Commits

commits@lists.einsteintoolkit.org

2 participants
6997 discussions

[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}

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 305)
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: +2 -2 =================================================================== --- ET.tex 2012-03-13 14:40:26 UTC (rev 304) +++ ET.tex 2012-03-13 14:41:35 UTC (rev 305) @@ -696,7 +696,7 @@ \label{table:vars} {\centering \begin{tabular}{llll} -Symbol & Quantity & Eqn. & ET thorn::group \\ +Symbol & Quantity & Eqn. & Einstein Toolkit thorn::group \\ \hline $G_{\mu\nu}$ & Einstein Tensor & \protect\ref{eq:einstein} & N/A\\ $T_{\mu\nu}$ & Stress-Energy Tensor & \protect\ref{eq:Tmunu} & TmunuBase::stress\_energy\_tensor\\ @@ -1111,7 +1111,7 @@ \subsubsection{TOVSolver} \label{sec:TOVSolver} -The \codename{TOVSolver} routine in the ET solves the standard TOV equations +The \codename{TOVSolver} routine in the Einstein Toolkit solves the standard TOV equations \cite{Tolman:1939jz,Oppenheimer:1939ne} for the pressure, enclosed gravitational mass $M_e$, and gravitational potential $\Phi=\log\alpha$ in the interior of a spherically symmetric star in hydrostatic equilibrium, expressed using the Schwarzschild (areal) radius $\hat{r}$: \begin{eqnarray}

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 304)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 09:40 AM Modified: / ET.tex Log: use Cactus notation also for ML_BSSN quantities File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +5 -5 =================================================================== --- ET.tex 2012-03-13 14:36:59 UTC (rev 303) +++ ET.tex 2012-03-13 14:40:26 UTC (rev 304) @@ -714,11 +714,11 @@ $h$ & 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\\ -$\psi$, ($\phi$) & (Logarithmic) conformal factor & \protect\ref{eq:confpsi},\protect\ref{eq:phi} & (ML\_BSSN/ML\_log\_confac) \\ -$\tilde{\gamma}_{ij}$ & Conformal 3-metric & \protect\ref{eq:tildegamma} & ML\_BSSN/ML\_metric \\ -$K$ & Trace of extrinsic curvature & \protect\ref{eq:trK} & ML\_BSSN/ML\_trace\_curv \\ -$\tilde{A}_{ij}$ & Conformal extrinsic curvature & \protect\ref{eq:Atij} & ML\_BSSN/ML\_curv \\ -$\tilde{\Gamma}^i$ & Conformal connection & \protect\ref{eq:Gammai} & ML\_BSSN/ML\_Gamma \\ +$\psi$, ($\phi$) & (Logarithmic) conformal factor & \protect\ref{eq:confpsi},\protect\ref{eq:phi} & (ML\_BSSN::ML\_log\_confac) \\ +$\tilde{\gamma}_{ij}$ & Conformal 3-metric & \protect\ref{eq:tildegamma} & ML\_BSSN::ML\_metric \\ +$K$ & Trace of extrinsic curvature & \protect\ref{eq:trK} & ML\_BSSN::ML\_trace\_curv \\ +$\tilde{A}_{ij}$ & Conformal extrinsic curvature & \protect\ref{eq:Atij} & ML\_BSSN::ML\_curv \\ +$\tilde{\Gamma}^i$ & Conformal connection & \protect\ref{eq:Gammai} & ML\_BSSN::ML\_Gamma \\ $D$ & Conservative density & \protect\ref{eq:p2c1} & GRHydro::dens\\ $S^i$ & Conservative momentum & \protect\ref{eq:p2c2} & GRHydro::scon\\ $\tau$ & Conservative energy density & \protect\ref{eq:p2c3} & GRHydro::tau\\

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 303)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 09:36 AM Modified: / ET.tex Log: remove question marks - please: this is so easy to overlook - mark todos like this somehow File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2012-03-13 14:34:22 UTC (rev 302) +++ ET.tex 2012-03-13 14:36:59 UTC (rev 303) @@ -559,9 +559,9 @@ GHz \\ HLRB II (LRZ Munich) & SGI Altix (Itanium) & NUMAlink & 1 & 9728 & 1.6 GHz \\ - Kraken (NICS) & Cray XT5 (AMD) & SeaStar & 9408(?) & 12 & 2.6 + Kraken (NICS) & Cray XT5 (AMD) & SeaStar & 9408 & 12 & 2.6 GHz \\ - Queen Bee (LONI) & Intel cluster & InfiniBand & 668(?) & 8 & + Queen Bee (LONI) & Intel cluster & InfiniBand & 668 & 8 & 2.33 GHz \\ Ranger (TACC) & AMD cluster & InfiniBand & 1888 & 16 & 2.3 GHz \\

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 302)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 09:34 AM Modified: / ET.tex Log: clarify 1/r^2 falloff File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +3 -1 =================================================================== --- ET.tex 2012-03-13 08:08:34 UTC (rev 301) +++ ET.tex 2012-03-13 14:34:22 UTC (rev 302) @@ -1473,7 +1473,9 @@ The spatial derivatives $\partial_i$ are evaluated by comparing neighboring grid points, corresponding to a second-order stencil evaluated in the middle between the two neighboring grid points. -Second-order decay is assumed, hence $p=2$. +Although strictly speaking different variables or even different +components of tensors can fall off differently, we find that +using $p=2$ works well in practice. As with the initial conditions above, this boundary condition is evaluated on several layers of grid points, starting from the

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 301)
by ian.hinder＠aei.mpg.de 13 Mar '12

13 Mar '12

User: hinder Date: 2012/03/13 03:08 AM Modified: / ET.tex Log: ET.tex: Add accuracy comment for longer waveforms and adjust wording slightly in that secton File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +6 -4 =================================================================== --- ET.tex 2012-03-13 06:27:49 UTC (rev 300) +++ ET.tex 2012-03-13 08:08:34 UTC (rev 301) @@ -2774,15 +2774,17 @@ should not be larger than $0.05$ radians at this reference time, and that this is roughly the scale of accuracy which might be useful for comparisons with analytic approximation methods. From the plot, we -assert that the phase difference between the higher and high +see that the phase difference between the higher and high resolutions and the one between high and medium-high resolutions -satisfies this criterion, while the phase difference between the +satisfy this criterion, while the phase difference between the medium-high and medium resolutions barely satisfies the criterion; and -the one between medium and low resolutions does not. We conclude then +the one between medium and low resolutions does not. We conclude that the three highest resolution runs do have the suggested accuracy. While the waveform shown here is too short for comparison with analytic methods, we illustrate here that these sorts of comparisons -can be made using the toolkit. +can be made using the toolkit. Note that simulations starting from greater +BBH separation leading to longer waveforms will require significantly more +resolution to achieve the same phase error. \begin{figure} \includegraphics[width=0.45\textwidth]{tracks}

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 300)
by cott＠tapir.caltech.edu 13 Mar '12

13 Mar '12

User: cott Date: 2012/03/13 01:27 AM Modified: / ET.tex Log: * add text clarifying hybrid EOS File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +11 -1 =================================================================== --- ET.tex 2012-03-13 06:03:14 UTC (rev 299) +++ ET.tex 2012-03-13 06:27:49 UTC (rev 300) @@ -1845,7 +1845,17 @@ \label{eq:hybrid_eos} \end{eqnarray}% In this, the total specific internal energy $\epsilon$ -consists of a polytropic and a thermal contribution. In iron core +consists of a polytropic and a thermal contribution. The variable $\Gamma$ +assumes one of two values, +\begin{equation} +\Gamma = \left\{\begin{array}{ll} +\Gamma_1 & \mathrm{for}\,\,\rho < \rho_\mathrm{nuc}\,\,,\\ +\Gamma_2 & \mathrm{for}\,\,\rho \ge \rho_\mathrm{nuc}\,\,, +\end{array} \right. +\end{equation} +where $\rho_\mathrm{nuc}$ is typically set to $2\times 10^{14}\,\mathrm{g}\,\mathrm{cm}^{-3}$. + +In iron core collapse, the pressure below nuclear density is dominated by the pressure of relativistically degenerate electrons. For this, one sets $K = 4.897 \times 10^{14}$ [cgs] in the above. The thermal index

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 299)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 01:03 AM Modified: / ET.tex Log: put PSD details into footnote File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +2 -2 =================================================================== --- ET.tex 2012-03-13 05:48:22 UTC (rev 298) +++ ET.tex 2012-03-13 06:03:14 UTC (rev 299) @@ -2867,10 +2867,10 @@ of the central density oscillations computed from a full 3D relativistic hydrodynamics simulation, compared to the corresponding frequencies as obtained with perturbative techniques (kindly provided by Kentaro Takami and -computed using the method described in~\cite{Yoshida:1999vj}). The PSD was computed +computed using the method described in~\cite{Yoshida:1999vj})\footnote{The PSD was computed using the entire time series of the high-resolution run, by removing the linear trend and averaging over Hanning windows overlapping half the signal length after -padding the signal to five times its length. The agreement of the +padding the signal to five times its length.}. The agreement of the fundamental mode and first three overtone frequencies is clearly visible, but are limited beyond this by the finite numerical resolution. Higher overtones should be measurable with higher

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 298)
by knarf＠cct.lsu.edu 13 Mar '12

13 Mar '12

User: knarf Date: 2012/03/13 12:48 AM Modified: / ET.tex /examples/collapse/ radii.pdf /examples/cosmology/figs/ err.pdf, kasner.pdf /examples/kerr/figs/ ah_mass.pdf, ah_mass_conv.pdf, kerr.py, qlm_mass.pdf, qlm_spin.pdf, waves.pdf, waves_conv.pdf, waves_l4.pdf, waves_l4_conv.pdf Log: regenerate some plots File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: <Unavailable> Directory: /examples/collapse/ ============================== File [modified]: radii.pdf Delta lines: <Unavailable> Directory: /examples/cosmology/figs/ ==================================== File [modified]: err.pdf Delta lines: <Unavailable> File [modified]: kasner.pdf Delta lines: <Unavailable> Directory: /examples/kerr/figs/ =============================== File [modified]: ah_mass.pdf Delta lines: <Unavailable> File [modified]: ah_mass_conv.pdf Delta lines: <Unavailable> File [modified]: kerr.py Delta lines: <Unavailable> File [modified]: qlm_mass.pdf Delta lines: <Unavailable> File [modified]: qlm_spin.pdf Delta lines: <Unavailable> File [modified]: waves.pdf Delta lines: <Unavailable> File [modified]: waves_conv.pdf Delta lines: <Unavailable> File [modified]: waves_l4.pdf Delta lines: <Unavailable> File [modified]: waves_l4_conv.pdf Delta lines: <Unavailable>

1 0

[svn:einsteintoolkit] Paper_EinsteinToolkit_2010/ (Rev. 297)
by bcmsma＠astro.rit.edu 13 Mar '12

13 Mar '12

User: bmundim Date: 2012/03/13 12:07 AM Modified: / ET.tex Log: (2,2) \psi_4 phase and amplitude convergence studies. File Changes: Directory: / ============ File [modified]: ET.tex Delta lines: +3 -2 =================================================================== --- ET.tex 2012-03-13 04:46:44 UTC (rev 296) +++ ET.tex 2012-03-13 05:07:41 UTC (rev 297) @@ -2714,10 +2714,11 @@ In order to evaluate the convergence of the numerical solution, we ran five simulations with different resolutions, and focus our analysis on the convergence -of the phase and amplitude of the Weyl scalar $\Psi_4$. +of the phase and amplitude of the Weyl scalar $(2,2)$ mode, +$\Psi_4^{(2,2)}$. Here, we consider the phase $\varphi(t)$ and -the amplitude $A(t)$ of the Weyl scalar $\Psi_4$ at +the amplitude $A(t)$ of the Weyl scalar $(2,2)$ mode $\Psi_4^{(2,2)}$ at $R_{\rm obs}=60\mathrm{M}$. In order to take differences between the numerical values at two different grid resolutions, we use an $8$-th order accurate Lagrange operator to interpolate the higher-accuracy finite difference solution

1 0

Jump to page:

2026

2025

2024

2023

2022

2021

2020

2019

2018

2017

2016

2015

2014

2013

2012

2011

2010

Commits