We obtain a canonical form of a quadratic Hamiltonian for linear waves in a weakly inhomogeneous medium. This is achieved by using the WKB representation of wave packets. The canonical form of the Hamiltonian is obtained via the series of canonical Bogolyubov-type and near-identical transformations. Various examples of the application illustrating the main features of our approach are presented...

We consider the interior transmission problem corresponding to the inverse scattering by an inhomogeneous (possibly anisotropic) media in which an impenetrable obstacle with Dirichlet boundary conditions is embedded. Our main focus is to understand the associated eigenvalue problem, more specifically to prove that the transmission eigenvalues form a discrete set and show that they exist. The pr...

Digital waveguide networks (DWNs) have recently been proposed as a means of simulating the time-evolution of various physical systems, especially within the context of musical sound synthesis [1, 2, 3, 4, 5]. In 1D, the technique has been applied to vibrations in acoustic tubes, and in strings; in this case, any uninterrupted stretch of air or string (uninterrupted by changes in tube crosssecti...

We present a methodology providing a new perspective on modeling and inversion of wave propagation satisfying time-reversal invariance and reciprocity in generally inhomogeneous media. The approach relies on a representation theorem of the wave equation to express the Green function between points in the interior as an integral over the response in those points due to sources on a surface surro...

We extend the applicability of the recently revised Kubelka-Munk (K-M) theory to inhomogeneous optical media by treating inhomogeneous ink penetration of the substrate. We propose a method for describing light propagation in either homogeneous or inhomogeneous layers using series representations for the K-M scattering and absorption coefficients as well as for intensities of the upward and down...

In this paper we consider diffusion of a passive substance C in a temporarily and spatially inhomogeneous two-dimensional medium. As a realization for the latter we choose a phase-separating medium consisting of two substances A and B , whose dynamics is determined by the Cahn-Hilliard equation. Assuming different diffusion coefficients of C in A and B , we find that the variance of the distrib...

I present a new differential equation system for dynamic raytracing in inhomogeneous anisotropic media. This new system is computationally much more efficient than the traditional elastic-parameter based system as the right-hand-side functions of this new system are simple. Evaluation of these functions involves only differentiation of phase velocities. Evaluation of the right-hand-side functio...

This paper presents an efficient algorithm to sample free path in inhomogeneous participating media. The method is based on the concept of mixing “virtual” particles to the medium, that complete the extinction coefficient to a piece-wise constant function. We use the sampling formulae developed for piece-wise homogeneous medium, but decide randomly whether a real or a virtual particle is hit.

In this Letter we show that an inhomogeneous input can induce wave propagation failure in an excitatory neural network due to the pinning of a stationary front or pulse solution. A subsequent reduction in the strength of the input can lead to a Hopf instability of the stationary solution resulting in breatherlike oscillatory waves.

Consider reaction-diffusion equation ut = ∆u+f(x, u) with x ∈ R and general inhomogeneous ignition reaction f ≥ 0 vanishing at u = 0, 1. Typical solutions 0 ≤ u ≤ 1 transition from 0 to 1 as time progresses, and we study them in the region where this transition occurs. Under fairly general qualitative hypotheses on f we show that in dimensions d ≤ 3, the Hausdorff distance of the super-level se...