Related papers: Diffraction of return time measures
Given $(M,g)$, a compact connected Riemannian manifold of dimension $d \geq 2$, with boundary $\partial M$, we consider an initial boundary value problem for a fractional diffusion equation on $(0,T) \times M$, $T>0$, with time-fractional…
We report on measurements and modeling of the mode structure of tunable Fabry-P\'erot optical microcavities with imperfect mirrors. We find that non-spherical mirror shape and finite mirror size lead to loss, mode deformation, and shifted…
There is increased interest in time-dependent (non-autonomous) Hamiltonians, stemming in part from the active field of Floquet quantum materials. Despite this, dispersive time-decay bounds, which reflect energy transport in such systems,…
In this paper we construct an analytical separation (diagonalization) of the full (minimal coupling) Dirac equation into particle and antiparticle components. The diagonalization is analytic in that it is achieved without transforming the…
We are concerned with the inverse scattering problem of recovering an inhomogeneous medium by the associated acoustic wave measurement. We prove that under certain assumptions, a single far-field pattern determines the values of a…
We show that a time-reversed formulation of Huygens-Kirchhoff diffraction can be used to deduce the transverse and longitudinal fields of a Gaussian laser beam, starting from a simple assumption of a Gaussian beam profile in the far field.…
This paper presents a simple and effective wideband method for the determination of material properties, such as the complex index of refraction and the complex permittivity and permeability. The method is explicit (non-iterative) and…
The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type-I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly…
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements used are the statistical moments of the realizations of single point data $u(x_0,t,\omega).$ We build the…
Eigenvalues and eigenfunctions of Mathieu's equation are found in the short wavelength limit using a uniform approximation (method of comparison with a `known' equation having the same classical turning point structure) applied in Fourier…
We present an algorithm for coherent diffractive imaging with phaseless measurements. It treats the forward model as a combination of coherent and incoherent waves. The algorithm reconstructs absorption and phase contrast that quantifies…
We consider the possibility that most of the reflection component, observed in the hard X-ray spectra of Seyfert galaxies, could be formed on an extended medium, at large distance from the central source of primary radiation (e.g. on a…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
Dispersive time-decay estimates are proved for a one-parameter family of one-dimensional Dirac Hamiltonians with dislocations; these are operators which interpolate between two phase-shifted massive Dirac Hamiltonians at $x=+\infty$ and…
Extracting information on the three-dimensional structure of hadrons from transverse-momentum data is a challenging task, requiring the separation of perturbative contributions under QCD control from genuinely non-perturbative effects,…
When a signal is emitted from a source, recorded by an array of transducers, time reversed and re-emitted into the medium, it will refocus approximately on the source location. We analyze the refocusing resolution in a high frequency,…
Let $D$ be an unbounded domain in $\RR^d$ with $d\geq 3$. We show that if $D$ contains an unbounded uniform domain, then the symmetric reflecting Brownian motion (RBM) on $\overline D$ is transient. Next assume that RBM $X$ on $\overline D$…
We regard the classic Thue--Morse diffraction measure as an equilibrium measure for a potential function with a logarithmic singularity over the doubling map. Our focus is on unusually fast scaling of the Birkhoff sums (superlinear) and of…