Related papers: Direct power spectral density estimation from stru…
The study of third-order statistics in large-scale structure analyses has been hampered by the increased complexity of bispectrum estimators (compared to power spectra), the large dimensionality of the data vector, and the difficulty in…
Here, we present a new method to evaluate the expectation value of the power spectrum of a time series. A statistical approach is adopted to define the method. After its demonstration, it is validated showing that it leads to the known…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
The statistics of signal increments are commonly used in order to test for possible intermittent properties in experimental or synthetic data. However, for signals with steep power spectra [i.e., $E(\omega) \sim \omega^{-n}$ with $n \geq…
A theory of non-homogeneous turbulence is developed and is applied to boundary-free shear flows. The theory introduces assumptions of inner and outer similarity for the non-homogeneity of two-point statistics and predicts power law scalings…
We present a systematic study of the influence of different forcing types on the statistical properties of supersonic, isothermal turbulence in both the Lagrangian and Eulerian frameworks. We analyse a series of high-resolution,…
The classical structure-function (SF) method in fully developed turbulence or for scaling processes in general is influenced by large-scale energetic structures, known as infrared effect. Therefore, the extracted scaling exponents…
In this paper, a new method based on Greens function theory and Fourier transform analysis has been proposed for calculating band structure with high accuracy and low processing time. This method utilizes sampling of potential energy in…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
A short, abrupt increase in energy injection rate into steady strongly-driven rotating turbulent flow is used as a probe for energy transfer in the system. The injected excessive energy is localized in time and space and its spectra differ…
The amplitude of density turbulence in the extended solar corona, especially near the dissipation scale, impinges on several problems of current interest. Radio sources observed through the turbulent solar wind are broadened due to…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…
Auto- and cross-spectral density functions for dynamic {random} fields and power are derived. These are based on first- and second-order Pad\'{e} approximants of correlation functions expanded in terms of spectral moments. The second-order…
The Fourier power spectrum is one of the most widely used statistical tools to analyze the nature of magnetohydrodynamic turbulence in the interstellar medium. Lazarian & Pogosyan (2004) predicted that the spectral slope should saturate to…
The spatio-temporal dynamics of the deformation of a vibrated plate is measured by a high speed Fourier transform profilometry technique. The space-time Fourier spectrum is analyzed. It displays a behavior consistent with the premises of…
We develop novel methods to compute auto-correlation functions, or power spectral densities, for chaotic dynamical systems generated by an inverse method whose starting point is an invariant distribution and a two-form. In general, the…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
Analytical contact mechanics theories depend on surface roughness through the surface roughness power spectrum. In the present study, we evaluated the usability of various experimental methods for studying surface roughness. Our findings…
In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the…