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Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both…
It is a deceptively simple question to ask how acoustic disturbances propagate in a non--homogeneous flowing fluid. If the fluid is barotropic and inviscid, and the flow is irrotational (though it may have an arbitrary time dependence),…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
The propagation of light in a scattering medium is described as the motion of a special kind of a Brownian particle on which the fluctuating forces act only perpendicular to its velocity. This enforces strictly and dynamically the…
Electronic matter waves traveling through the weak and smoothly varying disorder potential of a semi-conductor show branching behavior instead of a smooth spreading of flow. By transferring this phenomenon to optics, we show how the…
By solving Maxwell's equations the exact dispersion equation for electromagnetic waves propagating in a layered coaxial ferrite line is obtained. In particular the analytical consideration is carried out for a simpler case of complete…
Wavefield speckle patterns are generated by interference of randomly scattered coherent light. In the weak-coupling regime of the It\^o-Schr\"odinger paraxial model for long-distance wave propagation, we show the following multiscale…
The propagation of a narrow-band signal radiated by a point source in a randomly layered absorbing medium is studied asymptotically in the weak-scattering limit. It is shown that in a disordered stratified medium that is homogeneous on…
An effect of polarization-mode dispersion, nonlinearity and random variation of dispersion along an optical fiber on a pulse propagation in a randomly birefringent dispersion-shifted optical fiber with zero average dispersion is studied. An…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
We show that for an observer in translational, rotational or gravitational motion, a linearly polarized plane wave has two modes of propagation in a stationary, homogeneous and isotropic medium according to Hertz's version of Maxwell's…
Introducing correlations between the spatial and temporal degrees of freedom of a pulsed optical beam (or wave packet) can profoundly alter its propagation in free space. Indeed, appropriate spatio-temporal spectral correlations can render…
Power law generalized covariance functions provide a simple model for describing the local behavior of an isotropic random field. This work seeks to extend this class of covariance functions to spatial-temporal processes for which the…
We compare the behavior of propagating and evanescent light waves in absorbing media with that of electrons in the presence of inelastic scattering. The imaginary part of the dielectric constant results primarily in an exponential decay of…
In this study, we experimentally investigate the application of a transient signal with complex frequencies to the absorption and transmission of sound waves. Indeed, the emission of a wave with an exponentially varying amplitude in time is…
We develop a theoretical model to investigate wave propagation in media with random time-varying properties, where temporal fluctuations lead to complex scattering dynamics. Focusing on the ensemble-averaged field, we derive an exact…
The propagation of signalling molecules within cellular networks is affected by network topology, but also by the spatial arrangement of cells in the networks. Understanding the collective reaction--diffusion behaviour in space of signals…
Pulsed Bessel beams of light propagating in free-space experience diffraction effects that resemble those of anomalous dispersion on pulse propagation. It is then shown that a pulsed Bessel beam in a normally dispersive material can remain…
Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic…
Space-time wave packets (STWPs) are pulsed optical beams whose spatiotemporal structure enables propagation invariance. However, STWPs allow for a unique propagation configuration that we call axial spectral encoding, in which the spectrum…