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Periodic standing-wave approximation: Overview and three-dimensional scalar models

Andrade, Zeferino and Beetle, Christopher and Blinov, Alexey and Bromley, Benjamin and Burko, Lior M. and Cranor, Maria and Owen, Robert and Price, Richard H. (2004) Periodic standing-wave approximation: Overview and three-dimensional scalar models. Physical Review D, 70 (6). Art. No. 064001. ISSN 2470-0010. doi:10.1103/PhysRevD.70.064001.

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The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important features of this method presented here are: (i) the mathematical nature of the "mixed" partial differential equations to be solved, (ii) the meaning of standing waves in the method, (iii) computational difficulties, and (iv) the "effective linearity" that ultimately justifies the approximation. The method is applied to three-dimensional nonlinear scalar model problems, and the numerical results are used to demonstrate extraction of the outgoing solution from the standing-wave solution, and the role of effective linearity.

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Additional Information:©2004 The American Physical Society. (Received 30 September 2003; revised 10 May 2004; published 1 September 2004) We gratefully acknowledge the support of the National Science Foundation under Grants No. PHY9734871 and No. PHY0244605. We also thank the University of Utah Research Foundation for support during this work. We thank Christopher Johnson and the Scientific Computing and Imaging Institute of the University of Utah for time on their supercomputers to produce the non-FFT results of Sec. III. We have also made use of supercomputing facilities provided by funding from JPL Institutional Computing and Information Services and the NASA Offices of Earth Science, Aeronautics, and Space Science. We thank John Friedman and Kip Thorne for helpful discussions and suggestions about this work.
Subject Keywords:binary stars; gravitational waves; Einstein field equations; partial differential equations; numerical analysis
Issue or Number:6
Record Number:CaltechAUTHORS:ANDprd04
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9097
Deposited By: Archive Administrator
Deposited On:26 Oct 2007
Last Modified:08 Nov 2021 20:56

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