Ian Jauslin
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-rw-r--r--figs/atoms.fig/Makefile15
-rw-r--r--figs/atoms.fig/nematic-base.gp21
-rw-r--r--figs/atoms.fig/nematic.py90
-rw-r--r--figs/dimer_example.fig/Makefile32
-rw-r--r--figs/dimer_example.fig/dimer_conf.py235
l---------figs/dimer_example.fig/libs/dimer.sty1
-rw-r--r--figs/libs/Makefile25
-rw-r--r--figs/libs/dimer.sty33
8 files changed, 452 insertions, 0 deletions
diff --git a/figs/atoms.fig/Makefile b/figs/atoms.fig/Makefile
new file mode 100644
index 0000000..8e8462f
--- /dev/null
+++ b/figs/atoms.fig/Makefile
@@ -0,0 +1,15 @@
+PROJECTNAME=nematic
+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/nematic-base.gp b/figs/atoms.fig/nematic-base.gp
new file mode 100644
index 0000000..92ffc4d
--- /dev/null
+++ b/figs/atoms.fig/nematic-base.gp
@@ -0,0 +1,21 @@
+set terminal pngcairo size 2048,2048
+
+set key off
+unset colorbox
+unset border
+unset xtics
+unset ytics
+unset ztics
+
+set parametric
+
+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/nematic.py b/figs/atoms.fig/nematic.py
new file mode 100644
index 0000000..5c779c0
--- /dev/null
+++ b/figs/atoms.fig/nematic.py
@@ -0,0 +1,90 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=30
+# number of rods
+N=75
+# aspect ratio
+a=10
+# spread in theta angle
+spread=pi/30
+
+# 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])-2<abs(sin(relative_ang[0]))*a and abs(relative_pos[2])-a-2<abs(cos(relative_ang[0])*a)):
+ if(abs(relative_pos[1])<2 and abs(relative_pos[0])-2<abs(sin(relative_ang[0]))*a and abs(sin(relative_ang[0])*relative_pos[2]-cos(relative_ang[0])*relative_pos[0])-2<abs(sin(relative_ang[0])*a)):
+ return(True)
+ return(False)
+
+# def subtract vectors
+def subtract(x,y):
+ return([x[0]-y[0],x[1]-y[1],x[2]-y[2]])
+# rotate vector
+def unrotate(x,w):
+ ret=[x[0],x[1],x[2]]
+ # rotate phi
+ tmp=cos(w[1])*ret[0]+sin(w[1])*ret[1]
+ ret[1]=-sin(w[1])*ret[0]+cos(w[1])*ret[1]
+ ret[0]=tmp
+ # rotate theta
+ tmp=cos(w[0])*ret[0]-sin(w[0])*ret[2]
+ ret[2]=sin(w[0])*ret[0]+cos(w[0])*ret[2]
+ ret[0]=tmp
+ return(ret)
+
+# convert coordinates
+def spherical_to_cart(w):
+ return([cos(w[1])*sin(w[0]),sin(w[1])*sin(w[0]),cos(w[0])])
+def cart_to_spherical(x):
+ w=[0,0]
+ w[0]=acos(x[2])
+ if(sin(w[0]==0)):
+ return([w[0],0])
+ c=x[0]/sin(w[0])
+ s=x[1]/sin(w[0])
+ # to avoid truncation errors
+ if(abs(c)>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)<N:
+ # random position and angles
+ x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+ w=[abs(random.gauss(0,spread)), random.uniform(0,2*pi)]
+ # chek it does not interfere with other rods
+ fine=True
+ for rod in config:
+ if(check_overlap(rod,[x,w])):
+ fine=False
+ break
+ if fine:
+ config.append([x,w])
+
+for i in range(len(config)):
+ rod=config[i]
+ print(str(rod[0][0])+"+("+str(cos(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(-sin(rod[1][1]))+")*sin(u)*sin(v)+("+str(cos(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+ print(str(rod[0][1])+"+("+str(sin(rod[1][1])*cos(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][1]))+")*sin(u)*sin(v)+("+str(sin(rod[1][1])*sin(rod[1][0])*a)+")*cos(v)", end=", ")
+ print(str(rod[0][2])+"+("+str(-sin(rod[1][0]))+")*cos(u)*sin(v)+("+str(cos(rod[1][0])*a)+")*cos(v)", end=" ")
+ print("with pm3d", end="")
+ if i<len(config)-1:
+ print(", \\")
diff --git a/figs/dimer_example.fig/Makefile b/figs/dimer_example.fig/Makefile
new file mode 100644
index 0000000..386ecd1
--- /dev/null
+++ b/figs/dimer_example.fig/Makefile
@@ -0,0 +1,32 @@
+PROJECTNAME=grid dimers interaction
+LIBS=$(notdir $(wildcard libs/*))
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+SOURCES=$(addsuffix .tikz.tex, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS): $(SOURCES) $(LIBS)
+ echo $(LIBS)
+ pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
+
+$(SOURCES):
+ python3 dimer_conf.py
+
+$(LIBS):
+ ln -fs libs/$@ ./
+
+clean-libs:
+ rm -f $(LIBS)
+
+clean-aux:
+ rm -f $(addsuffix .aux, $(PROJECTNAME))
+ rm -f $(addsuffix .log, $(PROJECTNAME))
+
+clean-tex:
+ rm -f $(PDFS)
+
+clean-sources:
+ rm -f $(SOURCES)
+
+clean: clean-libs clean-aux clean-tex clean-sources
diff --git a/figs/dimer_example.fig/dimer_conf.py b/figs/dimer_example.fig/dimer_conf.py
new file mode 100644
index 0000000..f8838bd
--- /dev/null
+++ b/figs/dimer_example.fig/dimer_conf.py
@@ -0,0 +1,235 @@
+#!/usr/bin/env python3
+
+import random
+from math import *
+
+# size of the grid
+L=24
+# boundary thickness (must be even)
+l0=4
+# activity and interaction
+z=3
+J=5
+
+
+# draw random dimers in a select area
+def fill_dimers(mask,direction):
+ if(direction=="h"):
+ d=[1,0]
+ else:
+ d=[0,1]
+
+ dimers=[]
+
+ # keep track of which sites are occupied
+ occupied=[]
+ for i in range(L):
+ occupied.append([])
+ for j in range(L):
+ occupied[i].append(0)
+
+ for i in range(10000):
+ # pick a random edge (indexed by its lower-left corner)
+ e=None
+ while(e==None or e[0]+d[0]>=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]<L and e[1]+2*d[1]<L and occupied[e[0]+2*d[0]][e[1]+2*d[1]]==1):
+ interactions=interactions+1
+ if(e[0]-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)
+
+# draw loops
+def draw_loops(loops,file_desc,color):
+ for loop in loops:
+ print("\\draw[color="+color+", line width=3pt]",end="",file=file_desc)
+ for e in loop:
+ print("("+str(e[0])+","+str(e[1])+")--",end="",file=file_desc)
+ print("cycle;",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)
+
+# loops
+loop1=[]
+for i in range(0,2*l0):
+ loop1.append([mu-l0+i,mu+4.5])
+for i in range(0,4):
+ loop1.append([mu+l0-1+0.5,mu+4-i])
+for i in range(0,l0):
+ loop1.append([mu+l0+i,mu+0.5])
+for i in range(0,6):
+ loop1.append([mu+2*l0-1+0.5,mu-i])
+for i in range(0,4*l0):
+ loop1.append([mu+2*l0-1-i,mu-5.5])
+for i in range(0,6):
+ loop1.append([mu-2*l0-0.5,mu-5+i])
+for i in range(0,l0):
+ loop1.append([mu-2*l0+i,mu+0.5])
+for i in range(0,4):
+ loop1.append([mu-l0-0.5,mu+1+i])
+# core of loop1
+core_loop1=[]
+for i in range(0,2*l0-4):
+ core_loop1.append([mu-l0+2+i,mu+3.5])
+for i in range(0,3):
+ core_loop1.append([mu+l0-3+0.5,mu+3-i])
+core_loop1.append([mu+l0-2,mu+0.5])
+core_loop1.append([mu+l0-1,mu+0.5])
+for i in range(0,l0-2):
+ core_loop1.append([mu+l0+i,mu-1+0.5])
+for i in range(0,4):
+ core_loop1.append([mu+2*l0-3+0.5,mu-1-i])
+for i in range(0,4*l0-4):
+ core_loop1.append([mu+2*l0-3-i,mu-4.5])
+for i in range(0,4):
+ core_loop1.append([mu-2*l0+2-0.5,mu-4+i])
+for i in range(0,l0-2):
+ core_loop1.append([mu-2*l0+2+i,mu-1+0.5])
+core_loop1.append([mu-l0,mu+0.5])
+core_loop1.append([mu-l0+1,mu+0.5])
+for i in range(0,3):
+ core_loop1.append([mu-l0+2-0.5,mu+1+i])
+
+loop2=[[mu-1,mu+2.5],[mu-0.5,mu+2],[mu-0.5,mu+1],[mu-1,mu+0.5],[mu-1.5,mu+1],[mu-1.5,mu+2]]
+loop3=[[mu-1,mu-1.5],[mu,mu-1.5],[mu+0.5,mu-2],[mu+0.5,mu-3],[mu,mu-3.5],[mu-1,mu-3.5],[mu-1.5,mu-3],[mu-1.5,mu-2]]
+
+
+loops=[loop1,loop2,loop3]
+
+
+# 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
+
+grid=init_tikz("grid.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=grid)
+close_tikz(grid)
+
+dimers=init_tikz("dimers.tikz.tex")
+print("\\grid{"+str(L-1)+"}{"+str(L-1)+"}{(0,0)}\n", file=dimers)
+draw_dimers(v_dimers+v_mantle,h_dimers+h_mantle,dimers,"black")
+close_tikz(dimers)
+
+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 120000
index 0000000..2d83c8a
--- /dev/null
+++ b/figs/dimer_example.fig/libs/dimer.sty
@@ -0,0 +1 @@
+../../libs/dimer.sty \ No newline at end of file
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/dimer.sty b/figs/libs/dimer.sty
new file mode 100644
index 0000000..0f087ef
--- /dev/null
+++ b/figs/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
+}