Related papers: Diffraction of return time measures
We present measurements of transmission and reflection spectra of a microwave photonic crystal composed of 874 metallic cylinders arranged in a triangular lattice. The spectra show clear evidence of a Dirac point, a characteristic of a…
Time-reflection occurs when a wave is propagating in a medium undergoing a large and abrupt change in its properties: the original wave splits into a time-refracted wave and a time-reflected wave, each displaying different features. The…
Bragg diffraction is comparable to a hard-wall reflection if the Bragg condition is exactly fulfilled. However, in a neutron interferometer in the gravitational field (COW experiment) this is not the case and the momentum transfers should…
We present a unified approach to extensions of Bourgain's Double Recurrence Theorem and Bourgain's Return Times Theorem to integer parts of the Kronecker sequence, emphasizing stopping times and metric entropy. Specifically, we prove the…
A novel test of time-reversal invariance in proton-deuteron scattering is planned as an internal target transmission experiment at the cooler synchrotron COSY. The P-even, T-odd observable is the polarization correlation $A_{y,xz}$ of the…
The diffraction spectrum of the dart-rhombus random tiling of the plane is derived in rigorous terms. Using the theory of dimer models, it is shown that it consists of Bragg peaks and an absolutely continuous diffuse background, but no…
For each integer $n\ge 1$, denote by $T_{n}$ the map $x\mapsto nx\mod 1$ from the circle group $\mathbb{T} = \mathbb{R}/\mathbb{Z}$ into itself. Let $p,q\ge 2$ be two multiplicatively independent integers. Using Baire Category arguments, we…
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…
This article is concerned with the inverse problem on determining the temporal component of the source term in a coupled system of time-fractional diffusion equations by single point observation. Under a non-degeneracy condition on the…
This work addresses the problem of uniquely determining a rotational motion from continuous time-dependent measurements within the frameworks of parallel-beam and diffraction tomography. The motivation stems from the challenge of imaging…
We investigate a family of Riesz products and show that they can be regarded as diffraction measures of generalized Thue-Morse sequences, possibly over an infinite alphabet. These measures are closely related to the dynamical system arising…
When a plane electromagnetic wave impinges upon a diffraction grating or other periodic structures, reflected and transmitted waves propagate away from the structure in different radiation channels. A diffraction anomaly occurs when the…
Consider the extended hull of a weak model set together with its natural shift action. Equip the extended hull with the Mirsky measure, which is a certain natural pattern frequency measure. It is known that the extended hull is a…
Diffraction imaging of non-equilibrium dynamics at atomic resolution is becoming possible with X-ray free-electron lasers. However, there are unresolved problems with applying this method to objects that are confined in only one dimension.…
The Thue-Morse system is a paradigm of singular continuous diffraction in one dimension. Here, we consider a planar system, constructed by a bijective block substitution rule, which is locally equivalent to the squiral inflation rule. For…
Suppose that T is a map of the Wiener space into itself, of the following type: T=I+u where u takes its values in the Cameron-Martin space H. Assume also that u is a finite sum of H-valued multiple Ito-Wiener integrals. In this work we…
Diffusion models have established new state of the art in a multitude of computer vision tasks, including image restoration. Diffusion-based inverse problem solvers generate reconstructions of exceptional visual quality from heavily…
Let $\mu$ be a probability measure (or corresponding random variable) such that all moments $\mu_n$ exist. Knowledge of the moments is not sufficient to determine infinite divisibility of the measure; we show also that infinitely divisible,…
The main goal of this work is to provide a description of transitions from uniform to non-uniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of…
We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression…