Initial commit
This commit is contained in:
commit
baec072d2a
321
Bibliography.bib
Normal file
321
Bibliography.bib
Normal file
@ -0,0 +1,321 @@
|
||||
% Crystallization
|
||||
@article{Mainini2014,
|
||||
title={Crystallization in carbon nanostructures},
|
||||
author={Mainini, Edoardo and Stefanelli, Ulisse},
|
||||
journal={Communications in Mathematical Physics},
|
||||
volume={328},
|
||||
pages={545--571},
|
||||
year={2014},
|
||||
publisher={Springer}
|
||||
}
|
||||
@article{Theil2006,
|
||||
title={A proof of crystallization in two dimensions},
|
||||
author={Theil, Florian},
|
||||
journal={Communications in Mathematical Physics},
|
||||
volume={262},
|
||||
pages={209--236},
|
||||
year={2006},
|
||||
publisher={Springer}
|
||||
}
|
||||
@article{Jansen2014,
|
||||
title={Wigner crystallization in the quantum 1D jellium at all densities},
|
||||
author={Jansen, Sabine and Jung, Paul},
|
||||
journal={Communications in Mathematical Physics},
|
||||
volume={331},
|
||||
pages={1133--1154},
|
||||
year={2014},
|
||||
publisher={Springer}
|
||||
}
|
||||
|
||||
% Insight into continuous systems
|
||||
@article{Ruelle1971,
|
||||
title={Existence of a phase transition in a continuous classical system},
|
||||
author={Ruelle, David},
|
||||
journal={Physical Review Letters},
|
||||
volume={27},
|
||||
number={16},
|
||||
pages={1040},
|
||||
year={1971},
|
||||
publisher={APS}
|
||||
}
|
||||
|
||||
% Mermin-Wagner
|
||||
@article{Mermin1966,
|
||||
title={Absence of ferromagnetism or antiferromagnetism in one-or two-dimensional isotropic Heisenberg models},
|
||||
author={Mermin, N David and Wagner, Herbert},
|
||||
journal={Physical Review Letters},
|
||||
volume={17},
|
||||
number={22},
|
||||
pages={1133},
|
||||
year={1966},
|
||||
publisher={APS}
|
||||
}
|
||||
|
||||
% J-L
|
||||
@article{Jauslin2017,
|
||||
title={Crystalline ordering and large fugacity expansion for hard-core lattice particles},
|
||||
author={Jauslin, Ian and Lebowitz, Joel L},
|
||||
journal={The Journal of Physical Chemistry B},
|
||||
volume={122},
|
||||
number={13},
|
||||
pages={3266--3271},
|
||||
year={2017},
|
||||
publisher={ACS Publications}
|
||||
}
|
||||
@article{Jauslin2018,
|
||||
title={High-Fugacity Expansion, Lee--Yang Zeros, and Order--Disorder Transitions in Hard-Core Lattice Systems},
|
||||
author={Jauslin, Ian and Lebowitz, Joel L},
|
||||
journal={Communications in Mathematical Physics},
|
||||
volume={364},
|
||||
pages={655--682},
|
||||
year={2018},
|
||||
publisher={Springer}
|
||||
}
|
||||
|
||||
% Series by Mazel et al
|
||||
@article{Mazel2018,
|
||||
title={High-density hard-core model on triangular and hexagonal lattices},
|
||||
author={Mazel, A and Stuhl, I and Suhov, Y},
|
||||
journal={arXiv preprint arXiv:1803.04041},
|
||||
year={2018}
|
||||
}
|
||||
@article{Mazel2019,
|
||||
title={High-density hard-core model on $\mathbb{Z}^2$ and norm equations in ring $\mathbb{Z}[\sqrt[6]{-1}]$},
|
||||
author={Mazel, A and Stuhl, I and Suhov, Y},
|
||||
journal={arXiv preprint arXiv:1909.11648},
|
||||
year={2019}
|
||||
}
|
||||
@article{Mazel2020,
|
||||
title={The hard-core model on planar lattices: the disk-packing problem and high-density Gibbs distributions},
|
||||
author={Mazel, A and Stuhl, I and Suhov, Y},
|
||||
journal={arXiv preprint arXiv:2011.14156},
|
||||
year={2020}
|
||||
}
|
||||
@article{Mazel2021,
|
||||
title={Kepler's conjecture and phase transitions in the high-density hard-core model on $\mathbb{Z}^3$},
|
||||
author={Mazel, A and Stuhl, I and Suhov, Y},
|
||||
journal={arXiv preprint arXiv:2112.14250},
|
||||
year={2021}
|
||||
}
|
||||
|
||||
% Voronoi diagram for graphs
|
||||
@article{Mehlhorn1988,
|
||||
title={A faster approximation algorithm for the Steiner problem in graphs},
|
||||
author={Mehlhorn, Kurt},
|
||||
journal={Information Processing Letters},
|
||||
volume={27},
|
||||
number={3},
|
||||
pages={125--128},
|
||||
year={1988},
|
||||
publisher={Elsevier}
|
||||
}
|
||||
@article{Erwig2000,
|
||||
title={The graph Voronoi diagram with applications},
|
||||
author={Erwig, Martin},
|
||||
journal={Networks: An International Journal},
|
||||
volume={36},
|
||||
number={3},
|
||||
pages={156--163},
|
||||
year={2000},
|
||||
publisher={Wiley Online Library}
|
||||
}
|
||||
|
||||
% Voronoi dual on graphs
|
||||
@article{Honiden2010,
|
||||
title={Approximate shortest path queries using Voronoi duals},
|
||||
author={Honiden, Shinichi and Houle, Michael E and Sommer, Christian and Wolff, Martin},
|
||||
journal={Transactions on computational science IX: special issue on Voronoi diagrams in science and engineering},
|
||||
pages={28--53},
|
||||
year={2010},
|
||||
publisher={Springer}
|
||||
}
|
||||
|
||||
% Pirogov-Sinai theory
|
||||
@article{Pirogov1975,
|
||||
title={Phase diagrams of classical lattice systems},
|
||||
author={Pirogov, SA and Sinai, Ya G},
|
||||
journal={Theoretical and Mathematical Physics},
|
||||
volume={25},
|
||||
number={3},
|
||||
pages={1185--1192},
|
||||
year={1975}
|
||||
}
|
||||
@article{Zahradnk1984,
|
||||
title={An alternate version of Pirogov-Sinai theory},
|
||||
author={Milo{\v s} Zahradn{\'i}k},
|
||||
journal={Communications in Mathematical Physics},
|
||||
year={1984},
|
||||
volume={93},
|
||||
pages={559-581}
|
||||
}
|
||||
@article{Borgs1989,
|
||||
title={A unified approach to phase diagrams in field theory and statistical mechanics},
|
||||
author={Borgs, Christian and Imbrie, John Z},
|
||||
journal={Communications in mathematical physics},
|
||||
volume={123},
|
||||
number={2},
|
||||
pages={305--328},
|
||||
year={1989},
|
||||
publisher={Springer}
|
||||
}
|
||||
@book{Presutti2008,
|
||||
title={Scaling limits in statistical mechanics and microstructures in continuum mechanics},
|
||||
author={Presutti, Errico},
|
||||
year={2008},
|
||||
publisher={Springer Science \& Business Media}
|
||||
}
|
||||
|
||||
% m-potential
|
||||
@article{Holsztynski1978,
|
||||
title={Peierls condition and number of ground states},
|
||||
author={Holsztynski, W and Slawny, J},
|
||||
journal={Communications in Mathematical Physics},
|
||||
volume={61},
|
||||
pages={177--190},
|
||||
year={1978},
|
||||
publisher={Springer}
|
||||
}
|
||||
|
||||
% Cluster expansion
|
||||
@book{Friedli2017,
|
||||
title={Statistical mechanics of lattice systems: a concrete mathematical introduction},
|
||||
author={Friedli, Sacha and Velenik, Yvan},
|
||||
year={2017},
|
||||
publisher={Cambridge University Press}
|
||||
}
|
||||
@article{Ueltschi2003,
|
||||
author = {Ueltschi, Daniel},
|
||||
year = {2003},
|
||||
month = {05},
|
||||
pages = {},
|
||||
title = {Cluster Expansions and Correlation Functions},
|
||||
volume = {4},
|
||||
journal = {Moscow Mathematical Journal},
|
||||
doi = {10.17323/1609-4514-2004-4-2-511-522}
|
||||
}
|
||||
|
||||
% GFc's
|
||||
@article{Timar2013,
|
||||
title={Boundary-connectivity via graph theory},
|
||||
author={Tim{\'a}r, {\'A}d{\'a}m},
|
||||
journal={Proceedings of the American Mathematical Society},
|
||||
volume={141},
|
||||
number={2},
|
||||
pages={475--480},
|
||||
year={2013}
|
||||
}
|
||||
@article{Gaunt1965,
|
||||
title={Hard-sphere lattice gases. I. Plane-square lattice},
|
||||
author={Gaunt, David S and Fisher, Michael E},
|
||||
journal={The Journal of Chemical Physics},
|
||||
volume={43},
|
||||
number={8},
|
||||
pages={2840--2863},
|
||||
year={1965},
|
||||
publisher={American Institute of Physics}
|
||||
}
|
||||
|
||||
% Sphere packing
|
||||
@article{Hales2005,
|
||||
title={A proof of the Kepler conjecture},
|
||||
author={Hales, Thomas C},
|
||||
journal={Annals of mathematics},
|
||||
pages={1065--1185},
|
||||
year={2005},
|
||||
publisher={JSTOR}
|
||||
}
|
||||
@article{Hales2010,
|
||||
title={The dodecahedral conjecture},
|
||||
author={Hales, Thomas and McLaughlin, Sean},
|
||||
journal={Journal of the American Mathematical Society},
|
||||
volume={23},
|
||||
number={2},
|
||||
pages={299--344},
|
||||
year={2010}
|
||||
}
|
||||
@article{Berryman1983,
|
||||
title={Random close packing of hard spheres and disks},
|
||||
author={Berryman, James G},
|
||||
journal={Physical Review A},
|
||||
volume={27},
|
||||
number={2},
|
||||
pages={1053},
|
||||
year={1983},
|
||||
publisher={APS}
|
||||
}
|
||||
@article{Adams1972,
|
||||
title={Computation of dense random packings of hard spheres},
|
||||
author={Adams, DJ and Matheson, AJ},
|
||||
journal={The Journal of Chemical Physics},
|
||||
volume={56},
|
||||
number={5},
|
||||
pages={1989--1994},
|
||||
year={1972},
|
||||
publisher={American Institute of Physics}
|
||||
}
|
||||
@article{Viazovska2017,
|
||||
title={The sphere packing problem in dimension 8},
|
||||
author={Viazovska, Maryna S},
|
||||
journal={Annals of Mathematics},
|
||||
pages={991--1015},
|
||||
year={2017},
|
||||
publisher={JSTOR}
|
||||
}
|
||||
@article{Cohn2017,
|
||||
title={The sphere packing problem in dimension 24},
|
||||
author={Cohn, Henry and Kumar, Abhinav and Miller, Stephen and Radchenko, Danylo and Viazovska, Maryna},
|
||||
journal={Annals of Mathematics},
|
||||
volume={185},
|
||||
number={3},
|
||||
pages={1017--1033},
|
||||
year={2017},
|
||||
publisher={Department of Mathematics, Princeton University Princeton, New Jersey, USA}
|
||||
}
|
||||
@article{Isobe2015,
|
||||
title={Hard-sphere melting and crystallization with event-chain Monte Carlo},
|
||||
author={Isobe, Masaharu and Krauth, Werner},
|
||||
journal={The Journal of chemical physics},
|
||||
volume={143},
|
||||
number={8},
|
||||
pages={084509},
|
||||
year={2015},
|
||||
publisher={AIP Publishing LLC}
|
||||
}
|
||||
|
||||
% Sliding
|
||||
@article{Hadas2022,
|
||||
title={Columnar order in random packings of $2\times 2$ squares on the square lattice},
|
||||
author={Hadas, Daniel and Peled, Ron},
|
||||
journal={arXiv preprint arXiv:2206.01276},
|
||||
year={2022}
|
||||
}
|
||||
|
||||
|
||||
% Physics
|
||||
@article{WJ57, doi = {10.1063/1.1743956}, url = {https://doi.org/10.1063%2F1.1743956}, year = 1957, month = {nov},publisher = {{AIP} Publishing}, volume = {27}, number = {5}, pages = {1207--1208}, author = {W. W. Wood and J. D. Jacobson}, title = {Preliminary Results from a Recalculation of the Monte Carlo Equation of State of Hard Spheres}, journal = {The Journal of Chemical Physics} }
|
||||
@article{AW57, doi = {10.1063/1.1743957}, url = {https://doi.org/10.1063%2F1.1743957}, year = 1957, month = {nov},publisher = {{AIP} Publishing}, volume = {27}, number = {5}, pages = {1208--1209}, author = {B. J. Alder and T. E. Wainwright}, title = {Phase Transition for a Hard Sphere System}, journal = {The Journal of Chemical Physics} }
|
||||
@article{PM86, doi = {10.1038/320340a0}, url = {https://doi.org/10.1038%2F320340a0}, year = 1986, month = {mar},publisher = {Springer Nature}, volume = {320}, number = {6060}, pages = {340--342}, author = {P. N. Pusey and W. van Megen}, title = {Phase behaviour of concentrated suspensions of nearly hard colloidal spheres}, journal = {Nature} }
|
||||
@article{St88, doi = {10.1103/revmodphys.60.161}, url = {https://doi.org/10.1103%2Frevmodphys.60.161}, year = 1988, month = {jan}, publisher = {American Physical Society ({APS})}, volume = {60}, number = {1}, pages = {161--207}, author = {Katherine J. Strandburg}, title = {Two-dimensional melting}, journal = {Reviews of Modern Physics} }
|
||||
@book{Mc10, title={Advanced statistical mechanics}, author={McCoy, Barry M}, series={International Series of Monographs on Physics}, volume={146}, year={2010}, publisher={Oxford University Press}}
|
||||
@article{BK11, doi = {10.1103/physrevlett.107.155704}, url = {https://doi.org/10.1103%2Fphysrevlett.107.155704}, year = 2011, month = {oct}, publisher = {American Physical Society ({APS})}, volume = {107}, number = {15},author = {Etienne P. Bernard and Werner Krauth}, title = {Two-Step Melting in Two Dimensions: First-Order Liquid-Hexatic Transition}, journal = {Physical Review Letters} , pages={155704}}
|
||||
|
||||
% High fugacity expansions
|
||||
@article{Do68, doi = {10.1007/bf01075682}, url = {https://doi.org/10.1007%2Fbf01075682}, year = 1969, publisher = {Springer Nature}, volume = {2}, number = {4}, pages = {302--312}, author = {R. L. Dobrushin}, title = {The problem of uniqueness of a gibbsian random field and the problem of phase transitions}, journal = {Functional Analysis and Its Applications} }
|
||||
@article{HP74, doi = {10.1088/0305-4470/7/15/017}, url = {https://doi.org/10.1088%2F0305-4470%2F7%2F15%2F017}, year = 1974, month = {oct}, publisher = {{IOP} Publishing}, volume = {7}, number = {15}, pages = {1913--1917}, author = {O J Heilmann and E Praestgaard}, title = {Phase transition in a lattice gas with third nearest neighbour exclusion on a square lattice}, journal = {Journal of Physics A: Mathematical, Nuclear and General} }
|
||||
@article{EB05, doi = {10.1209/epl/i2005-10166-3}, url = {https://doi.org/10.1209%2Fepl%2Fi2005-10166-3}, year = 2005, month = {sep}, publisher = {{IOP} Publishing}, volume = {71}, number = {6}, pages = {900--905}, author = {E Eisenberg and A Baram}, title = {A first-order phase transition and a super-cooled fluid in a two-dimensional lattice gas model}, journal = {Europhysics Letters ({EPL})} }
|
||||
|
||||
|
||||
% Exactly solvable
|
||||
@book{Ba82, title={Exactly solved models in statistical mechanics}, author={Baxter, Rodney J}, year={1982}, publisher={Academic Press}}
|
||||
|
||||
% Lee-Yang
|
||||
@article{YL52, doi = {10.1103/physrev.87.404}, url = {https://doi.org/10.1103%2Fphysrev.87.404}, year = 1952, month = {aug}, publisher = {American Physical Society ({APS})}, volume = {87}, number = {3}, pages = {404--409}, author = {C. N. Yang and T. D. Lee}, title = {Statistical Theory of Equations of State and Phase Transitions. I. Theory of Condensation}, journal = {Physical Review} }
|
||||
@article{LY52, doi = {10.1103/physrev.87.410}, url = {https://doi.org/10.1103%2Fphysrev.87.410}, year = 1952, month = {aug}, publisher = {American Physical Society ({APS})}, volume = {87}, number = {3}, pages = {410--419}, author = {T. D. Lee and C. N. Yang}, title = {Statistical Theory of Equations of State and Phase Transitions. {II}. Lattice Gas and Ising Model}, journal = {Physical Review} }
|
||||
|
||||
% Mayer expansion
|
||||
@article{Ma37, doi = {10.1063/1.1749933}, url = {https://doi.org/10.1063%2F1.1749933}, year = 1937, month = {jan},publisher = {{AIP} Publishing}, volume = {5}, number = {1}, pages = {67--73}, author = {Joseph E. Mayer}, title = {The Statistical Mechanics of Condensing Systems. I}, journal = {The Journal of Chemical Physics} }
|
||||
@article{Ur27, doi = {10.1017/s0305004100011191}, url = {https://doi.org/10.1017%2Fs0305004100011191}, year = 1927, month = {apr}, publisher = {Cambridge University Press ({CUP})}, volume = {23}, number = {06}, pages = {685}, author = {H. D. Ursell}, title = {The evaluation of Gibbs{\textquotesingle} phase-integral for imperfect gases}, journal = {Mathematical Proceedings of the Cambridge Philosophical Society} }
|
||||
@article{Ru63, doi = {10.1016/0003-4916(63)90336-1}, url = {https://doi.org/10.1016%2F0003-4916%2863%2990336-1}, year = 1963, month = {oct}, publisher = {Elsevier {BV}}, volume = {25}, number = {1}, pages = {109--120}, author = {David Ruelle}, title = {Correlation functions of classical gases}, journal = {Annals of Physics} }
|
||||
|
||||
% Textbook
|
||||
@book{FV17, doi = {10.1017/9781316882603}, url = {https://doi.org/10.1017%2F9781316882603}, year = 2017, month = {nov}, publisher = {Cambridge University Press}, author = {Sacha Friedli and Yvan Velenik}, title = {Statistical Mechanics of Lattice Systems} }
|
||||
2779
He_Jauslin_2024.tex
Normal file
2779
He_Jauslin_2024.tex
Normal file
File diff suppressed because it is too large
Load Diff
48
Makefile
Normal file
48
Makefile
Normal file
@ -0,0 +1,48 @@
|
||||
PROJECTNAME=$(basename $(wildcard *.tex))
|
||||
FIGS=$(notdir $(wildcard figs/*.fig))
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
SYNCTEXS=$(addsuffix .synctex.gz, $(PROJECTNAME))
|
||||
|
||||
all: $(PROJECTNAME)
|
||||
|
||||
$(PROJECTNAME): $(FIGS)
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -file-line-error $@.tex
|
||||
pdflatex -synctex=1 $@.tex
|
||||
|
||||
$(PROJECTNAME).aux: $(FIGS)
|
||||
pdflatex -file-line-error -draftmode $(PROJECTNAME).tex
|
||||
|
||||
$(SYNCTEXS): $(FIGS)
|
||||
pdflatex -synctex=1 $(patsubst %.synctex.gz, %.tex, $@)
|
||||
|
||||
$(PROJECTNAME).bbl: $(PROJECTNAME).aux
|
||||
bibtex $(PROJECTNAME).aux
|
||||
|
||||
|
||||
figs: $(FIGS)
|
||||
|
||||
$(FIGS):
|
||||
make -C figs/$@
|
||||
for pdf in $$(find figs/$@/ -name '*.pdf'); do ln -fs "$$pdf" ./ ; done
|
||||
|
||||
clean-aux: clean-figs-aux
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .out, $(PROJECTNAME))
|
||||
|
||||
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-bibliography:
|
||||
rm -f bibliography/bibliography.tex
|
||||
|
||||
clean: clean-aux clean-tex clean-figs
|
||||
42
README
Normal file
42
README
Normal file
@ -0,0 +1,42 @@
|
||||
This directory contains the source files to typeset the article, and generate
|
||||
the figures. This can be accomplished by running
|
||||
make
|
||||
|
||||
|
||||
* Dependencies:
|
||||
|
||||
pdflatex
|
||||
TeXlive packages:
|
||||
amsfonts
|
||||
amsmath
|
||||
array
|
||||
authblk
|
||||
bm
|
||||
bbm
|
||||
caption
|
||||
dsfont
|
||||
enumitem
|
||||
geometry
|
||||
graphicx
|
||||
hyperref
|
||||
latex
|
||||
makecell
|
||||
mathtools
|
||||
multirow
|
||||
pgf
|
||||
ragged2e
|
||||
standalone
|
||||
subcaption
|
||||
xcolor
|
||||
GNU make
|
||||
python
|
||||
BibTeX
|
||||
|
||||
* Files:
|
||||
|
||||
He_Jauslin_2024.tex:
|
||||
main LaTeX file
|
||||
|
||||
figs:
|
||||
source code for the figures
|
||||
|
||||
290
figs/GFc.fig/GFc_gen.py
Normal file
290
figs/GFc.fig/GFc_gen.py
Normal file
@ -0,0 +1,290 @@
|
||||
#!/usr/bin/env python3
|
||||
|
||||
import sys
|
||||
|
||||
# This script generates a configuration of 3-staircases in which there is a
|
||||
# grid of particles in one phase, and the rest of space is filled with
|
||||
# particles in another phase.
|
||||
|
||||
# size of grid
|
||||
L1=100
|
||||
L2=100
|
||||
|
||||
# grid of particles in phase 1
|
||||
N11=12
|
||||
N12=12
|
||||
|
||||
# position of lower left particle in phase 1
|
||||
x01=30+N12
|
||||
x02=30
|
||||
|
||||
# only print from here to there
|
||||
l11=16
|
||||
l12=16
|
||||
l21=80
|
||||
l22=88
|
||||
|
||||
# R2 of the model
|
||||
R2=3
|
||||
|
||||
def main():
|
||||
# particles in phase 1
|
||||
particles1=[]
|
||||
# particles in phase 2
|
||||
particles2=[]
|
||||
|
||||
fill_particles1(particles1)
|
||||
fill_particles2(particles2,particles1)
|
||||
|
||||
# join particles
|
||||
particles=particles1+particles2
|
||||
|
||||
# compute which particles have a Voronoi cells containing a given site
|
||||
voronoi_index=particles_in_voronoi(particles)
|
||||
# compute the Voronoi cells of each particle
|
||||
voronois=voronoi_of_particles(voronoi_index,particles)
|
||||
|
||||
# check whether the particles are in the GFc
|
||||
GFc=particles_in_GFc(voronois,particles1,particles2)
|
||||
|
||||
# boundary of GFc
|
||||
support=GFc_support(GFc,voronois)
|
||||
GFc_boundary=boundary(support)
|
||||
|
||||
# print
|
||||
print_headers()
|
||||
print_particles(particles1,particles2,GFc)
|
||||
print_boundary(GFc_boundary)
|
||||
print_footers()
|
||||
|
||||
# generate grid of particles in phase 1
|
||||
def fill_particles1(particles1):
|
||||
for k1 in range(N11):
|
||||
for k2 in range(N12):
|
||||
particles1.append((x01+2*k1-k2,x02+k1+3*k2,1))
|
||||
|
||||
# fill the rest of space with particles in phase 2
|
||||
def fill_particles2(particles2, particles1):
|
||||
for x1 in range(L1):
|
||||
for x2 in range(L2):
|
||||
# index of particle
|
||||
k1=(x1+3*x2)/7
|
||||
k2=(2*x1-x2)/7
|
||||
|
||||
# check the indices are integers:
|
||||
if k1 != int(k1) or k2 != int(k2):
|
||||
continue
|
||||
|
||||
# check overlap with particles in phase 1
|
||||
if check_overlap_1((x1,x2),particles1):
|
||||
continue
|
||||
|
||||
particles2.append((x1,x2,2))
|
||||
|
||||
# check overlap with particles in phase 1
|
||||
def check_overlap_1(x,particles1):
|
||||
for p in particles1:
|
||||
if check_overlap(x,p):
|
||||
return True
|
||||
return False
|
||||
|
||||
# check overlap between two 3-staircases
|
||||
def check_overlap(x,y):
|
||||
if max(abs(y[0]-x[0]),abs(y[1]-x[1]))>2:
|
||||
return False
|
||||
if abs((y[1]-x[1])+(y[0]-x[0]))<=2:
|
||||
return True
|
||||
return False
|
||||
|
||||
|
||||
# given a site, compute the particles whose Voronoi cell the site is in
|
||||
def particles_in_voronoi(particles):
|
||||
out=[]
|
||||
for x1 in range(L1):
|
||||
for x2 in range(L2):
|
||||
# minimize distance
|
||||
mindist=L1+L2+1
|
||||
candidate_list=[]
|
||||
for p in particles:
|
||||
dd=dist_support((x1,x2),p)
|
||||
if dd<mindist:
|
||||
# reset candidate list
|
||||
candidate_list=[p]
|
||||
mindist=dd
|
||||
elif dd==mindist:
|
||||
# append candidate
|
||||
candidate_list.append(p)
|
||||
|
||||
# add list to output (keep x1,x2 as index)
|
||||
out.append(((x1,x2),candidate_list))
|
||||
return out
|
||||
|
||||
# distance between a point and the support of a particle
|
||||
def dist_support(x,p):
|
||||
# if x is in support then 0
|
||||
if abs(p[0]-x[0])+abs(p[1]-x[1])<=2 and x[0]>=p[0] and x[1]>=p[1]:
|
||||
return 0
|
||||
|
||||
# base
|
||||
out=abs(x[0]-p[0])+abs(x[1]-p[1])
|
||||
# correct this depending on which site in \sigma_p is actually closest
|
||||
# lower left quadrant: p is the closest
|
||||
if x[0]-p[0]<=0 and x[1]-p[1]<=0:
|
||||
return out
|
||||
# lines next to lower left quadrant: neighbor of p closest
|
||||
if x[0]-p[0]==1 and x[1]-p[1]<=0 or x[1]-p[1]==1 and x[0]-p[0]<=0:
|
||||
return out-1
|
||||
# otherwise: second neightbor of p closest
|
||||
return out-2
|
||||
|
||||
# from a table associating sites to voronoi cells, get particles
|
||||
def voronoi_of_particles(voronoi_index,particles):
|
||||
out=[]
|
||||
# output is indexed in the same order as particles
|
||||
for p in particles:
|
||||
vois=[]
|
||||
for v in voronoi_index:
|
||||
if p in v[1]:
|
||||
vois.append(v[0])
|
||||
out.append((p,vois))
|
||||
|
||||
return out
|
||||
|
||||
# find which particles are in the GFc
|
||||
def particles_in_GFc(voronois,particles1,particles2):
|
||||
out=[]
|
||||
# loop over particles
|
||||
for v in voronois:
|
||||
# check all other particles
|
||||
for w in voronois:
|
||||
# skip v
|
||||
if v==w:
|
||||
continue
|
||||
# check whether the distance between the cells is <=R2
|
||||
if set_dist(v[1],w[1])>R2:
|
||||
continue
|
||||
# check whether w is #-correct
|
||||
if not ((w[0][2]==1 and sharp_correct1(w[0],particles1)) or (w[0][2]==2 and sharp_correct2(w[0],particles2))):
|
||||
# in GFc
|
||||
out.append(v[0])
|
||||
break
|
||||
|
||||
return out
|
||||
|
||||
|
||||
# distance between two sets
|
||||
def set_dist(s1,s2):
|
||||
if len(s1)==0 or len(s2)==0:
|
||||
print("error: computing the distance between two sets, one of which is empty",file=sys.stderr)
|
||||
exit(-1)
|
||||
return -1
|
||||
mind=abs(s1[0][0]-s2[0][0])+abs(s1[0][1]-s2[0][1])
|
||||
for x in s1:
|
||||
for y in s2:
|
||||
if abs(x[0]-y[0])+abs(x[1]-y[1])<mind:
|
||||
mind=abs(x[0]-y[0])+abs(x[1]-y[1])
|
||||
return mind
|
||||
|
||||
# check whether a particle of type 1 is #-correct:
|
||||
def sharp_correct1(x,particles1):
|
||||
if (x[0]+2,x[1]+1,1) not in particles1:
|
||||
return False
|
||||
if (x[0]-2,x[1]-1,1) not in particles1:
|
||||
return False
|
||||
if (x[0]-3,x[1]+2,1) not in particles1:
|
||||
return False
|
||||
if (x[0]+3,x[1]-2,1) not in particles1:
|
||||
return False
|
||||
if (x[0]+1,x[1]-3,1) not in particles1:
|
||||
return False
|
||||
if (x[0]-1,x[1]+3,1) not in particles1:
|
||||
return False
|
||||
return True
|
||||
|
||||
# check whether a particle of type 2 is #-correct:
|
||||
def sharp_correct2(x,particles2):
|
||||
if (x[0]+1,x[1]+2,2) not in particles2:
|
||||
return False
|
||||
if (x[0]-1,x[1]-2,2) not in particles2:
|
||||
return False
|
||||
if (x[0]+2,x[1]-3,2) not in particles2:
|
||||
return False
|
||||
if (x[0]-2,x[1]+3,2) not in particles2:
|
||||
return False
|
||||
if (x[0]-3,x[1]+1,2) not in particles2:
|
||||
return False
|
||||
if (x[0]+3,x[1]-1,2) not in particles2:
|
||||
return False
|
||||
return True
|
||||
|
||||
|
||||
# support of a GFc
|
||||
def GFc_support(GFc,voronois):
|
||||
out=[]
|
||||
for p in GFc:
|
||||
# find Voronoi cell
|
||||
for v in voronois:
|
||||
if p==v[0]:
|
||||
out=out+v[1]
|
||||
break
|
||||
|
||||
# remove duplicates
|
||||
return list(set(out))
|
||||
|
||||
# boundary of a set
|
||||
def boundary(S):
|
||||
out=[]
|
||||
for s in S:
|
||||
if (s[0]+1,s[1]) not in S:
|
||||
out.append(((s[0]+0.5,s[1]-0.5),(s[0]+0.5,s[1]+0.5)))
|
||||
if (s[0]-1,s[1]) not in S:
|
||||
out.append(((s[0]-0.5,s[1]-0.5),(s[0]-0.5,s[1]+0.5)))
|
||||
if (s[0],s[1]+1) not in S:
|
||||
out.append(((s[0]-0.5,s[1]+0.5),(s[0]+0.5,s[1]+0.5)))
|
||||
if (s[0],s[1]-1) not in S:
|
||||
out.append(((s[0]-0.5,s[1]-0.5),(s[0]+0.5,s[1]-0.5)))
|
||||
return out
|
||||
|
||||
|
||||
# print particles
|
||||
def print_headers():
|
||||
print(r'''\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
|
||||
''')
|
||||
|
||||
# print grid
|
||||
print(r'\grid{'+str(l21-l11+1+3)+'}{'+str(l22-l12+1+3)+'}{('+str(l11-1)+','+str(l12-1)+')}')
|
||||
|
||||
def print_particles(particles1,particles2,GFc):
|
||||
for p in particles1:
|
||||
if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
|
||||
if p in GFc:
|
||||
print(r'\staircase{green}{('+str(p[0])+','+str(p[1])+')}')
|
||||
else:
|
||||
print(r'\staircase{cyan}{('+str(p[0])+','+str(p[1])+')}')
|
||||
for p in particles2:
|
||||
if p[0]>=l11 and p[0]<=l21 and p[1]>=l12 and p[1]<=l22:
|
||||
if p in GFc:
|
||||
print(r'\staircase{yellow}{('+str(p[0])+','+str(p[1])+')}')
|
||||
else:
|
||||
print(r'\staircase{red}{('+str(p[0])+','+str(p[1])+')}')
|
||||
|
||||
def print_boundary(boundary):
|
||||
for seg in boundary:
|
||||
if seg[0][0]>=l11 and seg[0][0]<=l21 and seg[0][1]>=l12 and seg[0][1]<=l22:
|
||||
if seg[1][0]>=l11 and seg[1][0]<=l21 and seg[1][1]>=l12 and seg[1][1]<=l22:
|
||||
print(r'\draw[line width=8pt]('+str(seg[0][0])+','+str(seg[0][1])+')--('+str(seg[1][0])+','+str(seg[1][1])+');')
|
||||
|
||||
def print_footers():
|
||||
print(r'''
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}''')
|
||||
|
||||
main()
|
||||
31
figs/GFc.fig/Makefile
Normal file
31
figs/GFc.fig/Makefile
Normal file
@ -0,0 +1,31 @@
|
||||
PROJECTNAME=GFc
|
||||
LIBS=$(notdir $(wildcard libs/*))
|
||||
|
||||
PDFS=$(addsuffix .pdf, $(PROJECTNAME))
|
||||
|
||||
all: $(PDFS)
|
||||
|
||||
$(PDFS): $(LIBS) GFc.tikz.tex
|
||||
pdflatex -jobname $(basename $@) -file-line-error $(patsubst %.pdf, %.tikz.tex, $@)
|
||||
|
||||
GFc.tikz.tex:
|
||||
python3 GFc_gen.py > GFc.tikz.tex
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
$(LIBS):
|
||||
ln -fs libs/$@ ./
|
||||
|
||||
clean-libs:
|
||||
rm -f $(LIBS)
|
||||
|
||||
clean-aux:
|
||||
rm -f $(addsuffix .aux, $(PROJECTNAME))
|
||||
rm -f $(addsuffix .log, $(PROJECTNAME))
|
||||
|
||||
clean-tex:
|
||||
rm -f $(PDFS)
|
||||
rm -f GFc.tikz.tex
|
||||
|
||||
clean: clean-libs clean-aux clean-tex
|
||||
1
figs/GFc.fig/shapes.sty
Symbolic link
1
figs/GFc.fig/shapes.sty
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/shapes.sty
|
||||
1
figs/boundary_rconnected.fig/Makefile
Symbolic link
1
figs/boundary_rconnected.fig/Makefile
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/Makefile
|
||||
43
figs/boundary_rconnected.fig/boundary_rconnected.tikz.tex
Normal file
43
figs/boundary_rconnected.fig/boundary_rconnected.tikz.tex
Normal file
@ -0,0 +1,43 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(0,0)}
|
||||
|
||||
\fill[color=gray](1.5,1.5)--++(5,0)--++(0,3)--++(2,0)--++(0,2)--++(-5,0)--++(0,2)--++(-2,0);
|
||||
|
||||
\fill[color=red](2,1)circle(0.1);
|
||||
\fill[color=red](3,1)circle(0.1);
|
||||
\fill[color=red](4,1)circle(0.1);
|
||||
\fill[color=red](5,1)circle(0.1);
|
||||
\fill[color=red](6,1)circle(0.1);
|
||||
\fill[color=red](7,2)circle(0.1);
|
||||
\fill[color=red](7,3)circle(0.1);
|
||||
\fill[color=red](7,4)circle(0.1);
|
||||
\fill[color=red](8,4)circle(0.1);
|
||||
\fill[color=red](9,5)circle(0.1);
|
||||
\fill[color=red](9,6)circle(0.1);
|
||||
\fill[color=red](8,7)circle(0.1);
|
||||
\fill[color=red](7,7)circle(0.1);
|
||||
\fill[color=red](6,7)circle(0.1);
|
||||
\fill[color=red](5,7)circle(0.1);
|
||||
\fill[color=red](4,7)circle(0.1);
|
||||
\fill[color=red](4,8)circle(0.1);
|
||||
\fill[color=red](3,9)circle(0.1);
|
||||
\fill[color=red](2,9)circle(0.1);
|
||||
\fill[color=red](1,8)circle(0.1);
|
||||
\fill[color=red](1,7)circle(0.1);
|
||||
\fill[color=red](1,6)circle(0.1);
|
||||
\fill[color=red](1,5)circle(0.1);
|
||||
\fill[color=red](1,4)circle(0.1);
|
||||
\fill[color=red](1,3)circle(0.1);
|
||||
\fill[color=red](1,2)circle(0.1);
|
||||
|
||||
\draw[color=red, dotted, line width=2pt](2,1)--(3,1)--(4,1)--(5,1)--(6,1)--(7,2)--(7,3)--(7,4)--(8,4)--(9,5)--(9,6)--(8,7)--(7,7)--(6,7)--(5,7)--(4,7)--(4,8)--(3,9)--(2,9)--(1,8)--(1,7)--(1,6)--(1,5)--(1,4)--(1,3)--(1,2)--cycle;
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
1
figs/boundary_rconnected.fig/shapes.sty
Symbolic link
1
figs/boundary_rconnected.fig/shapes.sty
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/shapes.sty
|
||||
1
figs/disk.fig/Makefile
Symbolic link
1
figs/disk.fig/Makefile
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/Makefile
|
||||
13
figs/disk.fig/disk.tikz.tex
Normal file
13
figs/disk.fig/disk.tikz.tex
Normal file
@ -0,0 +1,13 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{6}{6}{(-3,-3)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
19
figs/disk.fig/disk_max_1.tikz.tex
Normal file
19
figs/disk.fig/disk_max_1.tikz.tex
Normal file
@ -0,0 +1,19 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{6}{11}{(-3,-3)}
|
||||
|
||||
\square{yellow}{(-2,2)}
|
||||
\square{yellow}{(2,2)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
|
||||
\disk{magenta}{(0,5)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
19
figs/disk.fig/disk_max_2.tikz.tex
Normal file
19
figs/disk.fig/disk_max_2.tikz.tex
Normal file
@ -0,0 +1,19 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{7}{11}{(-3,-3)}
|
||||
|
||||
\square{green}{(-1,3)}
|
||||
\square{green}{(2,2)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
|
||||
\disk{magenta}{(1,5)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
32
figs/disk.fig/disk_neighbors.tikz.tex
Normal file
32
figs/disk.fig/disk_neighbors.tikz.tex
Normal file
@ -0,0 +1,32 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{8}{8}{(-4,-4)}
|
||||
|
||||
\square{green}{(-1,3)}
|
||||
\square{green}{(0,3)}
|
||||
\square{green}{(1,3)}
|
||||
\square{green}{(3,-1)}
|
||||
\square{green}{(3,0)}
|
||||
\square{green}{(3,1)}
|
||||
\square{green}{(-1,-3)}
|
||||
\square{green}{(0,-3)}
|
||||
\square{green}{(1,-3)}
|
||||
\square{green}{(-3,-1)}
|
||||
\square{green}{(-3,0)}
|
||||
\square{green}{(-3,1)}
|
||||
|
||||
\square{green}{(2,2)}
|
||||
\square{green}{(2,-2)}
|
||||
\square{green}{(-2,2)}
|
||||
\square{green}{(-2,-2)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
28
figs/disk.fig/disk_pack_1.tikz.tex
Normal file
28
figs/disk.fig/disk_pack_1.tikz.tex
Normal file
@ -0,0 +1,28 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{16}{16}{(-8,-8)}
|
||||
|
||||
\square{green}{(2,2)}
|
||||
\square{green}{(0,3)}
|
||||
\square{green}{(-3,1)}
|
||||
\square{green}{(-2,-2)}
|
||||
\square{green}{(0,-3)}
|
||||
\square{green}{(3,-1)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
|
||||
\disk{magenta}{(5,1)}
|
||||
\disk{magenta}{(2,5)}
|
||||
\disk{magenta}{(-3,4)}
|
||||
\disk{magenta}{(-5,-1)}
|
||||
\disk{magenta}{(-2,-5)}
|
||||
\disk{magenta}{(3,-4)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
26
figs/disk.fig/disk_pack_2.tikz.tex
Normal file
26
figs/disk.fig/disk_pack_2.tikz.tex
Normal file
@ -0,0 +1,26 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{16}{16}{(-8,-8)}
|
||||
|
||||
\square{yellow}{(2,2)}
|
||||
\square{yellow}{(-2,2)}
|
||||
\square{green}{(0,-3)}
|
||||
\square{green}{(3,-1)}
|
||||
\square{green}{(-3,-1)}
|
||||
|
||||
\disk{cyan}{(0,0)}
|
||||
|
||||
\disk{magenta}{(0,5)}
|
||||
\disk{magenta}{(5,1)}
|
||||
\disk{magenta}{(-5,1)}
|
||||
\disk{magenta}{(3,-4)}
|
||||
\disk{magenta}{(-3,-4)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
13
figs/disk.fig/octagon.tikz.tex
Normal file
13
figs/disk.fig/octagon.tikz.tex
Normal file
@ -0,0 +1,13 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{6}{6}{(-3,-3)}
|
||||
|
||||
\octagon{cyan}{(0,0)}
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
1
figs/disk.fig/shapes.sty
Symbolic link
1
figs/disk.fig/shapes.sty
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/shapes.sty
|
||||
28
figs/libs/Makefile
Normal file
28
figs/libs/Makefile
Normal file
@ -0,0 +1,28 @@
|
||||
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, $@)
|
||||
|
||||
install: $(PDFS)
|
||||
cp $^ $(INSTALLDIR)/
|
||||
|
||||
$(LIBS):
|
||||
ln -fs libs/$@ ./
|
||||
|
||||
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
|
||||
81
figs/libs/shapes.sty
Normal file
81
figs/libs/shapes.sty
Normal file
@ -0,0 +1,81 @@
|
||||
% 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);
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
% 3-staircase (color #1, position #2)
|
||||
% speedup
|
||||
\def\staircase#1#2{
|
||||
\fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
|
||||
\draw[color=white]#2++(-0.5,0)--++(3,0);
|
||||
\draw[color=white]#2++(-0.5,1)--++(2,0);
|
||||
\draw[color=white]#2++(-0.5,2)--++(1,0);
|
||||
\draw[color=white]#2++(0,-0.5)--++(0,3);
|
||||
\draw[color=white]#2++(1,-0.5)--++(0,2);
|
||||
\draw[color=white]#2++(2,-0.5)--++(0,1);
|
||||
\draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
|
||||
}
|
||||
%\def\staircase#1#2{
|
||||
% \fill[color=#1]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
|
||||
% \begin{scope}
|
||||
% \clip#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
|
||||
% \grid44{[color=white]#2++(-1,-1)}
|
||||
% \end{scope}
|
||||
% \draw[color=black]#2++(-0.5,-0.5)--++(3,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-3);
|
||||
%}
|
||||
|
||||
% 4-staircase (color #1, position #2)
|
||||
\def\Staircase#1#2{
|
||||
\fill[color=#1]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
|
||||
\begin{scope}
|
||||
\clip#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
|
||||
\grid55{[color=white]#2++(-1,-1)}
|
||||
\end{scope}
|
||||
\draw[color=black]#2++(-0.5,-0.5)--++(4,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-4);
|
||||
}
|
||||
|
||||
% 5-staircase (color #1, position #2)
|
||||
\def\staircaseV#1#2{
|
||||
\fill[color=#1]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
|
||||
\begin{scope}
|
||||
\clip#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
|
||||
\grid55{[color=white]#2++(-1,-1)}
|
||||
\end{scope}
|
||||
\draw[color=black]#2++(-0.5,-0.5)--++(5,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,1)--++(-1,0)--++(0,-5);
|
||||
}
|
||||
|
||||
% square (color #1, position #2)
|
||||
\def\square#1#2{
|
||||
\fill[color=#1]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
|
||||
\begin{scope}
|
||||
\clip#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
|
||||
\grid22{[color=white]#2++(-1,-1)}
|
||||
\end{scope}
|
||||
%\draw[color=black]#2++(-0.5,-0.5)--++(1,0)--++(0,1)--++(-1,0)--++(0,-1);
|
||||
}
|
||||
|
||||
% disk (color #1, position #2)
|
||||
\def\disk#1#2{
|
||||
\fill[color=#1]#2circle(2.5);
|
||||
\begin{scope}
|
||||
\clip#2circle(2.5);
|
||||
\grid66{[color=white]#2++(-3,-3)}
|
||||
\end{scope}
|
||||
\draw[color=black]#2circle(2.5);
|
||||
}
|
||||
|
||||
% octagon (color #1, position #2)
|
||||
\def\octagon#1#2{
|
||||
\fill[color=#1]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
|
||||
\begin{scope}
|
||||
\clip#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
|
||||
\grid66{[color=white]#2++(-3,-3)}
|
||||
\end{scope}
|
||||
\draw[color=black]#2++(-1,-2.5)--++(2,0)--++(1.5,1.5)--++(0,2)--++(-1.5,1.5)--++(-2,0)--++(-1.5,-1.5)--++(0,-2)--++(1.5,-1.5);
|
||||
}
|
||||
20
figs/nstaircase.fig/5staircase_case_1-1.tikz.tex
Normal file
20
figs/nstaircase.fig/5staircase_case_1-1.tikz.tex
Normal file
@ -0,0 +1,20 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(-1,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
\staircaseV{green}{(2,3)}
|
||||
|
||||
\square{gray}{(1,4)}
|
||||
\square{gray}{(3,2)}
|
||||
\square{gray}{(4,1)}
|
||||
\square{gray}{(4,2)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
25
figs/nstaircase.fig/5staircase_case_1-2.tikz.tex
Normal file
25
figs/nstaircase.fig/5staircase_case_1-2.tikz.tex
Normal file
@ -0,0 +1,25 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(-1,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
\staircaseV{green}{(3,4)}
|
||||
|
||||
\square{lightgray}{(3,3)}
|
||||
\square{lightgray}{(4,3)}
|
||||
|
||||
\square{gray}{(1,4)}
|
||||
\square{gray}{(2,3)}
|
||||
\square{gray}{(2,4)}
|
||||
\square{gray}{(3,2)}
|
||||
\square{gray}{(4,1)}
|
||||
\square{gray}{(4,2)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
26
figs/nstaircase.fig/5staircase_case_1-3.tikz.tex
Normal file
26
figs/nstaircase.fig/5staircase_case_1-3.tikz.tex
Normal file
@ -0,0 +1,26 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(-1,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
|
||||
\square{lightgray}{(2,4)}
|
||||
\square{lightgray}{(3,4)}
|
||||
\square{lightgray}{(4,2)}
|
||||
\square{lightgray}{(4,3)}
|
||||
\square{lightgray}{(4,4)}
|
||||
|
||||
\square{gray}{(1,4)}
|
||||
\square{gray}{(2,3)}
|
||||
\square{gray}{(3,2)}
|
||||
\square{gray}{(3,3)}
|
||||
\square{gray}{(4,1)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
20
figs/nstaircase.fig/5staircase_case_2-1.tikz.tex
Normal file
20
figs/nstaircase.fig/5staircase_case_2-1.tikz.tex
Normal file
@ -0,0 +1,20 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{14}{10}{(-9,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
\staircaseV{green}{(-5,2)}
|
||||
|
||||
\square{gray}{(-2,4)}
|
||||
\square{gray}{(-1,1)}
|
||||
\square{gray}{(-1,3)}
|
||||
\square{gray}{(-1,4)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
26
figs/nstaircase.fig/5staircase_case_2-2.tikz.tex
Normal file
26
figs/nstaircase.fig/5staircase_case_2-2.tikz.tex
Normal file
@ -0,0 +1,26 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{14}{10}{(-9,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
\staircaseV{green}{(-8,4)}
|
||||
|
||||
\square{lightgray}{(-3,3)}
|
||||
\square{lightgray}{(-2,2)}
|
||||
|
||||
\square{gray}{(-3,4)}
|
||||
\square{gray}{(-2,3)}
|
||||
\square{gray}{(-2,4)}
|
||||
\square{gray}{(-1,1)}
|
||||
\square{gray}{(-1,2)}
|
||||
\square{gray}{(-1,3)}
|
||||
\square{gray}{(-1,4)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
26
figs/nstaircase.fig/5staircase_case_2-3.tikz.tex
Normal file
26
figs/nstaircase.fig/5staircase_case_2-3.tikz.tex
Normal file
@ -0,0 +1,26 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{14}{10}{(-9,-1)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
|
||||
\square{lightgray}{(-4,4)}
|
||||
\square{lightgray}{(-3,3)}
|
||||
\square{lightgray}{(-3,4)}
|
||||
\square{lightgray}{(-2,2)}
|
||||
\square{lightgray}{(-2,4)}
|
||||
|
||||
\square{gray}{(-2,3)}
|
||||
\square{gray}{(-1,1)}
|
||||
\square{gray}{(-1,2)}
|
||||
\square{gray}{(-1,3)}
|
||||
\square{gray}{(-1,4)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
48
figs/nstaircase.fig/5staircase_regions.tikz.tex
Normal file
48
figs/nstaircase.fig/5staircase_regions.tikz.tex
Normal file
@ -0,0 +1,48 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(-5,-5)}
|
||||
|
||||
\staircaseV{blue}{(0,0)}
|
||||
|
||||
\square{lightgray}{(-4,4)}
|
||||
\square{lightgray}{(-3,3)}
|
||||
\square{lightgray}{(-3,4)}
|
||||
\square{lightgray}{(-2,2)}
|
||||
\square{lightgray}{(-2,3)}
|
||||
\square{lightgray}{(-2,4)}
|
||||
\square{lightgray}{(-1,1)}
|
||||
\square{lightgray}{(-1,2)}
|
||||
\square{lightgray}{(-1,3)}
|
||||
\square{lightgray}{(-1,4)}
|
||||
|
||||
\square{lightgray}{(1,4)}
|
||||
\square{lightgray}{(2,3)}
|
||||
\square{lightgray}{(2,4)}
|
||||
\square{lightgray}{(3,2)}
|
||||
\square{lightgray}{(3,3)}
|
||||
\square{lightgray}{(3,4)}
|
||||
\square{lightgray}{(4,1)}
|
||||
\square{lightgray}{(4,2)}
|
||||
\square{lightgray}{(4,3)}
|
||||
\square{lightgray}{(4,4)}
|
||||
|
||||
\square{lightgray}{(1,-1)}
|
||||
\square{lightgray}{(2,-2)}
|
||||
\square{lightgray}{(2,-1)}
|
||||
\square{lightgray}{(3,-3)}
|
||||
\square{lightgray}{(3,-2)}
|
||||
\square{lightgray}{(3,-1)}
|
||||
\square{lightgray}{(4,-4)}
|
||||
\square{lightgray}{(4,-3)}
|
||||
\square{lightgray}{(4,-2)}
|
||||
\square{lightgray}{(4,-1)}
|
||||
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
1
figs/nstaircase.fig/Makefile
Symbolic link
1
figs/nstaircase.fig/Makefile
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/Makefile
|
||||
1
figs/nstaircase.fig/shapes.sty
Symbolic link
1
figs/nstaircase.fig/shapes.sty
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/shapes.sty
|
||||
39
figs/nstaircase.fig/upper_triangular_boundary.tikz.tex
Normal file
39
figs/nstaircase.fig/upper_triangular_boundary.tikz.tex
Normal file
@ -0,0 +1,39 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{7}{7}{(-1,-1)}
|
||||
|
||||
\square{gray}{(1,4)}
|
||||
\square{gray}{(2,3)}
|
||||
\square{gray}{(2,4)}
|
||||
\square{gray}{(3,2)}
|
||||
\square{gray}{(3,3)}
|
||||
\square{gray}{(3,4)}
|
||||
\square{gray}{(4,1)}
|
||||
\square{gray}{(4,2)}
|
||||
\square{gray}{(4,3)}
|
||||
\square{gray}{(4,4)}
|
||||
|
||||
\square{yellow}{(0,4)}
|
||||
\square{yellow}{(1,3)}
|
||||
\square{yellow}{(2,2)}
|
||||
\square{yellow}{(3,1)}
|
||||
\square{yellow}{(4,0)}
|
||||
|
||||
\square{magenta}{(5,1)}
|
||||
\square{magenta}{(5,2)}
|
||||
\square{magenta}{(5,3)}
|
||||
\square{magenta}{(5,4)}
|
||||
|
||||
\square{green}{(1,5)}
|
||||
\square{green}{(2,5)}
|
||||
\square{green}{(3,5)}
|
||||
\square{green}{(4,5)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
13
figs/staircases.fig/3staircase.tikz.tex
Normal file
13
figs/staircases.fig/3staircase.tikz.tex
Normal file
@ -0,0 +1,13 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{4}{4}{(-1,-1)}
|
||||
|
||||
\staircase{cyan}{(0,0)}
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
20
figs/staircases.fig/3staircase_ground_state.tikz.tex
Normal file
20
figs/staircases.fig/3staircase_ground_state.tikz.tex
Normal file
@ -0,0 +1,20 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
|
||||
\clip(-2,6)--++(12,0)--++(0,12)--++(-12,0);
|
||||
|
||||
\grid{19}{24}{(-6,-1)}
|
||||
\foreach\x in {0,...,6}{
|
||||
\foreach\y in {0,...,6}{
|
||||
\staircase{cyan}{(2*\x-\y,\x+3*\y)}
|
||||
}
|
||||
}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
27
figs/staircases.fig/3staircase_max.tikz.tex
Normal file
27
figs/staircases.fig/3staircase_max.tikz.tex
Normal file
@ -0,0 +1,27 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{6}{6}{(-2,-2)}
|
||||
|
||||
\staircase{cyan}{(0,0)}
|
||||
|
||||
\square{green}{(0,-1)}
|
||||
\square{green}{(1,-1)}
|
||||
\square{green}{(2,-1)}
|
||||
|
||||
\square{magenta}{(-1,0)}
|
||||
\square{magenta}{(-1,1)}
|
||||
\square{magenta}{(-1,2)}
|
||||
|
||||
\square{yellow}{(1,2)}
|
||||
\square{yellow}{(2,1)}
|
||||
|
||||
\square{lightgray}{(0,3)}
|
||||
\square{lightgray}{(3,0)}
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
25
figs/staircases.fig/3staircase_pack.tikz.tex
Normal file
25
figs/staircases.fig/3staircase_pack.tikz.tex
Normal file
@ -0,0 +1,25 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{10}{10}{(-4,-4)}
|
||||
|
||||
\staircase{cyan}{(0,0)}
|
||||
|
||||
\staircase{magenta}{(2,1)}
|
||||
\staircase{magenta}{(-2,-1)}
|
||||
\staircase{magenta}{(-3,2)}
|
||||
\staircase{magenta}{(3,-2)}
|
||||
\staircase{magenta}{(1,-3)}
|
||||
\staircase{magenta}{(-1,3)}
|
||||
|
||||
\square{green}{(2,-1)}
|
||||
\square{green}{(-1,1)}
|
||||
\square{green}{(1,2)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
13
figs/staircases.fig/4staircase.tikz.tex
Normal file
13
figs/staircases.fig/4staircase.tikz.tex
Normal file
@ -0,0 +1,13 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{5}{5}{(-1,-1)}
|
||||
|
||||
\Staircase{cyan}{(0,0)}
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
31
figs/staircases.fig/4staircase_max.tikz.tex
Normal file
31
figs/staircases.fig/4staircase_max.tikz.tex
Normal file
@ -0,0 +1,31 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{7}{7}{(-2,-2)}
|
||||
|
||||
\Staircase{cyan}{(0,0)}
|
||||
|
||||
\square{green}{(0,-1)}
|
||||
\square{green}{(1,-1)}
|
||||
\square{green}{(2,-1)}
|
||||
\square{green}{(3,-1)}
|
||||
|
||||
\square{magenta}{(-1,0)}
|
||||
\square{magenta}{(-1,1)}
|
||||
\square{magenta}{(-1,2)}
|
||||
\square{magenta}{(-1,3)}
|
||||
|
||||
\square{yellow}{(3,1)}
|
||||
\square{yellow}{(2,2)}
|
||||
\square{yellow}{(1,3)}
|
||||
|
||||
\square{lightgray}{(0,4)}
|
||||
\square{lightgray}{(4,0)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
28
figs/staircases.fig/4staircase_pack.tikz.tex
Normal file
28
figs/staircases.fig/4staircase_pack.tikz.tex
Normal file
@ -0,0 +1,28 @@
|
||||
\documentclass{standalone}
|
||||
|
||||
\usepackage{tikz}
|
||||
\usepackage{shapes}
|
||||
|
||||
\begin{document}
|
||||
\begin{tikzpicture}
|
||||
\grid{13}{13}{(-5,-5)}
|
||||
|
||||
\Staircase{cyan}{(0,0)}
|
||||
|
||||
\Staircase{magenta}{(2,2)}
|
||||
\Staircase{magenta}{(-2,4)}
|
||||
\Staircase{magenta}{(-4,2)}
|
||||
\Staircase{magenta}{(-2,-2)}
|
||||
\Staircase{magenta}{(2,-4)}
|
||||
\Staircase{magenta}{(4,-2)}
|
||||
|
||||
\square{green}{(1,-1)}
|
||||
\square{green}{(3,-1)}
|
||||
\square{green}{(3,1)}
|
||||
\square{green}{(-1,1)}
|
||||
\square{green}{(-1,3)}
|
||||
\square{green}{(1,3)}
|
||||
|
||||
\end{tikzpicture}
|
||||
\end{document}
|
||||
|
||||
1
figs/staircases.fig/Makefile
Symbolic link
1
figs/staircases.fig/Makefile
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/Makefile
|
||||
1
figs/staircases.fig/shapes.sty
Symbolic link
1
figs/staircases.fig/shapes.sty
Symbolic link
@ -0,0 +1 @@
|
||||
../libs/shapes.sty
|
||||
Loading…
Reference in New Issue
Block a user