The localization of electromagnetic waves in lossless inhomogeneous dielectric media is studied. We consider a three-dimensional lossless periodic medium (photonic crystal) having a gap in the frequency spectrum (photonic bandgap). If such a medium is perturbed by either a single defect or a random array of defects, exponentially localized electromagnetic waves arise with frequencies in the gap...

We derive and analyze transport equations for the energy density of waves of any kind in a random medium. The equations take account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization e ects, coupling of di erent types of waves, etc. We also show that di usive behavior occurs on long time and distance scales and we determine the di usion coe cients. ...

Understanding of wave hydrodynamics and its effects are important for engineers and scientists. Important insights may be gained from laboratory studies.  Often the waves are simulated in laboratory flumes do not have the full characteristics of real sea waves. It is then necessary to present reliable methods of wave generation in wave flumes.  In this paper, the results of numerically simulate...

Unidirectional deep-water waves are studied theoretically and experimentally. Theoretically we apply the theory of the nonlinear Schroedinger equation (NLS) using the inverse scattering transform, a kind of generalized, nonlinear Fourier analysis. We discover from the theoretical study that there are essentially four kinds of physical effects that can lead to extreme waves: (1) the superpositio...

Abstract. We study long range propagation of electromagnetic waves in random waveguides with rectangular cross-section and perfectly conducting boundaries. The waveguide is filled with an isotropic linear dielectric material, with randomly fluctuating electric permittivity. The fluctuations are weak, but they cause significant cumulative scattering over long distances of propagation of the wave...

We discuss the influence of material anisotropy on the possible depolarization and diffusion of elastic waves in randomly heterogeneous media. Anisotropy is considered at two levels. The first one is related to the constitutive law of random materials, which may be handled by a random matrix theory for the elasticity tensor. The second level is related to the correlation structure of these rand...

The propagation of sound waves and electromagnetic radiation in a background medium is strongly innuenced by the addition of random scatterers. We study random perturbations of a background medium which has a spectral gap in its permissible energy spectrum. We prove that the randomness localizes waves at energies near the band edges of the spectral gap of the background medium. The perturbation...

The immature retina generates spontaneous waves of spiking activity that sweep across the ganglion cell layer during a limited period of development before the onset of visual experience. The spatiotemporal patterns encoded in the waves are believed to be instructive for the wiring of functional connections throughout the visual system. However, the ontogeny of retinal waves is still poorly doc...