1 files changed, 79 insertions, 6 deletions

diff --git a/aps_mm_2020.tex b/aps_mm_2020.tex
index 2adf567..5ecc099 100644
--- a/aps_mm_2020.tex
+++ b/aps_mm_2020.tex
@@ -1,15 +1,18 @@
 
 \documentclass[fleqn,aspectratio=169]{beamer}
 
+\renewcommand\vec[1]{\mathbf{#1}}
+
+\setbeamerfont{title}{family=\bf}
 \setbeamerfont{frametitle}{family=\bf}
 \setbeamerfont{normal text}{family=\rm}
 \setbeamertemplate{navigation symbols}{}
 
 \usepackage{textcomp,rotating}
 
-\title{Cluster-flip colloidal and atomistic algorithms with background potentials}
+\title{Cluster-flip colloidal \& atomistic algorithms with background potentials}
 \author{Jaron Kent-Dobias \and James P Sethna}
-\institute{Cornell University}
+\institute{\includegraphics[width=7em]{figs/bold_cornell_seal_black.pdf}}
 \date{}
 
 \begin{document}
@@ -27,6 +30,14 @@
   
   \begin{columns}
     \begin{column}{0.5\textwidth}
+      \begin{enumerate}
+        \item \alert<2>{Pick a symmetry transformation.}
+        \item \alert<3>{Pick a seed.}
+        \item \alert<4>{Transform the seed.}
+        \item \alert<5>{Identify particles with intersections.}
+        \item \alert<6>{Transform each intersecting particle.}
+        \item \alert<7-12>{Repeat 5--6 until exhausted.}
+      \end{enumerate}
     \end{column}
     \begin{column}{0.5\textwidth}
       \begin{overprint}
@@ -67,12 +78,19 @@
       \end{overprint}
     \end{column}
     \begin{column}{0.5\textwidth}
+      Interacting particles with pair potential $V$ have `Ising' Hamiltonian
       \[
-        H=-\sum_{ij}V(\vec r_i, d_i, \vec r_j, d_j)
-      \]
-      \[
-        p=1-e^{-\beta\Delta E}
+        H=\sum_{ij}V_{ij}(\vec r_i, \vec r_j)
       \]
+
+      \begin{enumerate}
+        \item \alert<2>{Pick a symmetry transformation.}
+        \item \alert<3>{Pick a seed.}
+        \item \alert<4>{Transform the seed.}
+        \item \alert<5>{Identify particles with $\Delta V_{ij}>0$.}
+        \item \alert<6>{Transform each particle with probability $1-e^{-\Delta V_{ij}/T}$.}
+        \item \alert<7-10>{Repeat 5--6 until exhausted.}
+      \end{enumerate}
     \end{column}
   \end{columns}
 
@@ -82,6 +100,16 @@
   \frametitle{Hard sphere cluster flips with hard potential}
   \begin{columns}
     \begin{column}{0.5\textwidth}
+      Hard potential? Treat it like a particle!
+
+      \begin{enumerate}
+        \item \alert<2>{Pick a symmetry transformation.}
+        \item \alert<3>{Pick a seed.}
+        \item \alert<4>{Transform the seed.}
+        \item \alert<5>{Identify `particles' with intersections.}
+        \item \alert<6>{Transform each intersecting particle.}
+        \item \alert<7-15>{Repeat 5--6 until exhausted.}
+      \end{enumerate}
     \end{column}
     \begin{column}{0.5\textwidth}
       \begin{overprint}
@@ -107,6 +135,37 @@
 \end{frame}
 
 \begin{frame}
+  \frametitle{Cluster flips with soft potential}
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      Soft potential? Treat it like a (big, soft, asymmetric) particle with effective pair potential $\tilde V$!
+      \begin{enumerate}
+        \item \alert<2>{Pick a symmetry transformation.}
+        \item \alert<3>{Pick a seed.}
+        \item \alert<4>{Transform the seed.}
+        \item \alert<5>{Identify `particles' with $\Delta\tilde V_{ij}>0$.}
+        \item \alert<6>{Transform each `particle' with probability $1-e^{-\Delta\tilde V_{ij}/T}$.}
+        \item \alert<7-15>{Repeat 5--6 until exhausted.}
+      \end{enumerate}
+    \end{column}
+    \begin{column}{0.5\textwidth}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Cluster flips with soft potential}
+  \begin{columns}
+    \begin{column}{0.5\textwidth}
+      Soft potential? Treat it like a (big, soft, asymmetric) particle transformed to $r_0$!
+
+    \end{column}
+    \begin{column}{0.5\textwidth}
+    \end{column}
+  \end{columns}
+\end{frame}
+
+\begin{frame}
   \frametitle{Caveats \& improvements}
 
   Symmetries of the torus versus all space
@@ -124,6 +183,20 @@
   \frametitle{Demo time}
 \end{frame}
 
+\begin{frame}
+  \frametitle{The dirty deets}
+
+  System with symmetry group $G$ and objects with state $s_i$ (including position, radius, orientation, spin, \dots)
+  \[
+    H=\sum_{ij}V(s_i, s_j)+\sum_iU(s_i)
+  \]
+  For $s_0\in G$ and new potential $\tilde V$ defined by $\tilde V_{0i}=U(s_0^{-1}\cdot s_i)$,
+  \begin{align*}
+    \tilde H&=\sum_{ij}V_{ij}(s_i, s_j)+\sum_iU_i(s_0^{-1}\cdot s_i) \\
+     &=\sum_{ij}\tilde V_{ij}(s_i, s_j)
+  \end{align*}
+  has the form of a system without a potential.
+\end{frame}
 
 \end{document}