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White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an adaptive convolution of Gaussian white noise with a real-space transfer function kernel together with an adaptive multi-grid Poisson solver is used to generate displacements and velocities following first- or second-order Lagrangian perturbation theory (2LPT).
Abstract: We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological 'zoom-in' simulations. The method uses an adaptive convolution of Gaussian white noise with a real-space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first- (1LPT) or second-order Lagrangian perturbation theory (2LPT). The new algorithm achieves rms relative errors of the order of 10{sup -4} for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier-space-induced interference ringing. An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is introduced which has identical Fourier-space behaviour as traditional approaches. Using a suite of re-simulations of a galaxy cluster halo our real-space-based approach is found to reproduce correlation functions, density profiles, key halo properties and subhalo abundances with per cent level accuracy. Finally, we generalize our approach for two-component baryon and dark-matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory. For initial baryon density fields, it is suggested to use the local Lagrangian approximation in order to generate a density field for mesh-based codes that is consistent with the Lagrangian perturbation theory instead of the current practice of using the Eulerian linearly scaled densities.

564 citations

Journal ArticleDOI
TL;DR: In this article, the power of tests for distinguishing between fractional Gaussian noise and white noise of a first-order autoregressive process was investigated, based on the beta-optimal principle, local optimality and rescaled range test.
Abstract: SUMMARY We consider the power of tests for distinguishing between fractional Gaussian noise and white noise of a first-order autoregressive process. Our tests are based on the beta-optimal principle (Davies, 1969), local optimality and the rescaled range test.

548 citations

Book
01 Jul 1992
TL;DR: Book on detection, estimation and modulation theory, Part 3, Gaussian and radar-sonar signals in noise, covering point targets, random process and scatter channels.
Abstract: Book on detection, estimation and modulation theory, Part 3, Gaussian and radar-sonar signals in noise, covering point targets, random process and scatter channels

534 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduce an approach to study singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths.
Abstract: We introduce an approach to study certain singular partial differential equations (PDEs) which is based on techniques from paradifferential calculus and on ideas from the theory of controlled rough paths. We illustrate its applicability on some model problems such as differential equations driven by fractional Brownian motion, a fractional Burgers-type stochastic PDE (SPDE) driven by space-time white noise, and a nonlinear version of the parabolic Anderson model with a white noise potential.

533 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537