Commit b3817022 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Extracted the kernel definition text from the wrapping tex.

parent 467b0fe7
......@@ -80,9 +80,9 @@ tests/testRiemannHLLC
tests/testMatrixInversion
theory/latex/swift.pdf
theory/SPH/kernel/kernels.pdf
theory/SPH/kernel/kernel_derivatives.pdf
theory/SPH/kernel/kernel_definitions.pdf
theory/SPH/Kernels/kernels.pdf
theory/SPH/Kernels/kernel_derivatives.pdf
theory/SPH/Kernels/kernel_definitions.pdf
theory/SPH/flavours/sph_flavours.pdf
theory/paper_pasc/pasc_paper.pdf
......
\documentclass[fleqn, usenatbib, useAMS,a4paper]{mnras}
\usepackage{graphicx}
\usepackage{amsmath,paralist,xcolor,xspace,amssymb}
\usepackage{times}
\newcommand{\swift}{{\sc Swift}\xspace}
%opening
\title{SPH kernels in SWIFT}
\author{Matthieu Schaller}
\begin{document}
\maketitle
We follow the definitions and notation of
\cite{Dehnen2012}. Motivation for all the material given here can be
found in their paper.
\section{General Definitions}
\subsection{General Definitions}
The desirable properties of an SPH kernels $W(\vec{x},h)$ are:
\begin{enumerate}
......@@ -83,7 +68,7 @@ the usual cubic spline kernel (see below), setting the simulation
resolution to $\eta=1.2348$ yields the commonly used value $N_{\rm
ngb} = 48$.
\section{Kernels available in \swift}
\subsection{Kernels available in \swift}
The \swift kernels are split into two categories, the B-splines
($M_{4,5,6}$) and the Wendland kernels ($C2$, $C4$ and $C6$). In all
......@@ -216,7 +201,7 @@ All kernels available in \swift are shown on Fig.~\ref{fig:sph:kernels}.
\end{figure}
\section{Kernel Derivatives}
\subsection{Kernel Derivatives}
The derivatives of the kernel function have relatively simple
expressions and are shown on Fig.~\ref{fig:sph:kernel_derivatives}:
......@@ -228,7 +213,3 @@ expressions and are shown on Fig.~\ref{fig:sph:kernel_derivatives}:
\end{align}
Note that for all the kernels listed above, $f'(0) = 0$.
\bibliographystyle{mnras}
\bibliography{./bibliography.bib}
\end{document}
\documentclass[fleqn, usenatbib, useAMS,a4paper]{mnras}
\usepackage{graphicx}
\usepackage{amsmath,paralist,xcolor,xspace,amssymb}
\usepackage{times}
\newcommand{\swift}{{\sc Swift}\xspace}
%opening
\title{SPH kernels in SWIFT}
\author{Matthieu Schaller}
\begin{document}
\maketitle
\input{kernel_definitions}
\bibliographystyle{mnras}
\bibliography{./bibliography.bib}
\end{document}
#!/bin/bash
python kernels.py
pdflatex -jobname=kernel_definitions kernel_definitions_standalone.tex
bibtex kernel_definitions.aux
pdflatex -jobname=kernel_definitions kernel_definitions_standalone.tex
pdflatex -jobname=kernel_definitions kernel_definitions_standalone.tex
#!/bin/bash
python kernels.py
pdflatex kernel_definitions.tex
bibtex kernel_definitions.aux
pdflatex kernel_definitions.tex
pdflatex kernel_definitions.tex
Supports Markdown
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment