Vector wave solutions are obtained for the propagation of beams of light in media having slow spatial variations of the gain, loss, or index of refraction. The formalism developed here is applicable to a wide range of problems, and an exa mple considered in detail is the propagation of off-axis beams in lenslike laser materials and optical waveguides. A procedure is also described for the diagn...

The problem of finding the source distribution for particles (or radiation) in a bounded domain D from the emitting flow through the boundary of D is considered. The particles are supposed to move with unit velocity along geodesics of a Riemannian metric and can be absorbed by the medium. The metric and the absorption are known. Uniqueness of the solution to this problem and a stability estimat...

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. Thi...

We extend the Huygens wavefront tracing algorithm, which is a part of an open source Madagascar project, to sound propagation in inhomogeneous, moving media and apply it to a series of benchmark tasks. One set of tasks admits exact analytic solutions and serves the purpose of validation of the new algorithm. Another set of calculations demonstrates applicability of the algorithm to the studies ...

– For the system of d-dim stochastic differential equations, dXε(t)= b(X(t))dt + εσ(X(t))dW(t), t ∈ [0,1], Xε(0)= x0 ∈Rd, where b(x) and σ(x) are smooth except possibly along the hyperplane {(x1, . . . , xd);x1 = 0}, we shall demonstrate that the natural setup of its large deviation principle is to consider the probability ε2 logP(‖Xε − φ‖< δ, ‖uε − ψ‖ < δ, ‖ ε − η‖< δ)∼−I (φ,ψ,η) of the triple...

The effect of a long length scale static inhomogeneity on spiral wave dynamics is studied in the two-dimensional complex Ginzburg-Landau equation. We find that the inhomogeneity leads to the formation of a dominant spiral domain that suppresses other spiral domains, and that the spiral vortices slowly drift in the presence of an inhomogeneity with a velocity that is proportional to the local pa...

Surface waves propagating through a laterally inhomogeneous medium undergo wavefield complications such as multiple scattering, wavefront healing, and backward scattering. Unless accounted for accurately, these effects will introduce a systematic isotropic bias in estimates of azimuthal anisotropy. We demonstrate with synthetic experiments that backward scattering near an observing station will...

All of these are of the form Au ˆ = f where  is self-adjoint and positive-definite (assuming zero Dirichlet boundary conditions and an appropriate inner product 〈u, v〉), as we’ve seen previously in class, so they should have unique solutions (excluding pathological c functions). However, the solutions may in general be quite different from those of −∇u = f . Can we relate them to G0, the Green...

When a physical object ("a source") without its own eigenfrequency moves through an acoustically homogeneous medium, the only possible form of acoustic radiation is the emission of Mach shock waves, which appear when the source velocity surpasses sonic speed. In nonhomogeneous media, in nonstationary media, or in the neighborhood of such media, the source motion is accompanied by the so-called ...

Wave propagation governed by reaction-diffusion equations in homogeneous media has been studied extensively, and initiation and propagation are well understood in scalar equations such as Fisher’s equation and the bistable equation. However, in many biological applications the medium is inhomogeneous, and in one space dimension a typical model is a series of cells, within each of which the dyna...