Related papers: Wavelet Analysis of One-Dimensional Cosmological D…
The nonlinear matter power spectrum in cosmology describes how matter density fluctuations vary with scale in the universe, providing critical insights into large-scale structure formation. The matter power spectrum includes both smooth…
We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multi-fractal detrended fluctuation analysis (MF-DFA) method and is quite…
Modeling the mass distribution of galaxy-scale strong gravitational lenses is a task of increasing difficulty. The high-resolution and depth of imaging data now available render simple analytical forms ineffective at capturing lens…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
The Delta-variance analysis is an efficient tool for measuring the structural scaling behaviour of interstellar turbulence in astronomical maps. In paper I we proposed essential improvements to the Delta-variance analysis. In this paper we…
The most popular tools for analysing the large scale distribution of galaxies are second-order spatial statistics such as the two-point correlation function or its Fourier transform, the power spectrum. In this review, we explain how our…
The large-scale structure of the universe is comprised of virialized blob-like clusters, linear filaments, sheet-like walls and huge near empty three-dimensional voids. Characterizing the large scale universe is essential to our…
We develop an exact wavelet transform on the three-dimensional ball (i.e. on the solid sphere), which we name the flaglet transform. For this purpose we first construct an exact transform on the radial half-line using damped Laguerre…
Weak lensing provides a direct measure of the distribution of mass in the universe, and is therefore a uniquely powerful probe of dark matter. Weak lensing can also be used to measure the twin phenomenon of dark energy, via its effect upon…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
We propose a new, simple, dedicated X-ray mission to measure the power spectrum of density fluctuations in the Universe, by accurately mapping the X-ray background on the whole sky on scales of arounf one sq deg. Since the method relies on…
In an undulant universe, cosmic expansion is characterized by alternating periods of acceleration and deceleration. We examine cosmologies in which the dark-energy equation of state varies periodically with the number of e-foldings of the…
We investigate the application of volume statistics to probe the distribution of underdense regions in the large-scale structure of the Universe. This statistic measures the distortion of Eulerian volume elements relative to Lagrangian ones…
In this letter, it is shown that by measuring quantities like density variance in the present state of an analogue universe one can assess information about its history due to the mere existence of small anisotropies in earlier times, here…
We explore a variety of statistics of clusters selected with cosmic shear measurement by utilizing both analytic models and large numerical simulations. We first develop a halo model to predict the abundance and the clustering of weak…
An exact solution of the homogeneous wave equation, which was found previously, is treated from the point of view of continuous wavelet analysis (CWA). If time is a fixed parameter, the solution represents a new multidimensional mother…
Fractal structures naturally emerge in quantum systems whose initial states exhibit spatial discontinuities, a phenomenon first identified by Berry in the paradigmatic case of a particle confined in an infinite potential well. While…
The cosmic web structure is studied with the concepts and methods of fractal geometry, employing the adhesion model of cosmological dynamics as a basic reference. The structures of matter clusters and cosmic voids in cosmological N-body…
Global and local regularities of functions are analyzed in anisotropic function spaces, under a common framework, that of hyperbolic wavelet bases. Local and directional regularity features are characterized by means of global quantities…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…