Commit edf1eb93 authored by Matthieu Schaller's avatar Matthieu Schaller
Browse files

Be more explicit about the softened expressions in the theory document

parent 77463e70
......@@ -51,9 +51,10 @@ r^{-3} & \mbox{if} & r \geq H,
\end{align}
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
branching, making it faster to evaluate than the softened force
derived from the \cite{Monaghan1985} spline kernel. Note also, the
useful expression for the norm of the forces:
branching (besides the always necessary check for $r<H$), making it
faster to evaluate than the softened force derived from the
\cite{Monaghan1985} spline kernel. Note also, the useful expression
for the norm of the forces:
\begin{align}
|\mathbf{\nabla}\varphi(r,H)| =
\left\lbrace\begin{array}{rcl}
......@@ -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
of~\cite{Price2007}). For comparison purposes, we also implemented the
more traditional spline-kernel softening in \swift.
\begin{figure}
\includegraphics[width=\columnwidth]{potential.pdf}
\caption{The density (top), potential (middle) and forces (bottom)
......@@ -81,3 +80,9 @@ more traditional spline-kernel softening in \swift.
potential at $r=H$ to better highlight the differences in shapes.}
\label{fig:fmm:softening}
\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.}\\
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