Andre Poenitz wrote: > On Thu, Jul 18, 2002 at 11:22:15AM +0200, Juergen Vigna wrote: > >>>Please try the attached patch against 1.2.1cvs. >>> >>And what are we doing with files saved by the user? Shouldn't >>this be fixed also in the reading part of 1.3.0? If the file >>is saved with 1.2.0 then the file is "doomed"? >> > > Good question. > > Allan, can you send me the file produced by 1.2.1 without the patch that > was not read by 1.3.0?
here it comes, read and saved with 1.2.1, but reading with 1.3 is also ok for me. Herbert -- http://www.lyx.org/help/
#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{gdot}\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{Kdot} \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{phiconstraint}\\ \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{Xconstraint} \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{philinear} \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{Xlinear} \end{eqnarray} \end_inset \layout Standard \begin_inset Formula \begin{equation} x^{\mu }\rightarrow x^{\mu }+\xi ^{\mu }.\label{gaugeperturbation}\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} \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}tdot}\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{Shiftdot} \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{gdiffuse}\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),\label{h_{p}lus}\\ h_{\times } & = & \gamma _{xy}.\label{h_{c}ross} \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
