As presented at UBC on 2020-01-10HEADv1.0master

11 files changed, 415 insertions, 0 deletions

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..5960ce6
--- /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", 1 "#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])-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(", \\")
diff --git a/figs/atoms.fig/crystal-base.gp b/figs/atoms.fig/crystal-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/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 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/crystal.py b/figs/atoms.fig/crystal.py
new file mode 100644
index 0000000..4b1ba3c
--- /dev/null
+++ b/figs/atoms.fig/crystal.py
@@ -0,0 +1,24 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+import sys
+
+# size of lattice
+N=5
+
+# configuration
+config=[]
+for i in range(N):
+    for j in range(N):
+        for k in range(N):
+            config.append([2*i+((j+k)%2),sqrt(3)*(j+(k%2)/3),2*sqrt(6)/3*k])
+
+
+for i in range(len(config)):
+    print(str(config[i][0])+"+cos(u)*sin(v)", end=",")
+    print(str(config[i][1])+"+sin(u)*sin(v)", end=",")
+    print(str(config[i][2])+"+cos(v)", end=" ")
+    print("with pm3d", end="")
+    if i<len(config)-1:
+        print(", \\")
diff --git a/figs/atoms.fig/gas-base.gp b/figs/atoms.fig/gas-base.gp
new file mode 100644
index 0000000..e95f005
--- /dev/null
+++ b/figs/atoms.fig/gas-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 0.5 specular 0.6
+
+set palette defined (0 "#339999", 1 "#339999")
+
+splot \
diff --git a/figs/atoms.fig/gas.py b/figs/atoms.fig/gas.py
new file mode 100644
index 0000000..8685999
--- /dev/null
+++ b/figs/atoms.fig/gas.py
@@ -0,0 +1,39 @@
+#!/usr/bin/env python3
+
+from math import *
+import random
+
+# size of space
+L=15
+# number of particles
+N=10
+
+# 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(", \\")
diff --git a/figs/atoms.fig/liquid-base.gp b/figs/atoms.fig/liquid-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /dev/null
+++ b/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 \
diff --git a/figs/atoms.fig/liquid.py b/figs/atoms.fig/liquid.py
new file mode 100644
index 0000000..99b09ba
--- /dev/null
+++ b/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(", \\")
diff --git a/figs/atoms.fig/nematic-base.gp b/figs/atoms.fig/nematic-base.gp
new file mode 100644
index 0000000..4de0ee2
--- /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", 1 "#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(", \\")