Related papers: Wave fronts and (almost) free divisors
For a non-relativistic particle, we consider the evolution of wave functions that consist of polynomial segments, usually joined smoothly together. These spline wave functions are compact (that is, they are initially zero outside a finite…
In this paper we extend some results from our earlier papers on wave-front sets, concerning wave-front sets of Fourier-Lebesgue and modulation space types, to a broader class of spaces of ultradistributions, and relate these wave-front sets…
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points…
We define ultradistributional wave front sets with respect to translation-modulation invariant Banach spaces of ultradistributions having solid Fourier image. The main result is their characterisation by the short-time Fourier transform.
Quasi-analytic wave-front sets of distributions which correspond to the Gevrey sequence $p!^s$, $s\in[1/2,1)$ are defined and investigated. The propagation of singularities are deduced by considering sequences of Gaussian windowed…
In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for…
Motivated by the product of periodic distributions, we give a new description of the wave front and the Sobolev-type wave front of a distribution $f\in\mathscr{D}'(\mathbb{R}^d)$ in terms of Fourier series coefficients.
We study the boundary of the nonnegative trigonometric polynomials from the algebraic point of view. In particularly, we show that it is a subset of an irreducible algebraic hypersurface and established its explicit form in terms of…
We prove that wave fronts on a flat torus become dense. As a corollary, wave fronts become dense for a square billiard or for the geodesic flow on the flat Klein bottle or the cube surface.
In this paper, we generalize the usual notions of waves, fronts and propagation speeds in a very general setting. These new notions, which cover all classical situations, involve uniform limits, with respect to the geodesic distance, to a…
We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.
We propose and implement a broadband, compact, and low-cost wavefront sensing scheme by simply placing a thin diffuser in the close vicinity of a camera. The local wavefront gradient is determined from the local translation of the speckle…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of…
A family of polynomials linked to the set of the deltoid tangents and its associated algebraic hypersurfaces has been presented in recent years. In this paper we study some related maximising and free plane curves. We also analyse the…
Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the…
We present a simple and new method of constructing superdistributions on superspace over a Grassmann-Banach algebra, which close to the de Rham's ``currents'' defined as dual objects to differential forms. The paper also contains the…
Numerically computed with high accuracy are periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow of an incompressible inviscid fluid, under gravity, without the effects of surface…
We develop a notion of wavefront set aimed at characterizing in Fourier space the directions along which a distribution behaves or not as an element of a specific Besov space. Subsequently we prove an alternative, albeit equivalent…
In this paper, we show that ``$L$-complete null hypersurfaces'' (i.e. ruled hypersurfaces foliated by entirety of light-like lines) as wave fronts in the $(n+1)$-dimensional Lorentz-Minkowski space are canonically induced by hypersurfaces…