<html><head></head><body><div class="ydp49fd74ddyahoo-style-wrap" style="font-family:Helvetica Neue, Helvetica, Arial, sans-serif;font-size:16px;"><div dir="ltr" data-setdir="false">Hello everyone,</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Could someone please clarify the shift evolution equation implemented in ML_BSSN?</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false">Just looking at the parameter file it seems like it is:</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><div dir="ltr" data-setdir="false"> <div><div dir="ltr" data-setdir="false"> d/dt beta^i = <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">shiftGammaCoeff</span></span> Xt^i - betaDriver alpha^shiftAlphaPower beta^i</div></div><br></div>looking at <span>McLachlan_BSSN.m (for GammaDriver and without advection and dissipation), I think it is:</span></div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt beta^a = <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">shiftGammaCoeff <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">alpha^shiftAlphaPower B^a</span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">with</span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt B^a = d/dt Xt^a - <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">betaDriver B^a</span></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></span></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Whereas looking at Alcubierre's book Eq 4.3.33 and 4.3.34 I would expect it to be </span></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></span></span></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><div><div dir="ltr" data-setdir="false" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt beta^i = B^i</div><div dir="ltr" data-setdir="false" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">with</div><div dir="ltr" data-setdir="false" style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt B^i = <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">shiftGammaCoeff </span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">alpha^shiftAlphaPower </span></span>d/dt Xt^a - betaDriver B^a</div><div><br></div></div><div dir="ltr" data-setdir="false">on the McLachlan webpage: <a href="https://www.cct.lsu.edu/~eschnett/McLachlan/" rel="nofollow" target="_blank">https://www.cct.lsu.edu/~eschnett/McLachlan/</a></div><div dir="ltr" data-setdir="false">the link to describe the Gamma driver shift condition <a href="http://grwiki.physics.ncsu.edu/wiki/Shift_Conditions" rel="nofollow" target="_blank">http://grwiki.physics.ncsu.edu/wiki/Shift_Conditions</a> doesn't work but looking at the 2019 version on the wayback machine the evolution described is</div><div dir="ltr" data-setdir="false"><br></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt beta^a = (3/4) B^a</div><div dir="ltr" data-setdir="false">with</div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"> </span></span>d/dt B^a = d/dt <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Xt^a - <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">betaDriver B^a</span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">where here (and in Alcubierre) d/dt = partial_t - beta^c partial_c. Does the McLachlan code have that second term <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">beta^c partial_c </span></span>?</span></span></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></span></span></span></span></div><div dir="ltr" data-setdir="false">This is confusing me, so what is actually implemented? Where are the parameters <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">shiftGammaCoeff</span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">, betaDriver and shiftAlphaPower in the evolution equation? And these are all constant positive reals right? In Alcubierre's book xi (that I think is <span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">shiftGammaCoeff</span></span>) can be function of space and the lapse.</span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><br></span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Thank you,</span></span></div><div dir="ltr" data-setdir="false"><span><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;">Robyn</span></span></div></span></span></span></span></span></div></div></body></html>