<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On 1 Feb 2012, at 05:02, Eloisa Bentivegna wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div>On Feb 1, 2012, at 3:12 AM, Jose Fiestas Iquira wrote:<br><br><blockquote type="cite">Dear all,<br></blockquote><blockquote type="cite">I am using WeylScal for BH binary coalescence, and I am obtaining 'weylscal4::psi4r...' and 'weylscal4::psi4i ...' files, with which I could plot the wave against distance/time.<br></blockquote><blockquote type="cite">Could somebody advise me how to get the energy emission due to grav. waves from the WeylScal output? I would like to construct a plot: GW Energy vs. distance/time.<br></blockquote><br>Hi Jose,<br><br>there's a couple of things to keep in mind:<br><br>1) In broad terms, there is no notion of gravitational-wave energy density; one can at best associate a mass with the whole spatial hypersurface, but not state how much of this is in gravitational waves or where it is localized;<br>2) Under reasonable assumptions, the radiated power at infinity can be expressed in terms of the Weyl scalars. You'd probably best start learning about this is in one of the numerical-relativity textbooks: either section 8.9 of <<a href="http://books.google.de/books?id=4hDvRvVJeEIC&dq=alcubierre&hl=de&sa=X&ei=GBopT--LC87ItAbI-b3FAQ&ved=0CDIQ6AEwAA">http://books.google.de/books?id=4hDvRvVJeEIC&dq=alcubierre&hl=de&sa=X&ei=GBopT--LC87ItAbI-b3FAQ&ved=0CDIQ6AEwAA</a>> or section 9.4 of <<a href="http://books.google.de/books?id=dxU1OEinvRUC&dq=baumgarte&hl=de&source=gbs_navlinks_s">http://books.google.de/books?id=dxU1OEinvRUC&dq=baumgarte&hl=de&source=gbs_navlinks_s</a>> (notice that this is still a function of time only -- no localization);<br></div></blockquote><div><br></div><div>Hi Jose,</div><div><br></div><div>Once you have an understanding of the theory, you could also read section II.A in <a href="http://arXiv.org/abs/arXiv:0804.4184">http://arXiv.org/abs/arXiv:0804.4184</a> which describes how this is usually done for NR calculations from the spherical harmonic modes. To compute the strain derivative you will probably want to use the method of <a href="http://arXiv.org/abs/arXiv:1006.1632">http://arXiv.org/abs/arXiv:1006.1632</a>. Before using any results of calculations such as this to draw physical conclusions, you also need to make sure that you have accurate enough simulation data. At a minimum, you should perform the simulation at different grid spacings and compare your final answer computed from each to get an idea of the effect. It is also important to extrapolate the results to infinite radius as discussed in the first reference above, because the energy flux is only defined asymptotically, and the results could be very different at different extraction radii.</div><div><br></div></div><div>
<span class="Apple-style-span" style="font-size: 12px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div>-- </div><div>Ian Hinder</div><div><a href="http://numrel.aei.mpg.de/people/hinder">http://numrel.aei.mpg.de/people/hinder</a></div></div></span></div></span></div></span>
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