Commits March 2012

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14 participants
128 discussions

[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 4)
by tanja.bode＠physics.gatech.edu 13 Mar '12

13 Mar '12

User: tbode Date: 2012/03/13 02:19 PM Added: /flyer/ etk-widescreen.png Log: Added Dennis' widescreen for slideshow-based advertisement. Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /flyer/ ================== File [added]: etk-widescreen.png Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: flyer/etk-widescreen.png ___________________________________________________________________

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 312)
by jfaber＠einsteintoolkit.org 13 Mar '12

13 Mar '12

User: jfaber Date: 2012/03/13 02:10 PM Modified: / ET.tex Log: Modified stress-energy source terms in initial data, vacuum evolution, anc constraint treatment to be in uniform notation. PLEASE DOUBLECHECK THE REVISED BSSN EQUATIONS BEFORE SUBMITTING! File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +17 -15 =================================================================== --- ET.tex 2012-03-13 18:18:06 UTC (rev 311) +++ ET.tex 2012-03-13 19:10:07 UTC (rev 312) @@ -1214,20 +1214,20 @@ \codename{Meudon\_Bin\_NS} handles binary NS data described in~\cite{Gourgoulhon:2000nn}, which represent solutions of the equations \begin{eqnarray*} -&&\nabla^2\nu_{(m)} = 4\pi\psi^4(\hat{E}_{(m)}+\hat{S}_{(m)})+\psi^4 K_{ij}K^{ij}_{(m)}-\nabla_i\nu_{(m)}\nabla^i\beta\\ -&&\nabla^2\beta_{(m)}=4\pi\psi^4\hat{S}_{(m)}+\frac{3}{4}\psi^4 K_{ij}K^{ij}_{(m)}-\frac{1}{2}(\nabla_i\nu_{(m)}\nabla^i\nu+\nabla_i\beta_{(m)}\nabla^i\beta)\\ -&&\nabla^2\beta^i_{(m)}+\frac{1}{3}\nabla^i\nabla_j \beta^j_{(m)} = -16\pi\alpha\psi^4(\hat{E}_{(m)}+P_{(m)})v^i_{(m)}+2\alpha\psi^4K^{ij}_{(m)}\nabla_j(3\beta-4\nu) +&&\nabla^2\nu_{(m)} = 4\pi\psi^4(E_{(m)}+S_{(m)})+\psi^4 K_{ij}K^{ij}_{(m)}-\nabla_i\nu_{(m)}\nabla^i\beta\\ +&&\nabla^2\beta_{(m)}=4\pi\psi^4S_{(m)}+\frac{3}{4}\psi^4 K_{ij}K^{ij}_{(m)}-\frac{1}{2}(\nabla_i\nu_{(m)}\nabla^i\nu+\nabla_i\beta_{(m)}\nabla^i\beta)\\ +&&\nabla^2\beta^i_{(m)}+\frac{1}{3}\nabla^i\nabla_j \beta^j_{(m)} = -16\pi\alpha\psi^4(E_{(m)}+P_{(m)})v^i_{(m)}+2\alpha\psi^4K^{ij}_{(m)}\nabla_j(3\beta-4\nu) \end{eqnarray*} where $\nu$ and $\beta$ are defined as \begin{equation} \nu\equiv \log\alpha;~~\beta\equiv\ln\alpha\psi^2. \end{equation} These equations are merely convenient reparameterizations of the ones used to generate binary BH data, with the matter source terms included. The extrinsic curvature is computed using~\ref{eq:lorextrcurv}, with both $K^{ij}$ and $\beta^i$ replaced by the split versions. -The matter sources terms are, respectively, -\begin{eqnarray} -\hat{E}&=&\alpha^2(u^0)^2 \rho h-P\\ -\hat{S}&=&3P+(\hat{E}+P)\frac{\alpha^2(u^0)^2 - 1}{\alpha^2(u^0)^2} -\end{eqnarray} +The matter sources terms $E$ and $S$, representing projections of the stress-energy tensor, are defined in~\ref{eq:e_tmunu} and \ref{eq:s_tmunu} below. +%\begin{eqnarray} +%e&=&n_\alpha n_\beta T^{\alpha\beta}=\alpha^2(u^0)^2 \rho h-P\\ +%S&=&3P+(\hat{E}+P)\frac{\alpha^2(u^0)^2 - 1}{\alpha^2(u^0)^2} +%\end{eqnarray} Lorene allows for two different NS spin states, either irrotational or synchronized. In the synchronized case, the velocity may be specified as a function of position once the orbital velocity is determined, while the irrotational case yields a rather complicated differential equation for the velocity potential which may then be used to determine the corresponding 3-velocity (see Equation~38 of \cite{Gourgoulhon:2000nn}). \codename{Meudon\_Mag\_NS} @@ -1277,7 +1277,7 @@ \\ \partial_0 K & = & -e^{-4\phi} \left[ \tilde{D}^i \tilde{D}_i \alpha + 2 \partial_i \phi \cdot \tilde{D}^i \alpha \right] + \alpha - \left( \tilde{A}^{ij} \tilde{A}_{ij} + \frac{1}{3} K^2 \right) - \alpha S + \left( \tilde{A}^{ij} \tilde{A}_{ij} + \frac{1}{3} K^2 \right) + \frac{\alpha}{2}(E+ S) \\ \partial_0 \beta^i & = & \alpha^2 G(\alpha,\phi,x^\mu) B^i \\ @@ -1298,7 +1298,7 @@ & & {} + \alpha K\tilde{A}_{ij} - 2\alpha\tilde{A}_{ik}\tilde{A}^k_{\; j} + 2\tilde{A}_{k(i}\partial_{j)}\beta^k - \frac{2}{3}\tilde{A}_{ij}\partial_k\beta^k - - \alpha e^{-4\phi} \hat{S}_{ij} + - \alpha e^{-4\phi} S_{ij}^{TF} \\ \partial_0\tilde{\Gamma}^i & = & \tilde{\gamma}^{kl}\partial_k\partial_l\beta^i @@ -1310,18 +1310,20 @@ + 2\alpha\left[ (m-1)\partial_k\tilde{A}^{ki} - \frac{2m}{3}\tilde{D}^i K \right. \nonumber \\ & & {} + m(\tilde{\Gamma}^i_{\; kl}\tilde{A}^{kl} + - 6\tilde{A}^{ij}\partial_j\phi) \Bigg] - S^i, + 6\tilde{A}^{ij}\partial_j\phi) \Bigg] -2\alpha \tilde{\gamma}^{ij} S_j \end{eqnarray} \end{widetext} with the momentum constraint damping constant set to $m=1$. The stress energy tensor $T_{\mu\nu}$ is incorporated via the projections \begin{eqnarray} - E & \equiv & \frac{1}{\alpha^2} \left( T_{00} - 2 \beta^i T_{0i} + - \beta^i \beta^j T^{ij} \right) + E & \equiv & n_\alpha n_\beta T^{\alpha\beta} = \frac{1}{\alpha^2} \left( T_{00} - 2 \beta^i T_{0i} + + \beta^i \beta^j T^{ij} \right)\label{eq:e_tmunu} + \\ + S_{ij} & \equiv & \gamma_{i\alpha} \gamma_{j\beta} T^{\alpha\beta} \\ - S & \equiv & g^{ij} T_{ij} + S&\equiv&S^i_i = \gamma^{ij} S_{ij} \label{eq:s_tmunu} \\ - S_i & \equiv & - \frac{1}{\alpha} \left( T_{0i} - \beta^j T_{ij} \right) . + S_i & \equiv &-\gamma_{i\alpha} n_\beta T^{\alpha\beta}= - \frac{1}{\alpha} \left( T_{0i} - \beta^j T_{ij} \right) . \end{eqnarray} We have introduced the notation $\partial_0 = \partial_t - \beta^j\partial_j$. All quantities with a tilde involve

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 311)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 01:18 PM Added: / iop_revised.tar.gz Removed: / arXiv-v2.tar.gz Log: add tarball uploaded to IOP as revised version Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: / ============ File [removed]: arXiv-v2.tar.gz Delta lines: +0 -0 =================================================================== (Binary files differ) File [added]: iop_revised.tar.gz Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: iop_revised.tar.gz ___________________________________________________________________

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[svn:einsteintoolkit] HydroBase/trunk/ (Rev. 48)
by bcmsma＠astro.rit.edu 13 Mar '12

13 Mar '12

User: bmundim Date: 2012/03/13 12:09 PM Modified: /trunk/ interface.ccl /trunk/doc/ documentation.tex Log: epsilon: specific internal energy (ie energy/mass) File Changes: Directory: /trunk/doc/ ====================== File [modified]: documentation.tex Delta lines: +1 -1 =================================================================== --- trunk/doc/documentation.tex 2012-02-04 15:49:06 UTC (rev 47) +++ trunk/doc/documentation.tex 2012-03-13 17:09:43 UTC (rev 48) @@ -137,7 +137,7 @@ \begin{itemize} \item \verb|rho|: rest mass density $\varrho$ \item \verb|press|: pressure $p$ - \item \verb|eps|: internal energy $\epsilon$ + \item \verb|eps|: specific internal energy $\epsilon$ \item \verb|vel[3]|: contravariant fluid three velocity $v^i$ defined as \begin{equation} v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha} Directory: /trunk/ ================== File [modified]: interface.ccl Delta lines: +1 -1 =================================================================== --- trunk/interface.ccl 2012-02-04 15:49:06 UTC (rev 47) +++ trunk/interface.ccl 2012-03-13 17:09:43 UTC (rev 48) @@ -31,7 +31,7 @@ CCTK_REAL rho type = GF Timelevels = 3 tags='ProlongationParameter="HydroBase::prolongation_type" tensortypealias="Scalar" interpolator="matter"' "rest mass density" CCTK_REAL press type = GF Timelevels = 3 tags='ProlongationParameter="HydroBase::prolongation_type" tensortypealias="Scalar" interpolator="matter"' "gas pressure" -CCTK_REAL eps type = GF Timelevels = 3 tags='ProlongationParameter="HydroBase::prolongation_type" tensortypealias="Scalar" interpolator="matter"' "internal energy density" +CCTK_REAL eps type = GF Timelevels = 3 tags='ProlongationParameter="HydroBase::prolongation_type" tensortypealias="Scalar" interpolator="matter"' "specific internal energy" CCTK_REAL vel[3] type = GF Timelevels = 3 tags='ProlongationParameter="HydroBase::prolongation_type" tensortypealias="U" interpolator="matter"' "velocity v^i"

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[svn:einsteintoolkit] GRHydro/trunk/ (Rev. 315)
by bcmsma＠astro.rit.edu 13 Mar '12

13 Mar '12

User: bmundim Date: 2012/03/13 12:06 PM Modified: /trunk/ param.ccl /trunk/doc/ documentation.tex Log: epsilon: specific internal energy (ie energy/mass) File Changes: Directory: /trunk/doc/ ====================== File [modified]: documentation.tex Delta lines: +6 -6 =================================================================== --- trunk/doc/documentation.tex 2012-02-16 23:18:45 UTC (rev 314) +++ trunk/doc/documentation.tex 2012-03-13 17:06:08 UTC (rev 315) @@ -204,11 +204,11 @@ For the equations of state, two ``types'' are recognized, controlled by the parameter {\tt GRHydro\_eos\_type}. These are {\tt "Polytype"} -where the pressure is a function of the density, $P=P(\rho)$, and the +where the pressure is a function of the rest-mass density, $P=P(\rho)$, and the more generic {\tt "General"} type where the pressure is a function -of the density and the internal energy, $P=P(\rho, \epsilon)$. For the +of the rest-mass density and the specific internal energy, $P=P(\rho, \epsilon)$. For the {\tt Polytype} equations of state one fewer equation is evolved and -the specific internal energy is set directly from the density. The +the specific internal energy is set directly from the rest-mass density. The actual equation of state used is controlled by the parameter {\tt GRHydro\_eos\_table}. Polytype equations of state include {\tt "2D\_Polytrope"} and general equations of state include {\tt @@ -312,8 +312,8 @@ $D$ is the generalized particle number density, $S^i$ are the generalized momenta in each direction, and $\tau$ is an internal energy term. These conserved variables are composed from a set of {\it primitive variables}, -which are $\rho$, the density, $p$, the -pressure, $v^i$, the fluid 3-velocities, $\epsilon$, the internal +which are $\rho$, the rest-mass density, $p$, the +pressure, $v^i$, the fluid 3-velocities, $\epsilon$, the specific internal energy, and $W$, the Lorentz factor, via the following relations % from GRHydro/src/Prim2con.F90 % w = 1.d0 / sqrt(1.d0 - (gxx*dvelx*dvelx + gyy*dvely*dvely + gzz & @@ -342,7 +342,7 @@ Only five of the primitive variables are independent. Usually the Lorentz factor is defined in terms of the velocities and the metric as $W = (1-\gamma_{ij}v^i v^j)^{-1/2}$. -Also one of the pressure, density or internal energy terms is given in +Also one of the pressure, rest-mass density or specific internal energy terms is given in terms of the other two by an {\it equation of state}. The fluxes are usually defined in terms of both the conserved Directory: /trunk/ ================== File [modified]: param.ccl Delta lines: +1 -1 =================================================================== --- trunk/param.ccl 2012-02-16 23:18:45 UTC (rev 314) +++ trunk/param.ccl 2012-03-13 17:06:08 UTC (rev 315) @@ -322,7 +322,7 @@ 0: :: "greater than zero" } 1.e-20 -real GRHydro_eps_min "Minimum value of internal energy - this is now only used in GRHydro_InitData's GRHydro_Only_Atmo routine" +real GRHydro_eps_min "Minimum value of specific internal energy - this is now only used in GRHydro_InitData's GRHydro_Only_Atmo routine" { 0: :: "Positive" } 1.e-10

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 310)
by jfaber＠einsteintoolkit.org 13 Mar '12

13 Mar '12

User: jfaber Date: 2012/03/13 11:19 AM Modified: / ET.tex Log: One more change to "specific internal energy" File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2012-03-13 16:15:16 UTC (rev 309) +++ ET.tex 2012-03-13 16:19:25 UTC (rev 310) @@ -1519,8 +1519,8 @@ hydrodynamic quantities, with several different reconstruction methods and Riemann solvers, as we discuss below. In such a scheme, we define a set of ``conserved'' hydrodynamic variables, defined in terms of the -``primitive'' physical variables such as mass and internal energy -density, pressure, and velocity. Wherever derivatives of hydrodynamic +``primitive'' physical variables such as mass density, specific internal energy, +pressure, and velocity. Wherever derivatives of hydrodynamic terms appear in the evolution equations for the conserved variables, they are restricted to appear only inside divergence terms (referred to as fluxes) and never in the source terms. By calculating fluxes between pairs of neighboring points where field and hydrodynamic terms are evaluated, we

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 309)
by jfaber＠einsteintoolkit.org 13 Mar '12

13 Mar '12

User: jfaber Date: 2012/03/13 11:15 AM Modified: / ET.tex Log: Fixed the description in to TOVSolver footnote about notation; no footnote necessary File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +5 -5 =================================================================== --- ET.tex 2012-03-13 15:14:05 UTC (rev 308) +++ ET.tex 2012-03-13 16:15:16 UTC (rev 309) @@ -710,7 +710,7 @@ $K_{ij}$ & Extrinsic curvature & \protect\ref{eq:extrcurv} & ADMBase::curv\\ $\rho$ & Rest mass density & \protect\ref{eq:Tmunu},\protect\ref{eq:enthalpy} & HydroBase::rho\\ $P$ & Fluid pressure & \protect\ref{eq:enthalpy} & HydroBase::press\\ -$\epsilon$ & Internal energy density & \protect\ref{eq:enthalpy} & Hydrobase::eps\\ +$\epsilon$ & Specific internal energy & \protect\ref{eq:enthalpy} & Hydrobase::eps\\ $h$ & Specific enthalpy & \protect\ref{eq:enthalpy} & N/A\\ $v^i$ & 3-velocity & \protect\ref{eq:3vel} & HydroBase::vel\\ $B^i$ & Magnetic field vector & \protect\ref{eq:Bi} & HydroBase::Bvec\\ @@ -884,7 +884,7 @@ \begin{itemize} \item \verb|rho|: rest mass density $\rho$ \item \verb|press|: pressure $P$ - \item \verb|eps|: internal energy density $\epsilon$ + \item \verb|eps|: Specific internal energy $\epsilon$ \item \verb|vel[3]|: contravariant fluid three velocity $v^i$ defined as \begin{equation} v^i = \frac{u^i}{\alpha u^0} + \frac{\beta^i}{\alpha}\label{eq:3vel} @@ -1116,14 +1116,14 @@ radius $\hat{r}$: \begin{eqnarray} \label{eq:TOViso} - \frac{d P}{d \hat{r}} & = & -(e + P) \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} - 2M_e)}\nonumber\\ + \frac{d P}{d \hat{r}} & = & -(\mu + P) \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} - 2M_e)}\nonumber\\ % - \frac{d M_e}{d \hat{r}} & = & 4 \pi \hat{r}^2 e\nonumber\\ + \frac{d M_e}{d \hat{r}} & = & 4 \pi \hat{r}^2 \mu\nonumber\\ % \frac{d \Phi}{d \hat{r}} & = & \frac{M_e + 4\pi \hat{r}^3 P}{\hat{r}(\hat{r} - 2M_e)}. \end{eqnarray} -where $e\equiv \rho(1+\epsilon)$ is the energy density of the fluid, including the internal energy contribution\footnote[1]{We note that since different application thorns may define their own local variables, the energy density is referred to as {\tt rho} within \codename{TOVSolver}, as the projected energy density $E$, defined in Sec.~\protect\ref{sec:Kevol}, is within \codename{McLachlan} and a few other thorns. Similar ambiguities exist for other commonly used variable names, particularly $\phi$ and $\alpha$.}. +where $\mu\equiv \rho(1+\epsilon)$ is the energy density of the fluid, including the internal energy contribution. The routine also supplies the analytically known solution in the exterior, \begin{eqnarray}

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 308)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 10:14 AM Added: / arXiv-v1.tar.gz, arXiv-v2.tar.gz Removed: / arXiv.tar.gz Log: rename old arXiv version to v1 and add proposed new version as v2 Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: / ============ File [added]: arXiv-v1.tar.gz Delta lines: +0 -0 =================================================================== (Binary files differ) File [added]: arXiv-v2.tar.gz Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: arXiv-v2.tar.gz ___________________________________________________________________ File [removed]: arXiv.tar.gz Delta lines: +0 -0 =================================================================== (Binary files differ)

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 307)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 09:49 AM Modified: / ET.tex Log: fix newly introduced typos File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +6 -6 =================================================================== --- ET.tex 2012-03-13 14:41:53 UTC (rev 306) +++ ET.tex 2012-03-13 14:49:04 UTC (rev 307) @@ -1195,7 +1195,7 @@ \end{figure} \codename{Meudon\_Bin\_BH} can read in BH-BH binary initial data described -in~\cite{Grandclement:2001ed}, representing solutions to the hamiltonian and momentum constraints, along with the trace of the spatial components of the Einstein equations, form the linked elliptic equation set: +in~\cite{Grandclement:2001ed}, representing solutions to the Hamiltonian and momentum constraints, along with the trace of the spatial components of the Einstein equations, form the linked elliptic equation set: \begin{eqnarray*} &&\nabla^2\alpha_{(m)} = \alpha \psi^4 K_{ij} K^{ij}_{(m)}\\ &&\nabla^2\psi_{(m)}=-\frac{\psi^5}{8}K_{ij}K^{ij}_{(m)}\\ @@ -2081,8 +2081,8 @@ \label{eq:christodoulou} \end{equation} that takes into account the -contributions of the irreducuble mass $M_{\mathrm{ir}}$ and angular -momemtum $S$ to the total black hole mass $M$. +contributions of the irreducible mass $M_{\mathrm{ir}}$ and angular +momentum $S$ to the total black hole mass $M$. Finally, the module \codename{HydroAnalysis} additionally locates the (coordinate) center of mass as well as the point of maximum rest mass density of a @@ -2496,7 +2496,7 @@ extracted at $R=30\mathrm{M}$, and its numerical convergence. In this and in the following sections, a numerical quantity $\Psi$ is said to converge with convergence order $Q$ if for a set of numerical -stepsizes $h_1$, $h_2$, $h_3$ the difference between successive +step sizes $h_1$, $h_2$, $h_3$ the difference between successive resolutions scales as \begin{equation} \frac{\Psi_{h_1}-\Psi_{h_2}}{\Psi_{h_2}-\Psi_{h_3}} = \frac{h_1^Q-h_2^Q}{h_2^Q-h_3^Q}\,. @@ -3021,8 +3021,8 @@ star's coordinate radius is twice the size of the forming apparent horizon~\cite{Thierfelder:2010dv}. At this point the majority of the matter is inside the apparent horizon, whose size quickly grows to its -final size while the numerical spacetime aproaches the final ``trumpet'' -configuraton. +final size while the numerical spacetime approaches the final ``trumpet'' +configuration. In Figure~\ref{fig:tov_collapse_H_convergence_at0}, we display the convergence factor for the Hamiltonian constraint

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[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 306)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 09:41 AM Modified: / ET.tex Log: don't use 'ET' within the paper File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +1 -1 =================================================================== --- ET.tex 2012-03-13 14:41:35 UTC (rev 305) +++ ET.tex 2012-03-13 14:41:53 UTC (rev 306) @@ -724,7 +724,7 @@ $\tau$ & Conservative energy density & \protect\ref{eq:p2c3} & GRHydro::tau\\ $W$ & Lorentz factor & \protect\ref{eq:Lorentz} & GRHydro::w\_lorentz\\ \end{tabular}\\} -\caption{Summary of key variables used throughout this paper, along with the equations that define them and the ET thorn and group name used to store the quantity, where applicable.} +\caption{Summary of key variables used throughout this paper, along with the equations that define them and the Einstein Toolkit thorn and group name used to store the quantity, where applicable.} \end{table}

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Commits March 2012