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#
# This is a rough approach to fit a model function to the density
# data of a liquid crystal. The function consists of a linear
# branch for the high temperature region and of a curved branch with
# linear asymptote for the low temperatuer branch
#
# free parameters:
# m1, m2 slopes of the linear function in the low and high T region
# Tc transition temperature
# dens_Tc density at the transition temperature
# g factor to scale tanh function
ml = -0.0001
mh = -0.0001
dens_Tc = 1.020
Tc = 45
g = 1
b = 0.1
high(x) = mh*(x-Tc) + dens_Tc
lowlin(x) = ml*(x-Tc) + dens_Tc
curve(x) = b*tanh(g*(Tc-x))
density(x) = x < Tc ? curve(x)+lowlin(x) : high(x)
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