<html><head><meta http-equiv="Content-Type" content="text/html charset=us-ascii"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br><div><div>On 6 May 2017, at 08:49, Gwyneth Allwright <<a href="mailto:allgwy001@myuct.ac.za">allgwy001@myuct.ac.za</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div dir="ltr"><div>Hi Ian,</div><div><br></div>I've been finding SimulationTools very useful for looking at the results of my Cactus simulations. I just have a question about the function called "Frequency", which is used in the context of gravitational waveforms. How is this frequency defined? Is it an angular frequency? I don't know how to interpret the negative values I'm getting.</div></blockquote><div><br></div><div>Hi Gwyneth,</div><div><br></div><div>There is actually some documentation for SimulationTools. You can get the brief usage message for Frequency by typing</div><div><br></div><div><div><span class="Apple-tab-span" style="white-space:pre"> </span>?Frequency</div><div><br></div><div>in the notebook. This tells you:</div><div><br></div><div><span class="Apple-tab-span" style="white-space:pre"> </span>Frequency[d] returns the first derivative of the complex phase of d.</div></div><div><br></div><div>That's maybe not as detailed as it could be.</div><div><br></div><div>So, if d is a DataTable of complex numbers (i.e. representing a list of {t, f(t)} pairs), Frequency[d] is the time derivative of arg f(t). </div><div><br></div><div>So yes, it is an angular frequency. The reason it is negative is probably because the orbital angular velocity is positive, and the dominant GW emission is proportional to Exp[-2 I omOrb t]. So omGW = - 2 omOrb. Usually I plot - Frequency[h].</div><div><br></div></div><div apple-content-edited="true">
<div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div style="color: rgb(0, 0, 0); letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><div>-- </div><div>Ian Hinder</div><div><a href="http://members.aei.mpg.de/ianhin">http://members.aei.mpg.de/ianhin</a></div></div></div></div></div>
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