From 7629eb82cc5e05ef514912d9f393d0f42feb8c93 Mon Sep 17 00:00:00 2001 From: Ian Jauslin Date: Thu, 26 Oct 2017 20:02:17 +0000 Subject: As presented at Rutgers University on 2017-10-26 --- Jauslin_Rutgers_2017.tex | 208 +++++++++++++++++++++++ Makefile | 49 ++++++ README | 41 +++++ figs/atoms.fig/Makefile | 15 ++ figs/atoms.fig/chiral-base.gp | 22 +++ figs/atoms.fig/chiral.py | 102 +++++++++++ figs/atoms.fig/crystal-base.gp | 21 +++ figs/atoms.fig/crystal.py | 24 +++ figs/atoms.fig/gas-base.gp | 21 +++ figs/atoms.fig/gas.py | 39 +++++ figs/atoms.fig/liquid-base.gp | 21 +++ figs/atoms.fig/liquid.py | 39 +++++ figs/atoms.fig/nematic-base.gp | 21 +++ figs/atoms.fig/nematic.py | 90 ++++++++++ figs/cross_sliding.fig/Makefile | 1 + figs/cross_sliding.fig/cross_sliding_2.tikz.tex | 14 ++ figs/cross_sliding.fig/cross_sliding_3a.tikz.tex | 14 ++ figs/cross_sliding.fig/cross_sliding_3b.tikz.tex | 16 ++ figs/cross_sliding.fig/libs/shapes.sty | 1 + figs/dimer_example.fig/Makefile | 32 ++++ figs/dimer_example.fig/dimer_conf.py | 170 ++++++++++++++++++ figs/dimer_example.fig/libs/dimer.sty | 33 ++++ figs/libs/Makefile | 25 +++ figs/libs/shapes.sty | 87 ++++++++++ figs/packings.fig/Makefile | 1 + figs/packings.fig/cross_packing_l.tikz.tex | 14 ++ figs/packings.fig/cross_packing_r.tikz.tex | 14 ++ figs/packings.fig/libs/shapes.sty | 1 + figs/shapes.fig/L_tetromino.tikz.tex | 11 ++ figs/shapes.fig/Makefile | 1 + figs/shapes.fig/P_pentomino.tikz.tex | 11 ++ figs/shapes.fig/T_tetromino.tikz.tex | 11 ++ figs/shapes.fig/V_triomino.tikz.tex | 11 ++ figs/shapes.fig/cross.tikz.tex | 11 ++ figs/shapes.fig/diamond.tikz.tex | 11 ++ figs/shapes.fig/hexagon.tikz.tex | 37 ++++ figs/shapes.fig/libs/shapes.sty | 1 + libs/ian-presentation.cls | 187 ++++++++++++++++++++ 38 files changed, 1428 insertions(+) create mode 100644 Jauslin_Rutgers_2017.tex create mode 100644 Makefile create mode 100644 README create mode 100644 figs/atoms.fig/Makefile create mode 100644 figs/atoms.fig/chiral-base.gp create mode 100644 figs/atoms.fig/chiral.py create mode 100644 figs/atoms.fig/crystal-base.gp create mode 100644 figs/atoms.fig/crystal.py create mode 100644 figs/atoms.fig/gas-base.gp create mode 100644 figs/atoms.fig/gas.py create mode 100644 figs/atoms.fig/liquid-base.gp create mode 100644 figs/atoms.fig/liquid.py create mode 100644 figs/atoms.fig/nematic-base.gp create mode 100644 figs/atoms.fig/nematic.py create mode 120000 figs/cross_sliding.fig/Makefile create mode 100644 figs/cross_sliding.fig/cross_sliding_2.tikz.tex create mode 100644 figs/cross_sliding.fig/cross_sliding_3a.tikz.tex create mode 100644 figs/cross_sliding.fig/cross_sliding_3b.tikz.tex create mode 120000 figs/cross_sliding.fig/libs/shapes.sty create mode 100644 figs/dimer_example.fig/Makefile create mode 100644 figs/dimer_example.fig/dimer_conf.py create mode 100644 figs/dimer_example.fig/libs/dimer.sty create mode 100644 figs/libs/Makefile create mode 100644 figs/libs/shapes.sty create mode 120000 figs/packings.fig/Makefile create mode 100644 figs/packings.fig/cross_packing_l.tikz.tex create mode 100644 figs/packings.fig/cross_packing_r.tikz.tex create mode 120000 figs/packings.fig/libs/shapes.sty create mode 100644 figs/shapes.fig/L_tetromino.tikz.tex create mode 120000 figs/shapes.fig/Makefile create mode 100644 figs/shapes.fig/P_pentomino.tikz.tex create mode 100644 figs/shapes.fig/T_tetromino.tikz.tex create mode 100644 figs/shapes.fig/V_triomino.tikz.tex create mode 100644 figs/shapes.fig/cross.tikz.tex create mode 100644 figs/shapes.fig/diamond.tikz.tex create mode 100644 figs/shapes.fig/hexagon.tikz.tex create mode 120000 figs/shapes.fig/libs/shapes.sty create mode 100644 libs/ian-presentation.cls diff --git a/Jauslin_Rutgers_2017.tex b/Jauslin_Rutgers_2017.tex new file mode 100644 index 0000000..13099f9 --- /dev/null +++ b/Jauslin_Rutgers_2017.tex @@ -0,0 +1,208 @@ +\documentclass{ian-presentation} + +\usepackage[hidelinks]{hyperref} +\usepackage{graphicx} +\usepackage{dsfont} + +\begin{document} +\pagestyle{empty} +\hbox{}\vfil +\bf\Large +\hfil High density phases\par +\smallskip +\hfil of hard-core lattice particle systems\par +\vfil +\large +\hfil Ian Jauslin +\normalsize +\vfil +\hfil\rm joint with {\bf Joel L. Lebowitz} and {\bf Elliott H. Lieb}\par +\vfil +arXiv: \vbox{ + \hbox{\tt \href{http://arxiv.org/abs/1708.01912}{1708.01912}} + \hbox{\tt \href{http://arxiv.org/abs/1709.05297}{1709.05297}} +} +\hfill{\tt \href{http://ian.jauslin.org}{http://ian.jauslin.org}} +\eject + +\setcounter{page}1 +\pagestyle{plain} + +\title{Gas-liquid-crystal} +\vfill +\hfil +\includegraphics[width=3cm]{gas.png} +\includegraphics[width=3cm]{liquid.png} +\includegraphics[width=3cm]{crystal.png} +\vfill +\eject + +\title{Hard-core lattice particle (HCLP) systems} +\vfill +\hfil\includegraphics[width=1.2cm]{diamond.pdf} +\hfil\includegraphics[width=1.2cm]{cross.pdf} +\hfil\includegraphics[width=1.2cm]{hexagon.pdf} +\par +\vfill +\hfil\includegraphics[width=0.9cm]{V_triomino.pdf} +\hfil\includegraphics[width=0.9cm]{T_tetromino.pdf} +\hfil\includegraphics[width=0.9cm]{L_tetromino.pdf} +\hfil\includegraphics[width=0.9cm]{P_pentomino.pdf} +\vfill +\eject + +\title{Non-sliding HCLPs} +\begin{itemize} + \item There exist a {\bf finite} number $\tau$ of tilings which are \penalty-1000{\bf periodic} and {\bf isometric} to each other. +\end{itemize} +\hfil\includegraphics[width=4cm]{cross_packing_l.pdf} +\hfil\includegraphics[width=4cm]{cross_packing_r.pdf} +\vfill +\eject + +\title{Non-sliding HCLPs} +\begin{itemize} + \item Defects are {\bf localized}: for every connected particle configuration $X$ that is {\it not} the subset of a close packing and every $Y\supset X$, there is empty space in $Y$ neighboring $X$. +\end{itemize} +\vfill +\hfil\includegraphics[width=2.1cm]{cross_sliding_2.pdf} +\hfil\includegraphics[width=2.1cm]{cross_sliding_3a.pdf} +\hfil\includegraphics[width=2.4cm]{cross_sliding_3b.pdf} +\vfill +\eject + +\title{Observables} +\begin{itemize} + \item Gibbs measure: + $$ + \left_{\nu} + := + \lim_{\Lambda\to\Lambda_\infty} + \frac1{\Xi_{\Lambda,\nu}(z)} + \sum_{X\subset\Lambda}A(X)z^{|X|}\mathfrak B_\nu(X)\prod_{x\neq x'\in X}\varphi(x,x') + $$ + \vskip-10pt + \begin{itemize} + \item $\Lambda$: finite subset of lattice $\Lambda_\infty$. + \item $z\geqslant 0$: fugacity. + \item $\varphi(x,x')$: hard-core interaction. + \item $\mathfrak B_\nu$: boundary condition: favors the $\nu$-th tiling. + \end{itemize} + \vskip-5pt + + \item Pressure: + \vskip-10pt + $$ + p(z):=\lim_{\Lambda\to\Lambda_\infty}\frac1{|\Lambda|}\log\Xi_{\Lambda,\nu}(z). + $$ +\end{itemize} +\vfill\eject + +\title{Theorem} +\begin{itemize} + \item $p(z)-\rho_m\log z$ and $\left<\mathds 1_{x_1}\cdots\mathds 1_{x_n}\right>_\nu$ are {\bf analytic} functions of $1/z$ for large values of $z$. + \vfill + + \item There are $\tau$ distinct Gibbs states: + $$ + \left<\mathds 1_x\right>_\nu= + \left\{\begin{array}{ll} + 1+O(y)&\mathrm{\ if\ }x\in\mathcal L_\nu\\[0.3cm] + O(y)&\mathrm{\ if\ not} + . + \end{array}\right. + $$ +\end{itemize} +\vfill +\eject + +\title{High-fugacity expansion} +$$ + p(y)=-\rho_m\log y+\sum_{k=1}^\infty c_k y^k +$$ +\begin{itemize} + \item \href{http://dx.doi.org/10.1063/1.1697217}{[Gaunt, Fisher, 1965]}: diamonds: for $k\leqslant 9$. + \item \href{http://dx.doi.org/10.1098/rsta.1988.0077}{[Joyce, 1988]}: hexagons (integrable, \href{http://dx.doi.org/10.1088/0305-4470/13/3/007}{[Baxter, 1980]}). + \item \href{http://dx.doi.org/10.1209/epl/i2005-10166-3}{[Eisenberg, Baram, 2005]}: crosses: for $k\leqslant 6$. + \item For sliding models, the high-fugacity expansion is ill-defined. +\end{itemize} +\vfill +\eject + +\title{Liquid crystals} +\begin{itemize} + \item Orientational order and positional disorder. +\end{itemize} +\hfil\includegraphics[width=4.5cm]{nematic.png} +\hfil\includegraphics[width=4.5cm]{chiral.png} +\vfill +\eject + +\title{Heilmann-Lieb model} +\hfil\href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]} +\vfil +\hfil\includegraphics[width=5cm]{interaction.pdf} +\vfil\eject + +\title{Heilmann-Lieb model} +\begin{itemize} + \item Gibbs measure: + $$ + \left_{\mathrm v} + := + \lim_{\Lambda\to\mathbb Z^2} + \frac1{\Xi_{\Lambda,\mathrm v}(z)} + \sum_{\underline\delta\in\Omega_{\mathrm v}(\Lambda)}A(\underline\delta)z^{|\underline\delta|}\prod_{\delta\neq \delta'\in \underline\delta}e^{\frac12J\mathds 1_{\delta\sim\delta'}} + $$ + \vskip-15pt + \begin{itemize} + \item $\Lambda$: finite box. + \item $\Omega_{\mathrm v}(\Lambda)$: non-overlapping dimer configurations satisfying the boundary condition. + \item $z\geqslant 0$: fugacity. + \item $J\geqslant 0$: interaction strength. + \item $\mathds 1_{\delta\sim\delta'}$ indicator that dimers are adjacent and aligned. + \end{itemize} +\end{itemize} +\vfill +\eject + +\title{Heilmann-Lieb conjecture} +\begin{itemize} + \item \href{http://dx.doi.org/10.1007/BF01009518}{[Heilmann, Lieb, 1979]}: proved orientational order using reflection positivity. + \item HL Conjecture: absence of positional order. + \item \href{http://dx.doi.org/10.1007/s10955-005-8085-8}{[Ioffe, Velenik, Zahradn\'\i k, 2006]}, \href{http://dx.doi.org/10.1007/s00220-013-1767-1}{[Disertori, Giuliani, 2013]}: nematic liquid crystal phase in systems of hard rods on $\mathbb Z^2$. + \item \href{http://dx.doi.org/10.1007/s10955-015-1421-8}{[Alberici, 2016]}: different fugacities for horizontal and vertical dimers. + \item \href{http://dx.doi.org/10.1103/PhysRevB.89.035128}{[Papanikolaou, Charrier, Fradkin, 2014]}: numerics. +\end{itemize} +\vfill +\eject + +\title{Theorem} +For $1\ll z\ll J$, $\|(x,y)\|_{\mathrm{HL}}:=J|x|+e^{-\frac32J}z^{-\frac12}|y|$, +\begin{itemize} + \item Given two vertical edges $e_{\mathrm v},f_{\mathrm v}$, $\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}$ is {\it independent} of $e_{\mathrm v}$ and + $$ + \begin{array}{c} + \left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v}=\frac12(1+O(e^{-\frac12J}z^{-\frac12})) + \\[0.3cm] + \left<\mathds 1_{e_{\mathrm v}}\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v} + -\left<\mathds 1_{e_{\mathrm v}}\right>_{\mathrm v} + \left<\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v} + =O(e^{-c\ \mathrm{dist}_{\mathrm{HL}}(e_{\mathrm v},f_{\mathrm v})}) + \end{array} + $$ + \vskip-5pt + \item Given two horizontal edges $e_{\mathrm h},f_{\mathrm h}$, $\left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v}$ is {\it independent} of $e_{\mathrm h}$ and + $$ + \begin{array}{c} + \left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v}=O(e^{-3J}) + \\[0.3cm] + \left<\mathds 1_{e_{\mathrm h}}\mathds 1_{f_{\mathrm v}}\right>_{\mathrm v} + -\left<\mathds 1_{e_{\mathrm h}}\right>_{\mathrm v} + \left<\mathds 1_{f_{\mathrm h}}\right>_{\mathrm v} + =O(e^{-3J-c\ \mathrm{dist}_{\mathrm{HL}}(e_{\mathrm v},f_{\mathrm v})}) + \end{array} + $$ +\end{itemize} + +\end{document} diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..d80e25c --- /dev/null +++ b/Makefile @@ -0,0 +1,49 @@ +PROJECTNAME=$(basename $(wildcard *.tex)) +LIBS=$(notdir $(wildcard libs/*)) +FIGS=$(notdir $(wildcard figs/*.fig)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) +SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME)) + +all: $(PROJECTNAME) + +$(PROJECTNAME): $(LIBS) $(FIGS) + pdflatex -file-line-error $@.tex + pdflatex -synctex=1 $@.tex + +$(SYNCTEXS): $(LIBS) $(FIGS) + pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@) + + +$(LIBS): + ln -fs libs/$@ ./ + + +figs: $(FIGS) + +$(FIGS): + make -C figs/$@ + for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done + for png in $$(find figs/$@/ -name '*.png'); do ln -fs "$$png" ./ ; done + + +clean-aux: clean-figs-aux + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + rm -f $(addsuffix .out, $(PROJECTNAME)) + +clean-libs: + rm -f $(LIBS) + +clean-figs: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean; ) + rm -f $(notdir $(wildcard figs/*.fig/*.pdf)) + +clean-figs-aux: + $(foreach fig,$(addprefix figs/, $(FIGS)), make -C $(fig) clean-aux; ) + + +clean-tex: + rm -f $(PDFS) $(SYNCTEXS) + +clean: clean-aux clean-tex clean-libs clean-figs diff --git a/README b/README new file mode 100644 index 0000000..8cf60d8 --- /dev/null +++ b/README @@ -0,0 +1,41 @@ +This directory contains the source files to typeset the presentation, and +generate the figures. This can be accomplished by running + make + +This document uses a custom class file, located in the 'libs' directory, which +defines a number of commands. + + +* Dependencies: + + pdflatex + TeXlive packages: + amsfonts + graphics + hyperref + latex + pgf + standalone + GNU make + python3 + gnuplot + +* Files: + + Jauslin_Rutgers_2017.tex: + main LaTeX file + + libs: + custom LaTeX class file + + figs: + source code for the figures + + figs/dimer_example.fig/dimer_conf.py: + this python script randomly generates a suitable dimer configuration for + the figure interaction.pdf + + figs/atoms.fig/*.py: + this python script randomly generates configurations of non-overlapping + spheres and ellipsoids for the figures gas.png, liquid.png, crystal.png, + nematic.png and chiral.png. diff --git a/figs/atoms.fig/Makefile b/figs/atoms.fig/Makefile new file mode 100644 index 0000000..a4b610f --- /dev/null +++ b/figs/atoms.fig/Makefile @@ -0,0 +1,15 @@ +PROJECTNAME=crystal liquid gas nematic chiral +PNGS=$(addsuffix .png, $(PROJECTNAME)) + +all: $(PNGS) + +$(PNGS): + cp $(patsubst %.png, %, $@)-base.gp $(patsubst %.png, %, $@).gp + python $(patsubst %.png, %, $@).py >> $(patsubst %.png, %, $@).gp + gnuplot $(patsubst %.png, %, $@).gp > $@ + +clean-aux: + rm -f $(addsuffix .gp, $(PROJECTNAME)) + +clean: clean-aux + rm -f $(PNGS) diff --git a/figs/atoms.fig/chiral-base.gp b/figs/atoms.fig/chiral-base.gp new file mode 100644 index 0000000..74db566 --- /dev/null +++ b/figs/atoms.fig/chiral-base.gp @@ -0,0 +1,22 @@ +set terminal pngcairo size 2048,2048 + +set key off +unset colorbox +unset border +unset xtics +unset ytics +unset ztics + +set parametric + +set view 80,10,1.5 +set view equal xyz + +set isosample 100 + +set pm3d depthorder +set pm3d lighting primary 0.50 specular 0.6 + +set palette defined (0 "#339999") + +splot \ diff --git a/figs/atoms.fig/chiral.py b/figs/atoms.fig/chiral.py new file mode 100644 index 0000000..eed6df8 --- /dev/null +++ b/figs/atoms.fig/chiral.py @@ -0,0 +1,102 @@ +#!/usr/bin/env python3 + +from math import * +import random +import sys + +# size of space +L=30 +# number of lines +H=5 +# heigh of lines +height=5 +# number of rods per line +N=16 +# aspect ratio +a=10 +# spread in theta angle +spread_t=pi/60 +# in phi +spread_p=pi/60 +# in height +spread_h=1/120 + +# check whether two rods overlap +def check_overlap(rod1,rod2): + # relative placement + relative_pos=unrotate(subtract(rod2[0],rod1[0]), rod1[1]) + if(abs(relative_pos[0])<2 and abs(relative_pos[1])<2 and abs(relative_pos[2])<2): + return(True) + # relative angle + relative_ang=cart_to_spherical(unrotate(spherical_to_cart(rod2[1]), rod1[1])) + # exclusion volume + # rotate other rod + relative_pos=unrotate(relative_pos, [0,relative_ang[1]]) + #if(abs(relative_pos[1])<2 and abs(relative_pos[0])-21 and abs(c)<1.0001): + if(c>0): + return([w[0],0]) + else: + return([w[0],pi]) + if(s>=0): + return([w[0],acos(c)]) + return([w[0],2*pi-acos(c)]) + +# configuration +config=[] +# add rods +for h in range(H): + config_h=[] + while len(config_h)1 and abs(c)<1.0001): + if(c>0): + return([w[0],0]) + else: + return([w[0],pi]) + if(s>=0): + return([w[0],acos(c)]) + return([w[0],2*pi-acos(c)]) + +# configuration +config=[] +# add rods +while len(config)=L or e[1]+d[1]>=L or mask[e[0]][e[1]]==0 or mask[e[0]+d[0]][e[1]+d[1]]==0): + e=[random.randint(0,L-1),random.randint(0,L-1)] + # check whether a dimer can be added to the edge + if(occupied[e[0]][e[1]]==0 and occupied[e[0]+d[0]][e[1]+d[1]]==0): + # number of interactions + interactions=0 + if(e[0]+2*d[0]=0 and e[1]-d[1]>=0 and occupied[e[0]-d[0]][e[1]-d[1]]==1): + interactions=interactions+1 + # probability of adding the dimer + p=1/(1+1/z*exp(-J*interactions)) + if(p>random.random()): + # add dimer + dimers.append(e) + occupied[e[0]][e[1]]=1 + occupied[e[0]+d[0]][e[1]+d[1]]=1 + + return(dimers) + +# find interactions +def interactions(dimers,direction): + if(direction=="h"): + d=[1,0] + else: + d=[0,1] + + out=[] + for d1 in dimers: + for d2 in dimers: + if(d1[0]-d2[0]==2*d[0] and d1[1]-d2[1]==2*d[1]): + out.append([d2[0]+d[0],d2[1]+d[1]]) + return(out) + + +# draw dimers +def draw_dimers(v_dimers,h_dimers,file_desc,color): + for d in v_dimers: + print("\\dimer{[color="+color+"]("+str(d[0])+","+str(d[1])+")}v", file=file_desc) + print("", file=file_desc) + for d in h_dimers: + print("\\dimer{[color="+color+"]("+str(d[0])+","+str(d[1])+")}h", file=file_desc) + print("", file=file_desc) + +# draw interactions +def draw_interactions(v_interactions,h_interactions,file_desc): + for d in v_interactions: + print("\\interaction{("+str(d[0])+","+str(d[1])+")}v", file=file_desc) + print("", file=file_desc) + for d in h_interactions: + print("\\interaction{("+str(d[0])+","+str(d[1])+")}h", file=file_desc) + print("", file=file_desc) + +# init tikz file +def init_tikz(filename): + file_desc=open(filename,"w") + print("\\documentclass{standalone}\n\n\\usepackage{tikz}\n\\usepackage{dimer}\n\\usetikzlibrary{decorations.pathmorphing}\n\n\\begin{document}\n\\begin{tikzpicture}\n\n", file=file_desc) + return(file_desc) + +# close tikz file +def close_tikz(file_desc): + print("\\end{tikzpicture}\n\\end{document}", file=file_desc) + file_desc.close() + + +mu=int(L/2) + +# masks +# init +v_mask=[] +h_mask=[] +for i in range(L): + v_mask.append([]) + h_mask.append([]) + for j in range(L): + v_mask[i].append(1) + h_mask[i].append(0) +# draw masks +for i in range(mu-l0,mu+l0): + for j in range(mu+1,mu+5): + v_mask[i][j]=0 +for i in range(mu-2*l0,mu+2*l0): + for j in range(mu-5,mu+1): + v_mask[i][j]=0 +for i in range(mu-l0+2,mu+l0-2): + for j in range(mu+1,mu+4): + h_mask[i][j]=1 +for i in range(mu-l0,mu+l0): + h_mask[i][mu]=1 +for i in range(mu-2*l0+2,mu+2*l0-2): + for j in range(mu-4,mu): + h_mask[i][j]=1 +h_mask[mu-1][mu+1]=0 +h_mask[mu-1][mu+2]=0 +h_mask[mu-1][mu-3]=0 +h_mask[mu-1][mu-2]=0 +h_mask[mu][mu-3]=0 +h_mask[mu][mu-2]=0 + +# random dimers in mask +v_dimers=fill_dimers(v_mask,"v") +h_dimers=fill_dimers(h_mask,"h") + +# mantle dimers +h_mantle=[] +for i in range(0,l0): + h_mantle.append([mu-l0+2*i,mu+4]) +for i in range(0,4): + h_mantle.append([mu+l0-2,mu+4-i]) + h_mantle.append([mu-l0,mu+4-i]) +for i in range(0,int(l0/2)): + h_mantle.append([mu+l0+2*i,mu]) + h_mantle.append([mu-l0-2-2*i,mu]) +for i in range(0,5): + h_mantle.append([mu+2*l0-2,mu-i]) + h_mantle.append([mu-2*l0,mu-i]) +for i in range(0,2*l0): + h_mantle.append([mu-2*l0+2*i,mu-5]) + +v_mantle=[] +v_mantle.append([mu-1,mu+1]) +v_mantle.append([mu-1,mu-3]) +v_mantle.append([mu,mu-3]) + +# interactions +v_interactions=interactions(v_dimers+v_mantle,"v") +h_interactions=interactions(h_dimers+h_mantle,"h") + + +# files + +interaction=init_tikz("interaction.tikz.tex") +print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=interaction) +draw_interactions(v_interactions,h_interactions,interaction) +draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,interaction,"black") +close_tikz(interaction) + diff --git a/figs/dimer_example.fig/libs/dimer.sty b/figs/dimer_example.fig/libs/dimer.sty new file mode 100644 index 0000000..0f087ef --- /dev/null +++ b/figs/dimer_example.fig/libs/dimer.sty @@ -0,0 +1,33 @@ +% square lattice (width #1, height #2, origin #3) +\def\grid#1#2#3{ + \foreach\i in {0,...,#2}{ + \draw#3++(0,\i)--++(#1,0); + } + \foreach\i in {0,...,#1}{ + \draw#3++(\i,0)--++(0,#2); + } +} + +% dimer (bottom-left vertex #1, vertical or horizontal #2) +\def\dimer#1#2{ + \if#2h + \draw[line width=5pt]#1--++(1,0); + \fill#1circle(7pt); + \fill#1++(1,0)circle(7pt); + \else + \draw[line width=5pt]#1--++(0,1); + \fill#1circle(7pt); + \fill#1++(0,1)circle(7pt); + \fi +} + +% interactions (bottom-left vertex #1, vertical or horizontal #2) +\def\interaction#1#2{ + \if#2h + \draw[line width=5pt, color=white]#1--++(1,0); + \draw[line width=4pt, decorate, decoration={snake}, color=red]#1--++(1,0); + \else + \draw[line width=5pt, color=white]#1--++(0,1); + \draw[line width=4pt, decorate, decoration={snake}, color=red]#1--++(0,1); + \fi +} diff --git a/figs/libs/Makefile b/figs/libs/Makefile new file mode 100644 index 0000000..994463b --- /dev/null +++ b/figs/libs/Makefile @@ -0,0 +1,25 @@ +PROJECTNAME=$(basename $(basename $(wildcard *.tikz.tex))) +LIBS=$(notdir $(wildcard libs/*)) + +PDFS=$(addsuffix .pdf, $(PROJECTNAME)) + +all: $(PDFS) + +$(PDFS): $(LIBS) + echo $(LIBS) + pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@) + +$(LIBS): + ln -fs libs/$@ ./ + +clean-libs: + rm -f $(LIBS) + +clean-aux: + rm -f $(addsuffix .aux, $(PROJECTNAME)) + rm -f $(addsuffix .log, $(PROJECTNAME)) + +clean-tex: + rm -f $(PDFS) + +clean: clean-libs clean-aux clean-tex diff --git a/figs/libs/shapes.sty b/figs/libs/shapes.sty new file mode 100644 index 0000000..ee9a343 --- /dev/null +++ b/figs/libs/shapes.sty @@ -0,0 +1,87 @@ +% square lattice (width #1, height #2, origin #3, spacing #4) +\def\grid#1#2#3{ + \foreach\i in {0,...,#2}{ + \draw#3++(0,\i)--++(#1,0); + } + \foreach\i in {0,...,#1}{ + \draw#3++(\i,0)--++(0,#2); + } +} + + +% cross (color #1, position #2) +\def\cross#1#2{ + \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); + \begin{scope} + \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); + \grid44{[color=white]#2++(-2,-2)} + \end{scope} + \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-1)--++(-1,0)--++(0,-1)--++(1,0)--++(0,-1)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); +} + +% V triomino (color #1, position #2) +\def\Vtriomino#1#2{ + \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0); + \begin{scope} + \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0); + \grid33{[color=white]#2++(-1,-1)} + \end{scope} + \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-2)--++(2,0)--++(0,1)--++(-1,0); +} + +% T tetromino (color #1, position #2) +\def\Ttetromino#1#2{ + \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); + \begin{scope} + \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); + \grid34{[color=white]#2++(-1,-2)} + \end{scope} + \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,1)--++(-1,0); +} + +% L tetromino (color #1, position #2) +\def\Ltetromino#1#2{ + \fill[color=#1]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1); + \begin{scope} + \clip#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1); + \grid34{[color=white]#2++(-1,-2)} + \end{scope} + \draw[color=black]#2++(0.5,0.5)--++(0,1)--++(-1,0)--++(0,-3)--++(2,0)--++(0,1)--++(-1,0)--++(0,1); +} + +% P pentomino (color #1, position #2) +\def\Ppentomino#1#2{ + \fill[color=#1]#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2); + \begin{scope} + \clip#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2); + \grid34{[color=white]#2++(-1,-2)} + \end{scope} + \draw[color=black]#2++(1.5,1.5)--++(-2,0)--++(0,-3)--++(1,0)--++(0,1)--++(1,0)--++(0,2); +} + +% 1x1 square (color #1, position #2) +\def\square#1#2{ + \fill[color=#1]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle; + \draw[color=black]#2++(-0.5,-0.5)--++(0,1)--++(1,0)--++(0,-1)--cycle; + \draw[color=white]#2++(-0.5,0)--++(1,0); + \draw[color=white]#2++(0,-0.5)--++(0,1); +} + +% 2x2 square (color #1, position #2) +\def\ttsquare#1#2{ + \fill[color=#1]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle; + \draw[color=black]#2++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle; +} +\def\ttsquareempty#1{ + \draw[color=black]#1++(-1,-1)--++(0,2)--++(2,0)--++(0,-2)--cycle; +} + +% diamond (color #1, position #2) +\def\diamond#1#2{ + \fill[color=#1]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle; + \begin{scope} + \clip#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle; + \grid22{[color=white]#2++(-1,-1)} + \end{scope} + \draw[color=black]#2++(0,-1)--++(1,1)--++(-1,1)--++(-1,-1)--cycle; +} diff --git a/figs/packings.fig/Makefile b/figs/packings.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/packings.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile \ No newline at end of file diff --git a/figs/packings.fig/cross_packing_l.tikz.tex b/figs/packings.fig/cross_packing_l.tikz.tex new file mode 100644 index 0000000..b7b6b74 --- /dev/null +++ b/figs/packings.fig/cross_packing_l.tikz.tex @@ -0,0 +1,14 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} + \foreach \k in {0,...,3}{ + \foreach \l in {0,...,3}{ + \cross{teal}{(-2*\l,\l)++(\k,2*\k)} + } + } +\end{tikzpicture} +\end{document} diff --git a/figs/packings.fig/cross_packing_r.tikz.tex b/figs/packings.fig/cross_packing_r.tikz.tex new file mode 100644 index 0000000..1332a68 --- /dev/null +++ b/figs/packings.fig/cross_packing_r.tikz.tex @@ -0,0 +1,14 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} + \foreach \k in {0,...,3}{ + \foreach \l in {0,...,3}{ + \cross{teal}{(-\l,2*\l)++(2*\k,\k)} + } + } +\end{tikzpicture} +\end{document} diff --git a/figs/packings.fig/libs/shapes.sty b/figs/packings.fig/libs/shapes.sty new file mode 120000 index 0000000..eaa25c7 --- /dev/null +++ b/figs/packings.fig/libs/shapes.sty @@ -0,0 +1 @@ +../../libs/shapes.sty \ No newline at end of file diff --git a/figs/shapes.fig/L_tetromino.tikz.tex b/figs/shapes.fig/L_tetromino.tikz.tex new file mode 100644 index 0000000..5c82766 --- /dev/null +++ b/figs/shapes.fig/L_tetromino.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid34{(-1,-2)} +\Ltetromino{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/Makefile b/figs/shapes.fig/Makefile new file mode 120000 index 0000000..704310e --- /dev/null +++ b/figs/shapes.fig/Makefile @@ -0,0 +1 @@ +../libs/Makefile \ No newline at end of file diff --git a/figs/shapes.fig/P_pentomino.tikz.tex b/figs/shapes.fig/P_pentomino.tikz.tex new file mode 100644 index 0000000..9ef3990 --- /dev/null +++ b/figs/shapes.fig/P_pentomino.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid34{(-1,-2)} +\Ppentomino{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/T_tetromino.tikz.tex b/figs/shapes.fig/T_tetromino.tikz.tex new file mode 100644 index 0000000..087e809 --- /dev/null +++ b/figs/shapes.fig/T_tetromino.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid34{(-1,-2)} +\Ttetromino{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/V_triomino.tikz.tex b/figs/shapes.fig/V_triomino.tikz.tex new file mode 100644 index 0000000..ba07c5f --- /dev/null +++ b/figs/shapes.fig/V_triomino.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid33{(-1,-1)} +\Vtriomino{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/cross.tikz.tex b/figs/shapes.fig/cross.tikz.tex new file mode 100644 index 0000000..ef5f391 --- /dev/null +++ b/figs/shapes.fig/cross.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid44{(-2,-2)} +\cross{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/diamond.tikz.tex b/figs/shapes.fig/diamond.tikz.tex new file mode 100644 index 0000000..6d9eaa4 --- /dev/null +++ b/figs/shapes.fig/diamond.tikz.tex @@ -0,0 +1,11 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} +\grid44{(-2,-2)} +\diamond{teal}{(0,0)} +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/hexagon.tikz.tex b/figs/shapes.fig/hexagon.tikz.tex new file mode 100644 index 0000000..a23b7dc --- /dev/null +++ b/figs/shapes.fig/hexagon.tikz.tex @@ -0,0 +1,37 @@ +\documentclass{standalone} + +\usepackage{tikz} +\usepackage{shapes} + +\begin{document} +\begin{tikzpicture} + +\draw(0,0)--++(2,0); +\draw(120:1)--++(3,0); +\draw(120:2)--++(4,0); +\draw(120:2)++(60:1)--++(3,0); +\draw(120:2)++(60:2)--++(2,0); + +\draw(0,0)--++(60:4); +\draw(1,0)--++(60:3); +\draw(2,0)--++(60:2); +\draw(120:1)--++(60:3); +\draw(120:2)--++(60:2); + +\draw(0,0)--++(120:2); +\draw(1,0)--++(120:3); +\draw(2,0)--++(120:4); +\draw(2,0)++(60:1)--++(120:3); +\draw(2,0)++(60:2)--++(120:2); + +\fill[color=teal](60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle; + +\draw[color=white](60:1)--++(60:2); +\draw[color=white](60:1)++(1,0)--++(120:2); +\draw[color=white](60:1)++(120:1)--++(2,0); + +\draw(60:1)--++(0:1)--++(60:1)--++(120:1)--++(180:1)--++(240:1)--++(300:1)--cycle; + + +\end{tikzpicture} +\end{document} diff --git a/figs/shapes.fig/libs/shapes.sty b/figs/shapes.fig/libs/shapes.sty new file mode 120000 index 0000000..eaa25c7 --- /dev/null +++ b/figs/shapes.fig/libs/shapes.sty @@ -0,0 +1 @@ +../../libs/shapes.sty \ No newline at end of file diff --git a/libs/ian-presentation.cls b/libs/ian-presentation.cls new file mode 100644 index 0000000..7d8331b --- /dev/null +++ b/libs/ian-presentation.cls @@ -0,0 +1,187 @@ +%% +%% Ian's presentation class +%% + +%% TeX format +\NeedsTeXFormat{LaTeX2e}[1995/12/01] + +%% class name +\ProvidesClass{ian-presentation}[2017/09/29] + +\def\ian@defaultoptions{ + \pagestyle{plain} + \RequirePackage{color} + \RequirePackage{amssymb} +} + +%% paper dimensions +\setlength\paperheight{240pt} +\setlength\paperwidth{320pt} + +%% fonts +\input{size11.clo} +\DeclareOldFontCommand{\rm}{\normalfont\rmfamily}{\mathrm} +\DeclareOldFontCommand{\sf}{\normalfont\sffamily}{\mathsf} +\DeclareOldFontCommand{\tt}{\normalfont\ttfamily}{\mathtt} +\DeclareOldFontCommand{\bf}{\normalfont\bfseries}{\mathbf} +\DeclareOldFontCommand{\it}{\normalfont\itshape}{\mathit} + +%% text dimensions +\textheight=208pt +\textwidth=272pt +\hoffset=-1in +\voffset=-1in +\oddsidemargin=24pt +\evensidemargin=24pt +\topmargin=8pt +\headheight=0pt +\headsep=0pt +\marginparsep=0pt +\marginparwidth=0pt +\footskip=16pt + + +%% remove default skips +\parindent=0pt +\parskip=0pt +\baselineskip=0pt + +%% something is wrong with \thepage, redefine it +\gdef\thepage{\the\c@page} + +%% correct vertical alignment at the end of a document +\AtEndDocument{ + % save total slide count + \immediate\write\@auxout{\noexpand\gdef\noexpand\slidecount{\thepage}} + \vfill + \eject +} + + +%% footer +\def\ps@plain{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{\tiny\hfill\thepage/\safe\slidecount\hfill} + \def\@evenfoot{\@oddfoot} +} +\def\ps@empty{ + \def\@oddhead{} + \def\@evenhead{\@oddhead} + \def\@oddfoot{} + \def\@evenfoot{\@oddfoot} +} + + +%% title of slide +\def\title#1{ + \hfil{\bf\large #1}\par + \hfil\vrule width0.75\textwidth height0.3pt\par + \vskip5pt +} + + +%% hyperlinks +% hyperlinkcounter +\newcounter{lncount} +% hyperref anchor +\def\hrefanchor{% +\stepcounter{lncount}% +\hypertarget{ln.\thelncount}{}% +} + +%% define a command and write it to aux file +\def\outdef#1#2{% + % define command% + \expandafter\xdef\csname #1\endcsname{#2}% + % hyperlink number% + \expandafter\xdef\csname #1@hl\endcsname{\thelncount}% + % write command to aux% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1\endcsname{\csname #1\endcsname}}% + \immediate\write\@auxout{\noexpand\expandafter\noexpand\gdef\noexpand\csname #1@hl\endcsname{\thelncount}}% +} + +%% can call commands even when they are not defined +\def\safe#1{% + \ifdefined#1% + #1% + \else% + {\color{red}\bf?}% + \fi% +} + + +%% itemize +\newlength\itemizeskip +% left margin for items +\setlength\itemizeskip{20pt} +\newlength\itemizeseparator +% space between the item symbol and the text +\setlength\itemizeseparator{5pt} +% penalty preceding an itemize +\def\itemizepenalty{0} +% counter counting the itemize level +\newcounter{itemizecount} + +% item symbol +\def\itemizept#1{ + \ifnum#1=1 + \textbullet + \else + $\scriptstyle\blacktriangleright$ + \fi +} + +\newlength\current@itemizeskip +\setlength\current@itemizeskip{0pt} +\def\itemize{ + \par\penalty\itemizepenalty\medskip\penalty\itemizepenalty + \addtocounter{itemizecount}{1} + \addtolength\current@itemizeskip{\itemizeskip} + \leftskip\current@itemizeskip +} +\def\enditemize{ + \addtocounter{itemizecount}{-1} + \addtolength\current@itemizeskip{-\itemizeskip} + \par\leftskip\current@itemizeskip + \medskip +} +\newlength\itempt@total +\def\item{ + \settowidth\itempt@total{\itemizept\theitemizecount} + \addtolength\itempt@total{\itemizeseparator} + \par + \medskip + \hskip-\itempt@total\itemizept\theitemizecount\hskip\itemizeseparator +} + +%% enumerate +\newcounter{enumerate@count} +\def\enumerate{ + \setcounter{enumerate@count}0 + \let\olditem\item + \let\olditemizept\itemizept + \def\item{ + % counter + \stepcounter{enumerate@count} + % set header + \def\itemizept{\theenumerate@count.} + % hyperref anchor + \hrefanchor + % define tag (for \label) + \xdef\tag{\theenumerate@count} + \olditem + } + \itemize +} +\def\endenumerate{ + \enditemize + \let\item\olditem + \let\itemizept\olditemizept +} + + +%% end +\ian@defaultoptions + +\endinput -- cgit v1.2.3-54-g00ecf