Initial commit

figs/atoms.fig/Makefile

@@ -0,0 +1,15 @@
+PROJECTNAME=nematic liquid crystal 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)

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", 1 "#339999")
+
+splot \

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])-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
+for h in range(H):
+    config_h=[]
+    while len(config_h)<N:
+        # random position and angles
+        x=[random.uniform(0,L), random.uniform(0,L), random.gauss(h*height,spread_h)]
+        w=[abs(random.gauss(pi/2,spread_t)), random.gauss(pi/2*(1-h/(H-1)),spread_p)]
+        # chek it does not interfere with other rods
+        fine=True
+        for rod in config+config_h:
+            if(check_overlap(rod,[x,w])):
+                fine=False
+                break
+        if fine:
+            config_h.append([x,w])
+    config=config+config_h
+
+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(", \\")

figs/atoms.fig/crystal-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 "#ff00ff", 1 "#00ff00")
+
+splot \

figs/atoms.fig/crystal.py

@@ -0,0 +1,26 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+import sys
+
+# number of Cl atoms
+N=5
+
+for i in range(N):
+    for j in range(N):
+        for k in range(N):
+            if ((i+j+k)%2==0):
+                color=1
+                size=1
+            else:
+                color=0
+                size=0.5
+            print("'++' u", end=" ")
+            print("("+str(1.5*i)+"+("+str(size)+")*cos($1)*sin($2))", end=":")
+            print("("+str(1.5*j)+"+("+str(size)+")*sin($1)*sin($2))", end=":")
+            print("("+str(1.5*k)+"+("+str(size)+")*cos($2))", end=":")
+            print("("+str(color)+")", end=" ")
+            print("with pm3d", end="")
+            if i<N**3-1:
+                print(", \\")

figs/atoms.fig/liquid-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", 1 "#339999")
+
+splot \

figs/atoms.fig/liquid.py

@@ -0,0 +1,39 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=15
+# number of particles
+N=100
+
+# check whether two rods overlap
+def check_overlap(sphere1,sphere2):
+    if(sqrt((sphere2[0]-sphere1[0])**2+(sphere2[1]-sphere1[1])**2+(sphere2[2]-sphere1[2])**2)<2):
+        return(True)
+    return(False)
+
+# configuration
+config=[]
+# add spheres
+while len(config)<N:
+    # random position
+    x=[random.uniform(0,L), random.uniform(0,L), random.uniform(0,L)]
+    # check it does not interfere with other spheres
+    fine=True
+    for sphere in config:
+        if(check_overlap(sphere,x)):
+            fine=False
+            break
+    if fine:
+        config.append(x)
+
+for i in range(len(config)):
+    sphere=config[i]
+    print(str(sphere[0])+"+cos(u)*sin(v)", end=", ")
+    print(str(sphere[1])+"+sin(u)*sin(v)", end=", ")
+    print(str(sphere[2])+"+cos(v)", end="  ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")

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", 1 "#339999")
+
+splot \

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(", \\")

figs/dimer_example.fig/Makefile

@@ -0,0 +1,32 @@
+PROJECTNAME=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

figs/dimer_example.fig/dimer_conf.py

@@ -0,0 +1,167 @@
+#!/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)
+
+# 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)

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
+}