Related papers: Crystallographic Multiwavelets in $L^2(R^d)$
The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data…
Periodic multilayers are nowadays widely used to perform x-ray analysis in the soft x-ray range (photon energy lower than 1 keV). However, they do not permit to obtain high-resolution spectra like natural or synthetic crystals. Thus,…
We propose a simple, versatile and fast computational model tounderstand the deviations from the well-known Kolmogorov-Johnson-Mehl-Avrami kinetic theoryfound in metal recrystallization and amorphous semiconductor crystallization. Our model…
The main goal of this paper is to develop the MRA theory along with wavelet theory in L2(Qp). Generalized scaling sets are important in wavelet theory because it determine multiwavelet sets. Although the theory of scaling set and…
We develop a formalism for the calculation of the macroscopic dielectric response of composite systems made of particles of one material embedded periodically within a matrix of another material, each of which is characterized by a well…
Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived…
We present a preconditioning method for the multi-dimensional Helmholtz equation with smoothly varying coefficient. The method is based on a frame of functions, that approximately separates components associated with different singular…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
New orthonormal basis of eigenfunctions for the Vladimirov operator of p-adic fractional derivation is constructed. The map of p-adic numbers onto real numbers (p-adic change of variables) is considered. This map (for p=2) provides an…
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods…
Multivariate time series with long-dependence are observed in many applications such as finance , geophysics or neuroscience. Many packages provide estimation tools for univariate settings but few are addressing the problem of…
The refractive index of a matter is foundational to quantify the light-matter interaction of the medium. However, the classical description of refractive index is based on macroscopic homogenization and is limited to describing the local…
We consider a simple two-dimemsional harmonic lattice with random, independent and identically distributed masses. Using the methods of stochastic homogenization, we show that solutions with long wave initial data converge in an appropriate…
Chiral metasurfaces provide invaluable tools capable of controlling structured light required for biosensing, photochemistry, holography, and quantum photonics. Here we suggest and realize a universal strategy for controlling the chiral…
We introduce the multi-width of a lattice polytope and use this to classify and count all lattice tetrahedra with multi-width $(1,w_2,w_3)$. The approach used in this classification can be extended into a computer algorithm to classify…
We review the separation of variables for the Kowalevski top and for its generalization to the algebra o(4). We notice that the corresponding separation equations allow an interpretation of the Kowalevski top as a B2 integrable lattice.…
In the theory of resonant scattering, the double differential cross section involves the computation of a multifold integral of a 4-point correlation function, which generalizes the traditional 2-point correlation function of Van-Hove for…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
We discuss the behavior of a crystalline surface with a disordered substrate. We focus on the possible existence of a {\em super-rough} glassy phase, with height-height correlation functions which vary as the square logarithm of the…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…