From c08bcb900b7524a1b474062ece3b23dfe76d350f Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Thu, 11 Mar 2021 15:08:04 +0100
Subject: More writing.

---
 stokes.tex | 12 ++++++++++++
 1 file changed, 12 insertions(+)

(limited to 'stokes.tex')

diff --git a/stokes.tex b/stokes.tex
index 41878b7..d07ec6a 100644
--- a/stokes.tex
+++ b/stokes.tex
@@ -271,6 +271,18 @@ The critical points of the 2-spin model are all adjacent: no critical point is s
 
 \section{(2 + 4)-spin}
 
+\section{Numerics}
+
+To confirm the presence of Stokes lines under certain processes in the $p$-spin, we studied the problem numerically.
+\begin{equation}
+  \mathcal L(z(t), z'(t))
+  = 1-\frac{\operatorname{Re}(\dot z^*_iz'_i)}{|\dot z||z'|}
+\end{equation}
+\begin{equation}
+  \mathcal C[\mathcal L]=\int dt\,\mathcal L(z(t), z'(t))
+\end{equation}
+$\mathcal C$ has minimum of zero, which is reached only by functions $z(t)$ whose tangent is everywhere parallel to the direction of the dynamics. Therefore, finding functions which reach this minimum will find time-reparameterized Stokes lines. For the sake of numeric stability, we look for functions whose tangent has constant norm.
+
 \begin{acknowledgments}
   MIT mathematicians have been no help
 \end{acknowledgments}
-- 
cgit v1.2.3-70-g09d2

