diff options
Diffstat (limited to 'figs')
| -rw-r--r-- | figs/atoms.fig/Makefile | 15 | ||||
| -rw-r--r-- | figs/atoms.fig/nematic-base.gp | 21 | ||||
| -rw-r--r-- | figs/atoms.fig/nematic.py | 90 | ||||
| -rw-r--r-- | figs/dimer_example.fig/Makefile | 32 | ||||
| -rw-r--r-- | figs/dimer_example.fig/dimer_conf.py | 235 | ||||
| l--------- | figs/dimer_example.fig/libs/dimer.sty | 1 | ||||
| -rw-r--r-- | figs/libs/Makefile | 25 | ||||
| -rw-r--r-- | figs/libs/dimer.sty | 33 |
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 +} |