From: Sam0h51 <75147348+Sam0h51@users.noreply.github.com>
Date: Mon, 19 Feb 2024 18:55:32 +0000 (-0700)
Subject: Update README.md
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=f3324e0a747b849aecd9a0c813c697cd5b3ee5e2;p=code-gallery.git

Update README.md
---

diff --git a/Swift-Hohenberg-Solver/README.md b/Swift-Hohenberg-Solver/README.md
index e3b8969..3a5ac6e 100755
--- a/Swift-Hohenberg-Solver/README.md
+++ b/Swift-Hohenberg-Solver/README.md
@@ -1,3 +1,9 @@
+---
+title: "Swift-Hohenberg Solver Write-up"
+bibliography: references.bib
+link-citations: true
+---
+
 # Introduction
 
 This program is used to solve the generalized Swift-Hohenberg equation
@@ -15,7 +21,7 @@ wavelength of $2\pi$. We choose $r = 0.3$ because solutions are
 reasonably well behaved for small values of $r$ and $g_1$, but there
 are interesting behaviors that occur when $g_1$ is smaller or larger
 than $r$ in magnitude, so this allows us room to vary $g_1$ and
-explore these behavior. To summarize, this code solves:
+explore these behavior. Additionally, we choose $r = 0.3$ because this matches the parameters used by Gurevich in \cite{Gurevich}. We chose our parameters to match so that we could compare the output of our program to the results presented in \cite{Gurevich}, which was useful for validating that our code was functioning properly during the developement process.  To summarize, this code solves:
 
 @f{align*}{
     \frac{\partial u}{\partial t} = 0.3u - (1 + \Delta)^2 u + g_1 u^2 - u^3
@@ -259,4 +265,4 @@ patterns that form. Each image sequence was taken at times 0, 10, 25,
 
 ![image](./doc/images/Sphere_Random_Table.png)
 
-![image](./doc/images/Sinusoid_Random_Table.png)
\ No newline at end of file
+![image](./doc/images/Sinusoid_Random_Table.png)