The inverse electromagnetic scattering problem by a penetrable cylinder at oblique incidence

In this work, we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We consider the indirect method and simple representations for the electric and the magnetic fields in order to derive a system of five integral equations, four on the boundary of the cylinder and one on the unit circle where we measure the far-field pattern of the scattered wave. We solve the system iteratively by linearizing only the far-field equation. Numerical results illustrate the feasibility of the proposed scheme.     

Evidence of a natural boundary and nonintegrability of the mixmaster universe model

Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically, we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence on initial conditions.     

A note on minimum distance estimates

It is shown that minimum distance estimates enjoy the invariance property of maximum likelihood estimates. Supported under Grant No. 18-2773 of the American University of Beirut.     

Detection of point-like scatterers using one type of scattered elastic waves

In this paper, we are concerned with the detection of point-like obstacles using elastic waves. We show that one type of waves, either the P or the S scattered waves, is enough for localizing the points. We also show how the use of S incident waves gives better resolution than the P waves. These affirmations are demonstrated by several numerical examples using a MUSIC type algorithm.     

Variational formulations for scattering in a three‐dimensional acoustic waveguide

Variational formulations for direct time‐harmonic scattering problems in a three‐dimensional waveguide are formulated and analyzed. We prove that the operators defined by the corresponding forms satisfy a Gårding inequality in adequately chosen spaces of test and trial functions and depend analytically on the wavenumber except at the modal numbers of the waveguide. It is also shown that these operators are strictly coercive if the wavenumber is small enough. It follows that these scattering problems are uniquely solvable except possibly for an infinite series of exceptional values of the wavenumber with no finite accumulation point. Furthermore, two geometric conditions for an obstacle are given, under which uniqueness of solution always holds in the case of a Dirichlet problem. Copyright © 2007 John Wiley & Sons, Ltd.     

Applying robust multibit watermarks to digital images

The current work is focusing on the implementation of a robust multibit watermarking algorithm for digital images, which is based on an innovative spread spectrum technique analysis. The paper presents the watermark embedding and detection algorithms, which use both wavelets and the Discrete Cosine Transform and analyzes the arising issues.     

The inverse scattering problem by an elastic inclusion

In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti’s formula (direct method), is equivalent to a system of four integral equations that are non linear with respect to the unknown boundary. Two equations are on the boundary and two on the unit circle where the far-field patterns of the scattered waves lie. We solve iteratively the system of integral equations by linearising only the far-field equations. Numerical results are presented that illustrate the feasibility of the proposed method.     

Chaos in nonlinear paradoxical games

Summary Paradoxical games are nonconstant sum conflicts, where individual and collective rationalities are at variance and refer to a dyadic antagonism where the contestants blackmail each other. The state space dynamics of a class of such games has been previously studied in the planar case of two variablesx ₁,x ₂ (representing the propensities of the two parties to cooperate), for which phase space portraits have been obtained for a wide range of control parameters. In this paper, we extend the analysis to 3 dimensions, by allowing two of these parameters (the so-called ?tempting factors?) to oscillate in time. We observe on a Poincaré surface of section that the invariant manifolds of twounstable fixed pointsU ₁ andU ₁ intersect, and form heteroclinic and homoclinic orbits. Thus, sufficiently close toU ₁ andU ₂, one finds ?horseshoe? chaos and extremely sensitive dependence to initial conditions. Moreover, since the equations of motion can be written in Hamiltonian form, all the known phenomena of periodic, quasi-periodic and chaotic orbits can be observed around twostable fixed points, where the two parties become ?deadlocked? in an inconclusive exchange that never ends. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.