Related papers: Scaling of the Thue-Morse diffraction measure
Three problems for a discrete analogue of the Helmholtz equation are studied analytically using the plane wave decomposition and the Sommerfeld integral approach. They are: 1) the problem with a point source on an entire plane; 2) the…
The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…
Infinite products associated with the $\pm 1$ Thue-Morse sequence whose value is rational or algebraic irrational have been studied by several authors. In this short note we prove three new infinite product identities involving ${\pi}$,…
Meyer sets have a relatively dense set of Bragg peaks and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in…
Evaluating the Kirchhoff-Fresnel diffraction integral is essential in studying wave effects in astrophysical lensing, but is often intractable because of the highly oscillatory integrated. A recent breakthrough was made by exploiting the…
Signal scaling is a fundamental operation of practical importance in which a signal is enlarged or shrunk in the coordinate direction(s). Scaling or magnification is not trivial for signals of a discrete variable since the signal values may…
We extend the analysis of [Zhou and Sornette, Physica D 165, 94-125, 2002] showing statistically significant log-periodic corrections to scaling in the moments of the energy dissipation rate in experiments at high Reynolds number ($\approx…
Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest…
The method of iterated conformal maps allows to study the harmonic measure of Diffusion Limited Aggregates with unprecedented accuracy. We employ this method to explore the multifractal properties of the measure, including the scaling of…
It is shown that the partial amplitudes of the pure point part of the diffraction spectrum of an aperiodic Delone point pattern of finite local complexity are linked by a set of linear constraints. These relations can be explicitly derived…
Ellipsometry is a technique whereby the measurement of the two orthogonal polarization components of light reflected at glancing incidence allows a characterization of the optical properties of a material at a particular frequency.…
We show that diffraction intensity into the First Order Laue Zone (FOLZ) of a crystal can have a strong azimuthal dependence, where this FOLZ ring appears solely because of unidirectional atom position modulation. Such a modulation was…
We examine the total mixed scalar curvature of a fixed distribution as a functional of a pseudo-Riemannian metric. We develop variational formulas for quantities of extrinsic geometry of the distribution to find the critical points of this…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
We consider the representation of the value of an optimal stopping problem of a linear diffusion as an expected supremum of a known function. We establish an explicit integral representation of this function by utilizing the explicitly…
Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…
We study the measurement of transverse diffusion through beam echoes. We revisit earlier observations of echoes in RHIC and apply an updated theoretical model to these measurements. We consider three possible models for the diffusion…
In this paper we analyze a dynamic recursive extension of the (static) notion of a deviation measure and its properties. We study distribution invariant deviation measures and show that the only dynamic deviation measure which is law…
We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ${\mathbb R}^d$ generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The…
We have begun a large-scale photometric survey of nearby open clusters and star-forming regions, the Monitor project, aiming to measure time-series photometry for >10,000 cluster members over >10 sq.deg of sky, to find low-mass eclipsing…