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Commit edf1eb93 authored by Matthieu Schaller's avatar Matthieu Schaller
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Be more explicit about the softened expressions in the theory document

parent 77463e70
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1 merge request!1077Improved multipole acceptance criterion (MAC)
...@@ -51,9 +51,10 @@ r^{-3} & \mbox{if} & r \geq H, ...@@ -51,9 +51,10 @@ r^{-3} & \mbox{if} & r \geq H,
\end{align} \end{align}
with $g(u) \equiv f'(u)/u = -21u^5+90u^4-140u^3+84u^2-14$. This last with $g(u) \equiv f'(u)/u = -21u^5+90u^4-140u^3+84u^2-14$. This last
expression has the advantage of not containing any divisions or expression has the advantage of not containing any divisions or
branching, making it faster to evaluate than the softened force branching (besides the always necessary check for $r<H$), making it
derived from the \cite{Monaghan1985} spline kernel. Note also, the faster to evaluate than the softened force derived from the
useful expression for the norm of the forces: \cite{Monaghan1985} spline kernel. Note also, the useful expression
for the norm of the forces:
\begin{align} \begin{align}
|\mathbf{\nabla}\varphi(r,H)| = |\mathbf{\nabla}\varphi(r,H)| =
\left\lbrace\begin{array}{rcl} \left\lbrace\begin{array}{rcl}
...@@ -68,8 +69,6 @@ resulting forces are shown on Fig. \ref{fig:fmm:softening} (for more ...@@ -68,8 +69,6 @@ resulting forces are shown on Fig. \ref{fig:fmm:softening} (for more
details about how these are constructed see section 2 details about how these are constructed see section 2
of~\cite{Price2007}). For comparison purposes, we also implemented the of~\cite{Price2007}). For comparison purposes, we also implemented the
more traditional spline-kernel softening in \swift. more traditional spline-kernel softening in \swift.
\begin{figure} \begin{figure}
\includegraphics[width=\columnwidth]{potential.pdf} \includegraphics[width=\columnwidth]{potential.pdf}
\caption{The density (top), potential (middle) and forces (bottom) \caption{The density (top), potential (middle) and forces (bottom)
...@@ -81,3 +80,9 @@ more traditional spline-kernel softening in \swift. ...@@ -81,3 +80,9 @@ more traditional spline-kernel softening in \swift.
potential at $r=H$ to better highlight the differences in shapes.} potential at $r=H$ to better highlight the differences in shapes.}
\label{fig:fmm:softening} \label{fig:fmm:softening}
\end{figure} \end{figure}
Users specify the value of the Plummer-equivalent softening
$\epsilon_{\rm Plummer}$ in the parameter file.
\subsubsection{Interaction of bodies with different softening lengths}
\textcolor{red}{MORE WORDS HERE.}\\
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