检索结果-内蒙古大学图书馆

Discontinuous Galerkin method for linear wave equations involving derivatives of the Dirac delta distribution

学校读者我要写书评

暂无评论

arXiv 2022年

作者： Field, Scott E. Gottlieb, Sigal Khanna, Gaurav McClain, Ed. Department of Mathematics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics Center for Scientific Computing & Visualization Research University of Massachusetts DartmouthMA02747 United States Department of Physics University of Rhode Island KingstonRI02881 United States

Linear wave equations sourced by a Dirac delta distribution δ(x) and its derivative(s) can serve as a model for many different phenomena. We describe a discontinuous Galerkin (DG) method to numerically solve such equations with source terms proportional to ∂nδ/∂xn. Despite the presence of singular source terms, which imply discontinuous or potentially singular solutions, our DG method achieves global spectral accuracy even at the source’s location. Our DG method is developed for the wave equation written in fully first-order form. The first-order reduction is carried out using a distributional auxiliary variable that removes some of the source term’s singular behavior. While this is helpful numerically, it gives rise to a distributional constraint. We show that a time-independent spurious solution can develop if the initial constraint violation is proportional to δ(x). Numerical experiments verify this behavior and our scheme’s convergence properties by comparing against exact solutions. Copyright © 2022, The Authors. All rights reserved.

关键词： Wave equations

Gravitational-wave template banks for novel compact binaries

学校读者我要写书评

暂无评论

Physical Review D 2024年第4期109卷 042005-042005页

作者： Stefano Schmidt Bhooshan Gadre Sarah Caudill Nikhef Science Park 105 1098 XG Amsterdam The Netherlands Institute for Gravitational and Subatomic Physics (GRASP) Utrecht University Princetonplein 1 3584 CC Utrecht The Netherlands Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA

We introduce a novel method to generate a bank of gravitational-waveform templates of binary black hole (BBH) mergers for matched-filter searches in LIGO, Virgo, and Kagra data. We derive a novel expression for the metric approximation to the distance between templates, which is suitable for precessing BBHs and/or systems with higher-order modes (HM) imprints and we use it to meaningfully define a template probability density across the parameter space. We employ a masked autoregressive normalizing flow model which can be conveniently trained to quickly reproduce the target probability distribution and sample templates from it. Thanks to the normalizing flow, our code takes a few hours to produce random template banks with millions of templates, making it particularly suitable for high-dimensional spaces, such as those associated to precession, eccentricity and/or HM. After validating the performance of our method, we generate a bank for precessing black holes and a bank for aligned-spin binaries with HMs: with only 5% of the injections with fitting factor below the target of 0.97, we show that both banks cover satisfactorily the space. Our publicly released code mbank will enable searches of high-dimensional regions of BBH signal space, hitherto unfeasible due to the prohibitive cost of bank generation.

关键词： Astronomical black holes Data analysis Gravitational wave detection

Interplay between numerical-relativity and black hole perturbation theory in the intermediate-mass-ratio regime

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Islam, Tousif Department of Physics University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) for quasi-circular non-spinning binary black holes in the intermediate mass ratio regime: 7 ≤ q ≤ 128 (where q := m1/m2 is the mass ratio of the binary with m1 and m2 being the mass of the primary and secondary black hole respectively). Initially, we conduct a comprehensive comparison between the dominant (,m) = (2,2) mode of the gravitational radiation obtained from state-of-the-art NR simulations and ppBHPT waveforms along with waveforms generated from recently developed NR-informed ppBHPT surrogate model, BHPTNRSur1dq1e4. This surrogate model employs a simple but non-trivial rescaling technique known as the α-β scaling to effectively match ppBHPT waveforms to NR in the comparable mass ratio regime. Subsequently, we analyze the amplitude and frequency differences between NR and ppBHPT waveforms to investigate the non-linearities, beyond adiabatic evolution, that are present during the merger stage of the binary evolution and propose fitting functions to describe these differences in terms of both the mass ratio and the symmetric mass ratio. Finally, we assess the performance of the α-β scaling technique in the intermediate mass ratio regime. Copyright © 2023, The Authors. All rights reserved.

关键词： Black holes

Robustness of Deep Learning Models to Precession in Gravitational-Wave Searches for Intermediate-Mass Black Hole Binaries

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Meijer, Quirijn van der Sluys, Marc Caudill, Sarah Department of Physics Utrecht University Princetonplein 1 Utrecht3584CC Netherlands Nikhef Science Park 105 Amsterdam1098XG Netherlands Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

Gravitational-wave searches for signals of intermediate-mass black hole binaries are hindered by detector glitches, as the increased masses from stellar-mass systems hinder current generation detectors from observing the inspiral phase of the binary evolution. This causes the waveforms to strongly resemble glitches, which are of similar duration within a similar frequency band. Additionally, precession of the orbital plane of a binary black hole may further warp signal waveforms. In this work three neural network-based classifiers for the task of distinguishing between signals and glitches are introduced, with each following different training regimes to study the impact of precession on the classifiers. Although all classifiers show highly accurate performance, the classifier found to perform best was trained following the principle of curriculum learning, where new examples are introduced only after the mastery of easier preceding examples. This classifier obtains an accuracy of approximately 95% on a synthetic test set consisting of signals and glitches injected into coloured noise from the O3 LIGO Hanford power spectral density. The model is compared to matched filtering, the state-of-the-art in modelled gravitational-wave searches, and analysed in search of particular sensitivities to black hole binary parameters. It was found that while the classifier is affected by the total mass of a system, the prediction of a misclassification is most strongly determined by visibility through the signal-to-noise ratio. The analysis of the three classifiers demonstrates that precession is handled differently depending on the training regime, meaning the architecture is not fully robust to precession and advancements can still be made through the development of training routines. Copyright © 2024, The Authors. All rights reserved.

关键词： Signal to noise ratio

Remnant black hole properties from numerical-relativity-informed perturbation theory and implications for waveform modeling

学校读者我要写书评

暂无评论

Physical Review D 2023年第6期108卷 064048-064048页

作者： Tousif Islam Scott E. Field Gaurav Khanna Department of Physics University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA Department of Physics and Center for Computational Research University of Rhode Island Kingston Rhode Island 02881 USA

During binary black hole (BBH) mergers, energy and momenta are carried away from the binary system as gravitational radiation. Access to the radiated energy and momenta allows us to predict the properties of the remnant black hole. We develop a Python package gw_remnant to extract the remnant mass, remnant spin, peak luminosity, and the final kick imparted on the remnant black hole from the gravitational waveforms. Using this package, we extract the remnant properties of the final black hole in case of nonspinning BBH mergers with mass ratios ranging from q=2.5 to q=1000 using waveform modes generated from BHPTNRSur1dq1e4, a recently developed numerical-relativity-informed surrogate model based on the black hole perturbation theory framework. We validate our results against the remnant properties estimated from numerical relativity (NR) surrogate models in the comparable mass-ratio regime and against recently available high-mass-ratio NR simulations at q=[15,32,64]. We find that our remnant property estimates computed from fluxes at future null infinity closely match the estimates obtained from the NR surrogate model of apparent horizon data. Using Gaussian process regression fitting methods, we train a surrogate model, BHPTNR_Remnant, for the properties of the remnant black hole arising from BBH mergers with mass ratios from q=2.5 to q=1000. Finally, we discuss potential improvements in the BHPTNRSur1dq1e4 waveform model when including remnant information. We make both the gw_remnant and BHPTNR_Remnant packages publicly available.

关键词： General relativity Gravitational waves

Interplay between numerical relativity and black hole perturbation theory in the intermediate-mass-ratio regime

学校读者我要写书评

暂无评论

Physical Review D 2023年第4期108卷 044013-044013页

作者： Tousif Islam Department of Physics University of Massachusetts Dartmouth 02747 MA United States Department of Mathematics University of Massachusetts Dartmouth 02747 MA United States Center for Scientific Computing and Visualization Research University of Massachusetts MA Dartmouth 02747 United States

We investigate the interplay between numerical relativity (NR) and point-particle black hole perturbation theory (ppBHPT) for quasi-circular nonspinning binary black holes in the intermediate mass ratio regime: 7≤q≤128 (where q≔m1/m2 is the mass ratio of the binary with m1 and m2 being the mass of the primary and secondary black hole respectively). Initially, we conduct a comprehensive comparison between the dominant (ℓ,m)=(2,2) mode of the gravitational radiation obtained from state-of-the-art NR simulations and ppBHPT waveforms along with waveforms generated from recently developed NR-informed ppBHPT surrogate model, BHPTNRSur1dq1e4. This surrogate model employs a simple but nontrivial rescaling technique known as the α−β scaling to effectively match ppBHPT waveforms to NR in the comparable mass ratio regime. Subsequently, we analyze the amplitude and frequency differences between NR and ppBHPT waveforms to investigate the nonlinearities, beyond adiabatic evolution, that are present during the merger stage of the binary evolution and propose fitting functions to describe these differences in terms of both the mass ratio and the symmetric mass ratio. Finally, we assess the performance of the α−β scaling technique in the intermediate mass ratio regime.

关键词： Gravitational waves

Learning orbital dynamics of binary black hole systems from gravitational wave measurements

学校读者我要写书评

暂无评论

Physical Review Research 2021年第4期3卷 043101-043101页

作者： Brendan Keith Akshay Khadse Scott E. Field Department of Mathematics University of Massachusetts Dartmouth Massachusetts 02747 USA and Center for Scientific Computing and Visualization Research University of Massachusetts Dartmouth Massachusetts 02747 USA

We introduce a gravitational waveform inversion strategy that discovers mechanical models of binary black hole (BBH) systems. We show that only a single time series of (possibly noisy) waveform data is necessary to construct the equations of motion for a BBH system. Starting with a class of universal differential equations parameterized by feed-forward neural networks, our strategy involves the construction of a space of plausible mechanical models and a physics-informed constrained optimization within that space to minimize the waveform error. We apply our method to various BBH systems including extreme and comparable mass ratio systems in eccentric and noneccentric orbits. We show that the resulting differential equations apply to time durations longer than the training interval, and relativistic effects, such as perihelion precession, radiation reaction, and orbital plunge, are automatically accounted for. The methods outlined here provide a data-driven approach to studying the dynamics of binary black hole systems.

关键词： General relativity equations & solutions Gravitational waves

Gravitational-wave template banks for novel compact binaries

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Schmidt, Stefano Gadre, Bhooshan Caudill, Sarah Nikhef Science Park 105 Amsterdam1098 XG Netherlands Utrecht University Princetonplein 1 Utrecht3584 CC Netherlands Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Visualization Research University of Massachusetts DartmouthMA02747 United States

We introduce a novel method to generate a bank of gravitational-waveform templates of binary black hole (BBH) mergers for matched-filter searches in LIGO, Virgo and Kagra data. We derive a novel expression for the metric approximation to the distance between templates, which is suitable for precessing BBHs and/or systems with higher-order modes (HM) imprints and we use it to meaningfully define a template probability density across the parameter space. We employ a masked autoregressive normalizing flow model which can be conveniently trained to quickly reproduce the target probability distribution and sample templates from it. Thanks to the normalizing flow, our code takes a few hours to produce random template banks with millions of templates, making it particularly suitable for high-dimensional spaces, such as those associated to precession, eccentricity and/or HM. After validating the performance of our method, we generate a bank for precessing black holes and a bank for aligned-spin binaries with HMs: with only 5% of the injections with fitting factor below the target of 0.97, we show that both banks cover satisfactorily the space. Our publicly released code mbank will enable searches of high-dimensional regions of BBH signal space, hitherto unfeasible due to the prohibitive cost of bank generation. Copyright © 2023, The Authors. All rights reserved.

关键词： Matched filters

Gravitational tuning forks and hierarchical triple systems

学校读者我要写书评

暂无评论

Physical Review D 2021年第8期103卷 L081501-L081501页

作者： Vitor Cardoso Francisco Duque Gaurav Khanna Department of Physics and Center for Scientific Computing and Visualization Research University of Massachusetts Darthmouth Massachusetts 02747 USA and Department of Physics The University of Rhode Island Kingston Rhode Island 02881

We study gravitational wave (GW) emission in the strong-field regime by a hierarchical triple system composed of a binary system placed in the vicinity of a supermassive black hole (SMBH). The LIGO-Virgo Collaboration recently reported evidence for coalescences with this dynamical origin. These systems are common in galactic centers and thus, are a target for the space-based LISA mission as well as other advanced detectors. Doppler shifts, aberration, lensing, and strong amplitude modulations are features present in the GW signal from these systems, built into our framework and with no need for phenomenological patches. We find that the binary can resonantly excite the quasinormal modes of the SMBH, as in the resonant excitation of two tuning forks with matching frequencies. The flux of energy crossing the SMBH horizon can be significant, when compared with that from standard extreme-mass-ratio inspirals. Therefore, these triple systems are excellent probes of strong-field physics and of the BH nature of compact objects.

关键词： Astrophysical studies of gravity General relativity equations & solutions Gravitational waves Classical black holes Galactic nuclei & quasars