The stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is applied to simulate electromagnetic and acoustic scattering from inhomogeneous objects embedded in a layered medium in two dimensions. Two-dimensional layered-media Green’s functions are computed adaptively by using Gaussian quadratures after singularity subtraction. The Green’s function is split into convolutional ...

This chapter describes the theory of carrier transport in two dimensional graphene sheets. At high carrier density, the conductivity of graphene depends on carrier density, the dielectric constant of the substrate and the properties of the impurity potential, which can all can be treated using the Boltzmann transport formalism. At low carrier density, disorder causes the local random fluctuatio...

The electromagnetic imaging of inhomogeneous dielectric cylinders buried in a slab medium by transverse electric (TE) wave illumination is investigated. Dielectric cylinders of unknown permittivities are buried in second space and scattered a group of unrelated waves incident from first space where the scattered field is recorded. By proper arrangement of the various unrelated incident fields, ...

Features of spatial power spectrum (SPS) of scattered radiation in a randomly inhomogeneous medium with strongly prolated anisotropic inhomogeneities of dielectric permittivity are investigated. In single scattering approximation, it has been shown that a pronounced gap along a direction of prolate inhomogeneities appears in SPS. Features of SPS of multiple scattered waves at oblique illuminati...

We show that wave excitation and propagation in an inhomogeneous medium leads to the simultaneous appearance of a huge number of waves with different phase velocities. This phenomenon arises in any medium with inhomogeneous parameters, e.g. in fluid jets where the inhomogeneity appears as a result of the boundary layer. Because of fluctuations (however small) the waves become randomised, i.e. t...

This review examines the localization of one-dimensional nonlinear waves in an inhomogeneous multiphase medium. Particular attention is devoted to the localization of two types of waves, namely, solitary waves (domains) and switching waves that are the separation boundaries between the corresponding phases (domain walls). The localized state of such waves on both point and slowly-varying (in sp...

Some of the basic developments in the theory of electromagnetic field representation in terms of Hertz vectors are reviewed. A solution for the field in an inhomogeneous anisotropic medium is given in terms of the two Hertz vectors. Conditions for presentation of the field in terms of uncoupled transverse electric and transverse magnetic modes, in a general orthogonal coordinate system, are der...

This paper deals with waves propagating in a one-dimensional flow moving through a randomly layered medium. The flow velocity is assumed to be greater than the group velocity of the waves in the reference system of the flow. As a result, in the laboratory reference system, all the waves propagate in a single direction. Amplitudes of these waves moving through a randomly inhomogeneous medium are...

We consider Fisher-KPP-type reaction-diffusion equations with spatially inhomogeneous reaction rates. We show that a sufficiently strong localized inhomogeneity may prevent existence of transition-front-type global in time solutions while creating a global in time bump-like solution. This is the first example of a medium in which no reaction-diffusion transition front exists. A weaker localized...