相关论文: Wavelet Notes
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
We present a new adaptive circuit simulation algorithm based on spline wavelets. The unknown voltages and currents are expanded into a wavelet representation, which is determined as solution of nonlinear equations derived from the circuit…
In three dimensional scattering, the energy continuum wavefunction is obtained by utilizing two independent solutions of the reference wave equation. One of them is typically singular (usually, near the origin of configuration space). Both…
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these…
In this paper high resolution wave probe records are examined using wavelet techniques with a view to determining the sources and relative contributions of capillary wave energy along representative wind wave forms. Wavelets enable…
We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each…
Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We introduce Wave Arithmetic, a smooth analytical framework in which natural, integer, and rational numbers are represented not as discrete entities, but as integrals of smooth, compactly supported or periodic kernel functions. In this…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
Periodic surface structures are nowadays standard building blocks of optical devices. If such structures are illuminated by aperiodic time-harmonic incident waves as, e.g., Gaussian beams, the resulting surface scattering problem must be…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
A study of correlations in tractable multiparticle cascade models in terms of wavelets reveals many promising features. The selfsimilar construction of the wavelet basis functions and their multiscale localization properties provide a new…
In this paper a mathematical model is given for the scattering of an incident wave from a surface covered with microscopic small Helmholtz resonators, which are cavities with small openings. More precisely, the surface is built upon a…
The performance of basis sets made of numerical atomic orbitals is explored in density-functional calculations of solids and molecules. With the aim of optimizing basis quality while maintaining strict localization of the orbitals, as…
Regularization techniques for the numerical solution of inverse scattering problems in two space dimensions are discussed. Assuming that the boundary of a scatterer is its most prominent feature, we exploit as model the class of…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…