis of finite diameter beams, particularly focused beams, is feasible. This geometry will be advantageous in many applications where the classical orientation of the sound beam, oblique to the flow, is not possible. With this motivation in mind, the theory and experimental feasibility of measuring Doppler spectra in transverse geometries is presently investigated.The comparison of flow flux measurements, and measurements performed using a standard ultrasound pulsed Doppler system, show that flow normal to the axis of a focused transducer can be measured with an accuracy comparable to that obtained with the conventional oblique orientation. The measured Doppler spectra are shown to agree well with theory.Although the experiments have been performed for acoustical waves, the present results should also be applicable to electromagnetic systems.

For almost a century, velocity dependent scattering problems are solved in the context of Einstein's Special Relativity theory. Most interesting problems involve non-uniform motion, which is heuristically justified by assuming the validity of the "instantaneous velocity" approximation. The present study attempts to provide a consistent postulational foundation by introducing boundary conditions based on the Lorentz force formulas. The methodology used here is dubbed "reverse engineering": Being aware of the relativistic results, we show that they are replicated, (at least) to the first order in β = v/c by the present method. Specific problems are discussed to demonstrate the power of the method, and pave the way to future research in this problem area. Specifically, by realizing that at the boundary we deal with signals, which are derived from waves, only the latter being subject to the wave equations, it is feasible to apply boundary conditions and construct appropriately the scattered waves in space. It is shown that the present approach is also consistent with the Minkowski constitutive relations which are exploited for solving problems where the medium moves parallel with respect to the boundaries.