Related papers: Direct power spectral density estimation from stru…
The estimation of power spectra from LDA data provides signal processing challenges for fluid dynamicists for several reasons: acquisition is dictated by randomly arriving particles, the registered particle velocities tend to be biased…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…
Modeling the large-scale structure of the universe on nonlinear scales has the potential to substantially increase the science return of upcoming surveys by increasing the number of modes available for model comparisons. One way to achieve…
A strategy is developed for writing the time-dependent Schr\"{o}dinger Equation (TDSE), and more generally the Dyson Series, as a convolution equation using recursive Fourier transforms, thereby decoupling the second-order integral from the…
The Eulerian cosmological fluid equations are used to study the nonlinear mode coupling of density fluctuations. We evaluate the second-order power spectrum including all four-point contributions. In the weakly nonlinear regime we find that…
A statistical model of discrete finite length random processes with negative power law spectral densities is presented. The definition of terms is followed by a description of the spectral density trend. An algorithmic construction of…
Energy degeneracy in physical systems may be induced by symmetries of the Hamiltonian, and the resonance of degeneracy states in carbon nanostructures can effectively enhance the stability of the system. Combining the octet rule, we…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…
We develop a method for estimating the shear power spectra from weak lensing observations and test it on simulated data. Our method describes the shear field in terms of angular power spectra and cross correlation of the two shear modes…
The solar photosphere provides us with a laboratory for understanding turbulence in a layer where the fundamental processes of transport vary rapidly and a strongly superadiabatic region lies very closely to a subadiabatic layer. Our tools…
Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
This article consists of a brief discussion of the energy density over time or frequency that is obtained with the wavelet transform. Also an efficient algorithm is suggested to calculate the continuous transform with the Morlet wavelet.…
The two-point summary statistics is one of the most commonly used tools in the study of cosmological structure. Starting from the theoretical power spectrum defined in the 3D volume and obtained via the process of ensemble averaging, we…
A new method for calculation of band structure has been proposed based on the Green's function theory and local sampling. Potential energy in the Hamiltonian of Schrodinger's equation is approximated with a series of sampled Dirac delta…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
We study the power spectrum of galaxies in redshift space, with third order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e. the galaxy density is sampled from some…
Ocean turbulence plays a key role in shaping large-scale circulation, heat uptake, and biogeochemical processes. The kinetic energy (KE) wavenumber spectrum is a fundamental diagnostic, quantifying how KE is distributed across spatial…
The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these…