On Tue, 30 Jul 2002, Allan Rae wrote: > On Thu, 18 Jul 2002, Andre Poenitz wrote: > [...] > > Jean-Marc: Should I simply commit it if it works? This really seems to be > > needed... > > It seems this patch was committed and maybe some other stuff too. > Anyway, something has changed so the behaviour when now loading my > scary_eqns.lyx file (the one I had previously loaded and saved as > version 220 before this patch arrived -- hmm... maybe I did that with > 1.3.0cvs?) is that lyx tries to use all the memory on the machine > climbing to about 380MB in size before being killed off by the OOM > handler.
I probably should have attached this yesterday. It is different to the one I sent earlier -- this one was converted with an early 1.2.1cvs which wouldn't have been much different to 1.2.0. That is, it was converted before André's recent patch. I haven't had time to test further to see where all the time and memory is being spent. Allan. (ARRae)
#LyX 1.2 created this file. For more info see http://www.lyx.org/ \lyxformat 220 \textclass article \begin_preamble \usepackage{amsfonts} \end_preamble \language english \inputencoding latin1 \fontscheme default \graphics default \paperfontsize default \spacing single \papersize Default \paperpackage a4 \use_geometry 0 \use_amsmath 1 \use_natbib 0 \use_numerical_citations 0 \paperorientation portrait \secnumdepth 3 \tocdepth 3 \paragraph_separation indent \defskip medskip \quotes_language english \quotes_times 2 \papercolumns 1 \papersides 1 \paperpagestyle default \layout Title An Efficient Method for Fully Relativistic Simulations of Coalescing Binary Neutron Stars \layout Author Walter Landry \newline Physics Dept., University of Utah, SLC, UT 84112 \layout Date \SpecialChar ~ \layout Standard These are all the equations from Walter's PhD thesis which he prepared using LyX. \layout Standard \begin_inset Formula \begin{equation} ds^{2}=g_{\mu \nu }dx^{\mu }dx^{\nu }=-\alpha ^{2}dt^{2}+\gamma _{ij}(dx^{i}+\beta ^{i}dt)(dx^{j}+\beta ^{j}dt).\label{first}\end{equation} \end_inset \begin_inset Formula \begin{equation} \frac{\partial \gamma _{ij}}{\partial t}=-2\alpha K_{ij}+\nabla _{i}\beta _{j}+\nabla _{j}\beta _{i},\label{g dot}\end{equation} \end_inset \layout Standard \begin_inset Formula \begin{eqnarray} \frac{\partial K_{ij}}{\partial t}=-\nabla _{i}\nabla _{j}\alpha +K_{lj}\nabla _{i}\beta ^{l}+K_{il}\nabla _{j}\beta ^{l}+\beta ^{l}\nabla _{l}K_{ij} & & \nonumber \\ +\alpha \left[R_{ij}-2K_{il}K_{j}^{l}+KK_{ij}-S_{ij}-\frac{1}{2}\gamma _{ij}(\rho +-S)\right]. & & \label{K dot} \end{eqnarray} \end_inset \layout Standard \begin_inset Formula \[ \Gamma _{jk}^{i}=\frac{\gamma ^{il}}{2}(\gamma _{lj,k}+\gamma _{lk,j}+\gamma _{jk,l}),\] \end_inset \begin_inset Formula \begin{eqnarray} R_{ij}=\frac{1}{2}\gamma ^{kl} & \left[\gamma _{kj,il}+\gamma _{il,kj}-\gamma _{kl,ij}-\gamma _{ij,kl}\right. & \nonumber \\ & \left.+2\left(\Gamma _{il}^{m}\Gamma _{mkj}-\Gamma _{ij}^{m}\Gamma _{mkl}\right)\right]. & \label{Ricci} \end{eqnarray} \end_inset \begin_inset Formula \[ n_{\mu }=(-\alpha ,0,0,0).\] \end_inset \begin_inset Formula \begin{eqnarray*} \rho & = & 8\pi n_{\mu }n_{\nu }T^{\mu \nu }=8\pi \alpha ^{2}T^{tt},\\ J^{i} & = & -8\pi n_{\mu }\gamma _{j}^{i}T^{\mu j},\\ S_{ij} & = & 8\pi \gamma _{ik}\gamma _{jl}T^{kl}, \end{eqnarray*} \end_inset \begin_inset Formula \[ S=\gamma ^{ij}S_{ij}.\] \end_inset \layout Standard \begin_inset Formula \begin{equation} R+K^{2}-K_{ij}K^{ij}=2\rho ,\label{Energy}\end{equation} \end_inset \begin_inset Formula \begin{equation} \nabla _{j}\left(K^{ij}-\gamma ^{ij}K\right)=J^{i}.\label{Momentum}\end{equation} \end_inset \layout Standard \begin_inset Formula \[ K^{ij}=\psi ^{-10}\left(\widetilde{A}^{ij}+\left(lX\right)^{ij}\right)+\frac{1}{3}\psi ^{-4}\widetilde{\gamma }^{ik}\mathrm{Tr}K,\] \end_inset \begin_inset Formula \[ \left(lX\right)^{ij}=\widetilde{\nabla }^{i}X^{j}+\widetilde{\nabla }^{j}X^{i}-\frac{2}{3}\widetilde{\gamma }^{ij}\widetilde{\nabla }_{k}X^{k},\] \end_inset \begin_inset Formula \begin{eqnarray} -8\widetilde{\nabla }^{2}\psi & = & -\widetilde{R}\psi -\frac{2}{3}\left(trK\right)^{2}\psi ^{5}\nonumber \\ & & +\left(\widetilde{A}^{ij}+\left(lX\right)^{ij}\right)^{2}\psi ^{-7}+2\rho \psi ^{5},\label{phi constraint}\\ \widetilde{\nabla }^{2}X^{i} & + & \frac{1}{3}\widetilde{\nabla }^{i}\widetilde{\nabla }_{j}X^{j}+\widetilde{R}_{j}^{i}X^{j}\nonumber \\ & = & J^{i}\psi ^{10}-\widetilde{\nabla }_{j}\widetilde{A}^{ij}+\frac{2}{3}\psi ^{6}\widetilde{\nabla }^{i}trK,\label{X constraint} \end{eqnarray} \end_inset \begin_inset Formula \begin{eqnarray} -8\widetilde{\nabla }^{2}(\psi _{0}+\delta \psi )=-\widetilde{R}(\psi _{0}+\delta \psi )-\frac{2}{3}\left(trK\right)^{2}\psi _{0}^{4}(\psi _{0}+5\delta \psi ) & & \nonumber \\ +\left(\widetilde{A}^{ij}+\left(lX_{0}\right)^{ij}\right)^{2}\psi _{0}^{-8}(\psi +_{0}-7\delta \psi )+2\rho \psi _{0}^{4}(\psi _{0}+5\delta \psi ), & & \label{phi +linear} \end{eqnarray} \end_inset \begin_inset Formula \begin{eqnarray} \nabla ^{2}(X_{0}^{i}+\delta X^{i})+\frac{1}{3}\widetilde{\nabla }^{i}\widetilde{\nabla }_{j}(X_{0}^{j}+\delta X)+\widetilde{R}_{j}^{i}(X_{0}^{j}+\delta X^{i}) & & \nonumber \\ =J^{i}\psi _{0}^{10}-\widetilde{\nabla }_{j}\widetilde{A}^{ij}+\frac{2}{3}\psi _{0}^{6}\widetilde{\nabla }^{i}trK. & & \label{X linear} \end{eqnarray} \end_inset \layout Standard \begin_inset Formula \begin{equation} x^{\mu }\rightarrow x^{\mu }+\xi ^{\mu }.\label{gauge perturbation}\end{equation} \end_inset \layout Standard \begin_inset Formula \begin{equation} \Box x^{\mu }=0.\label{gauge}\end{equation} \end_inset \begin_inset Formula \begin{equation} \Box \xi ^{\mu }=0.\label{perturbation}\end{equation} \end_inset \begin_inset Formula \begin{equation} tdot\frac{\partial g_{tt}}{\partial t}=\left(\gamma ^{ij}\alpha ^{2}-\beta ^{i}\beta ^{j}\right)\left(-\gamma _{ij,t}+2\beta _{i,j}\right)+2\beta ^{i}g_{tt,i}\label{g_{t}\end{equation} \end_inset \begin_inset Formula \begin{eqnarray} \frac{\partial \beta _{k}}{\partial t} & = & 2\beta ^{i}\left(\gamma _{ki,t}-\beta _{i,k}+\beta _{k,i}\right)\nonumber \\ & & -\left(\gamma ^{ij}\alpha ^{2}-\beta ^{i}\beta ^{j}\right)\left(\gamma _{ij,k}-2\gamma _{kj,i}\right)+g_{tt,k}.\label{Shift dot} \end{eqnarray} \end_inset \layout Standard \begin_inset Formula \[ \frac{\partial (\mathrm{variable})}{\partial t}+\partial _{i}(\mathrm{flux})^{i}=(\mathrm{source}),\] \end_inset \begin_inset Formula \[ \frac{\partial Q}{\partial t}=F(Q)\] \end_inset \begin_inset Formula \[ Q_{\mathrm{intermediate}}=Q_{t}+\frac{\Delta t}{2}F(Q_{t}),\] \end_inset \begin_inset Formula \[ Q_{t+\Delta t}=Q_{t}+\Delta t\, F(Q_{\mathrm{intermediate}}).\] \end_inset \layout Standard \begin_inset Formula \[ Q(t,r)=\frac{G(\alpha t-(\det \gamma )^{\frac{1}{6}}r)}{r},\] \end_inset \begin_inset Formula \begin{equation} \frac{\partial \gamma _{ij}}{\partial t}=-2\alpha K_{ij}+\nabla _{i}\beta _{j}+\nabla _{j}\beta _{i}-q\left(\Delta x\right)^{3}\nabla ^{4}\gamma _{ij},\label{g diffuse}\end{equation} \end_inset \begin_inset Formula \[ \gamma _{\mathrm{new}}=\gamma _{\mathrm{old}}+\Delta t(RHS),\] \end_inset \begin_inset Formula \[ \gamma _{\mathrm{new}}=\gamma _{\mathrm{old}}+\Delta t\lbrace RHS-q\Delta x^{3}\nabla ^{4}[\gamma _{\mathrm{old}}+\Delta t\left(RHS\right)]\rbrace .\] \end_inset \begin_inset Formula \begin{eqnarray} h_{+} & = & \frac{1}{2}\left(\gamma _{xx}-\gamma _{yy}\right),lus\label{h_{p}\\ h_{\times } & = & \gamma _{xy}.ross\label{h_{c} \end{eqnarray} \end_inset \begin_inset Formula \[ T_{\mu \nu }=\frac{1}{2}\left\langle h_{ij,\mu }h_{ij,\nu }\right\rangle ,\] \end_inset \begin_inset Formula \[ L\sim 4\pi \cdot \frac{1}{2}\frac{\left(h_{+}^{2}+h_{\times }^{2}\right)\left(4R_{*}\right)^{2}}{\left(10R_{*}\right)^{2}}=2\cdot 10^{-4}.\] \end_inset \layout Standard \begin_inset Formula \[ L=\frac{32}{5}\frac{\mu ^{3}M^{2}}{a^{5}}\sim 3\cdot 10^{-7},\] \end_inset \the_end
