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Related papers: Diffraction from conormal singularities

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We give a formula to count the number of $D_4$ singularities in a stable frontal perturbation of a corank $2$ wave front singularity $f\colon (\mathbb{C}^3,0) \to (\mathbb{C}^4,0)$ using Mond's method of stable perturbations of map germs.…

Algebraic Geometry · Mathematics 2025-05-13 C. Muñoz-Cabello , J. J. Nuño-Ballesteros , R. Oset Sinha

We study a class of linear parabolic equations in divergence form with degenerate coefficients on the upper half space. Specifically, the equations are considered in $(-\infty, T) \times \mathbb{R}^d_+$, where $\mathbb{R}^d_+ = \{x \in…

Analysis of PDEs · Mathematics 2021-06-15 Tuoc Phan , Hung Vinh Tran

We show that smooth, radially symmetric wave maps $U$ from $\mathbb R^{2+1}$ to a compact target manifold $N$, where $\partial_r U$ and $\partial_t U$ have compact support for any fixed time, scatter. The result will follow from the work of…

Analysis of PDEs · Mathematics 2011-12-02 Joules Nahas

The angular distribution of low-frequency radiation after single scattering by an isotropic distribution of relativistic electrons considerably differs from the Rayleigh angular function. In particular, the scattering by an ensemble of…

Astrophysics · Physics 2009-10-31 Sergei Y. Sazonov , Rashid A. Sunyaev

A note that points out the possibility to have p<1 in Sobolev type of inequalities by a use of the momomial structure of polynomials or power series. The proof is simple: Triangle angle inequality p*>1, monomial estimate from p* to exponent…

Functional Analysis · Mathematics 2007-05-23 Andreas Wannebo

We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…

Analysis of PDEs · Mathematics 2024-04-05 Louis Garénaux , L. Miguel Rodrigues

Multiple scattering of light by resonant vapor is characterized by Levy-type superdiffusion with a step size distribution $P(x) \propto 1/x^{1+{\alpha}}$, with $0 < {\alpha} < 2$. The Levy parameter ${\alpha}$ was measured from $P(x)$,…

Inhomogeneous metasurfaces have shown possibilities for unprecedented control of wave propagation and scattering. While it is conventional to shine a single incident plane wave from one side of these metastructures, illuminating by several…

Applied Physics · Physics 2021-08-04 F. S. Cuesta , G. A. Ptitcyn , M. S. Mirmoosa , S. A. Tretyakov

This study describes both experimentally and theoretically an important hitherto undiscovered feature of the scattering of micron_sized spherical objects when illuminated with highly focused circularly polarized light. This is a regime of…

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…

Disordered Systems and Neural Networks · Physics 2016-08-31 S. E. Skipetrov

We have made a high resolution study of the specularity of the atomic reflection from an evanescent wave mirror using velocity selective Raman transitions. We have observed a double structure in the velocity distribution after reflection: a…

We analyze electromagnetic scattering of TM polarized waves from a diffraction grating consisting of a periodic, anisotropic, and possibly negative-index dielectric material. Such scattering problems are important for the modelization of,…

Analysis of PDEs · Mathematics 2015-06-03 Armin Lechleiter , Dinh-Liem Nguyen

The light-rays and wave fronts in a flat class of Godel-type metric are examined to reveal the causality violating features of the space-time. Non-causal features demonstrated by the development of unusual wave front singularities are shown…

General Relativity and Quantum Cosmology · Physics 2025-08-19 Thomas P. Kling , Faizuddin Ahmed , Megan Lalumiere

The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the…

The summation of the partial wave series for Coulomb scattering amplitude, $f^C(\theta)$ is avoided because the series is oscillatorily and divergent. Instead, $f^C(\theta)$ is obtained by solving the Schr{\"o}dinger equation in parabolic…

Quantum Physics · Physics 2007-05-23 Zafar Ahmed

The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…

Astrophysics · Physics 2009-11-10 Dragan Huterer , Tanmay Vachaspati

The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…

High Energy Physics - Theory · Physics 2009-10-28 G. Delfino , G. Mussardo , P. Simonetti

We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are…

We consider the problem of characterizing the Sobolev wavefront set of a tempered distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous wavelet transform, with the latter being defined with respect to a suitably chosen…

Functional Analysis · Mathematics 2024-02-06 Hartmut Führ , Mahya Ghandehari

We study the effect of unidirectional reflectivity in the bilayer optical model with the balanced loss/gain terms. It was found that if the impedances characterizing the scattering part are different from those describing the leads, a new…

Optics · Physics 2017-08-09 J. Ramirez-Hernandez , F. M. Izrailev , N. M. Makarov