Initial commitv0.0

9 files changed, 857 insertions, 0 deletions

diff --git a/figs/Nk_transition.fig/.2pt_fourier_medeq.gnuplot.swp b/figs/Nk_transition.fig/.2pt_fourier_medeq.gnuplot.swp
new file mode 100644
index 0000000..3c809d7
--- /dev/null
+++ b/figs/Nk_transition.fig/.2pt_fourier_medeq.gnuplot.swp
diff --git a/figs/Nk_transition.fig/Makefile b/figs/Nk_transition.fig/Makefile
new file mode 100644
index 0000000..d94c145
--- /dev/null
+++ b/figs/Nk_transition.fig/Makefile
@@ -0,0 +1,45 @@
+PROJECT=$(basename $(wildcard *.gnuplot))
+
+SIMPLESOLV=simplesolv
+
+all: $(addsuffix .pdf, $(PROJECT))
+
+define gnuplot2pdf
+	gnuplot $(1).gnuplot > $(1).tikz.tex
+	pdflatex -jobname $(1) -file-line-error $(1).tikz.tex
+endef
+
+define medeq_run
+	julia $(SIMPLESOLV)/main.jl -p "eq=medeq;order=200;maxiter=100;v_a=8;rho=$(1)e-3;minlrho_init=-6;nlrho_init=100;window_L=100;kmin=0;kmax=$(2);nk=100" -M easyeq momentum_distribution > medeq_$(1).dat
+endef
+
+medeq_0.3.dat:
+	$(call medeq_run,0.3,1.34)
+medeq_1.1.dat:
+	$(call medeq_run,1.1,2.07)
+medeq_1.9.dat:
+	$(call medeq_run,1.9,2.48)
+medeq_2.7.dat:
+	$(call medeq_run,2.7,2.79)
+medeq_3.5.dat:
+	$(call medeq_run,3.5,3.04)
+medeq_4.3.dat:
+	$(call medeq_run,4.3,3.49)
+
+DATS=medeq_0.3.dat medeq_1.1.dat medeq_1.9.dat medeq_2.7.dat medeq_3.5.dat medeq_4.3.dat
+
+Nk.pdf: $(DATS)
+	$(call gnuplot2pdf,$(basename $@))
+
+
+clean-aux:
+	rm -f $(addsuffix .tikz.tex, $(PROJECT))
+	rm -f *.aux *.log
+
+clean-dat:
+	rm -f $(DATS)
+
+clean-pdf:
+	rm -f $(addsuffix .pdf, $(PROJECT))
+
+clean: clean-aux clean-pdf
diff --git a/figs/Nk_transition.fig/Nk.gnuplot b/figs/Nk_transition.fig/Nk.gnuplot
new file mode 100644
index 0000000..d72a0f6
--- /dev/null
+++ b/figs/Nk_transition.fig/Nk.gnuplot
@@ -0,0 +1,49 @@
+set ylabel "$N_\\kappa-N_\\kappa^{(\\mathrm{Bog})}$"
+set xlabel "$\\kappa\\rho^{-1/3}$"
+
+#set xtics 1e-6, 1000, 1e6
+#set xtics add ("$10^{-6}$" 0.000001, "$10^{-3}$" 0.001, "$10^{0}$" 1, "$10^{3}$" 1000, "$10^6$" 1000000)
+#unset mxtics
+set xrange [:20]
+
+#set ytics 0, 1e-5, 2e-5	
+#set ytics add ("$10^{-5}$" 1e-5)
+#set mytics
+#set yrange [-0.25:0.30]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key top right box linetype rgbcolor"#999999" width 5 height 0.3 spacing 1.3
+
+rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b)
+circle_2_rgb(x) = (x < 1./6 ? rgb(255,x*6*255,0) : \
+		  (x < 2./6 ? rgb((2./6-x)*6*255,255,0) : \
+		  (x < 3./6 ? rgb(0,255,(x-2./6)*6*255) : \
+		  (x < 4./6 ? rgb(0,(4./6-x)*6*255,255) : \
+		  (x < 5./6 ? rgb((x-4./6)*6*255,0,255) : \
+		              rgb(255,0,(1-x)*6*255) \
+		  )))))
+
+
+set style line 1 linetype rgbcolor "#0000FF" linewidth 2 dashtype (2,6)
+set style line 2 linetype rgbcolor "#1E90FF" linewidth 2 dashtype (2,4)
+set style line 3 linetype rgbcolor "#FF0000" linewidth 2
+set style line 4 linetype rgbcolor "#1CEB2E" linewidth 2 dashtype (2,2)
+set style line 5 linetype rgbcolor "#228B22" linewidth 2 dashtype (4,2)
+set style line 6 linetype rgbcolor "#2F4F4F" linewidth 2 dashtype (6,2)
+set style line 7 linetype rgbcolor "#000000" linewidth 1
+
+# scattering length
+a8=3.233946179033422
+# Bogolyubov prediction
+Nk(x,rho)=-0.5+0.5*(x**2+2*rho*4*pi*a8)/sqrt(x**4+4*x**2*rho*4*pi*a8)
+
+plot \
+ 0 ls 7 notitle ,\
+ "medeq_0.3.dat" using ($1/0.3e-3**(1./3)):(4*pi*$1**2*($2*0.3e-3-Nk($1,0.3e-3))) with lines ls 1 title "$\\rho=0.3\\times10^{-3}$" ,\
+ "medeq_1.1.dat" using ($1/1.1e-3**(1./3)):(4*pi*$1**2*($2*1.1e-3-Nk($1,1.1e-3))) with lines ls 2 title "$\\rho=1.1\\times10^{-3}$" ,\
+ "medeq_1.9.dat" using ($1/1.9e-3**(1./3)):(4*pi*$1**2*($2*1.9e-3-Nk($1,1.9e-3))) with lines ls 3 title "$\\rho=1.9\\times10^{-3}$" ,\
+ "medeq_2.7.dat" using ($1/2.7e-3**(1./3)):(4*pi*$1**2*($2*2.7e-3-Nk($1,2.7e-3))) with lines ls 4 title "$\\rho=2.7\\times10^{-3}$" ,\
+ "medeq_3.5.dat" using ($1/3.5e-3**(1./3)):(4*pi*$1**2*($2*3.5e-3-Nk($1,3.5e-3))) with lines ls 5 title "$\\rho=3.5\\times10^{-3}$" ,\
+ "medeq_4.3.dat" using ($1/4.3e-3**(1./3)):(4*pi*$1**2*($2*4.3e-3-Nk($1,4.3e-3))) with lines ls 6 title "$\\rho=4.3\\times10^{-3}$"   
diff --git a/figs/Nk_transition.fig/medeq_0.3.dat b/figs/Nk_transition.fig/medeq_0.3.dat
new file mode 100644
index 0000000..3de1887
--- /dev/null
+++ b/figs/Nk_transition.fig/medeq_0.3.dat
@@ -0,0 +1,109 @@
+ 1.306248914890270e+00  1.270718647019564e-05
+ 1.265634996924049e+00  3.767361427765447e-05
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diff --git a/figs/Nk_transition.fig/medeq_1.1.dat b/figs/Nk_transition.fig/medeq_1.1.dat
new file mode 100644
index 0000000..1fafed5
--- /dev/null
+++ b/figs/Nk_transition.fig/medeq_1.1.dat
@@ -0,0 +1,123 @@
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diff --git a/figs/Nk_transition.fig/medeq_4.3.dat b/figs/Nk_transition.fig/medeq_4.3.dat
new file mode 100644
index 0000000..d9b6420
--- /dev/null
+++ b/figs/Nk_transition.fig/medeq_4.3.dat
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