solver.setPotentialByName('LennardJones', 0.1) #epsilon/kT = 0.1 is default in SASfit
print "Energy scale of Lennard Jones Potential in kT units:", solver.getEpsilonInkTUnits()
#Initialize HMSA with some (random) start alpha
solver.doHMSAclosure(1.0)
else:
#Yukawa possible with RY: With negative K (attractive besides HS) convergence may be reached for exp shift only (real HS-Yukawa)
#positive (repulsive as HS) K converges for fully shifted potential (1/r included)
solver.setPotentialByName('Yukawa', 1.0, -1.0, True) #lamda in SASfit is different; K = 0.1 is default in SASfit
print "Energy scale of Yukawa HS Potential in kT units:", solver.getInteractionStrengthInKTunits()
print "Length scale of Yukawa HS Potential in sigma units:", solver.getShieldingConstantInSigmaUnits()
#Initialize RY with some (random) start alpha
solver.doRYclosure(1.0)
solver.setVolumeDensity(0.3)
print "Volume density of liquid:", solver.getVolumeDensity()
print "start solving for optimal closure alpha...."
#Should we minimize cost functional or find a root?
doUseMinimizer = False
doSearchIndependentPlot = False
#Save iterated points in alpha space as dict to plot later
finderFunctionGraph = {}
if doUseMinimizer:
#Ein Minimum macht noch keine Nullstelle, minimierungs algorithmen
#kommen aber (auch) mit doppelten (mehrfachen) Nullstellen klar. *Falls* eine Nullstelle vorliegt,
#ist sie in jedem Fall auch ein Minimum der quadrierten funktion (bei mehreren Nullstellen kein globales Minimum)
alpha_opt = optimize.minimize(finderFunctionForAlpha, alpha_initial, args=(solver, finderFunctionGraph, doUseMinimizer,))
startDensity = 0.58
targetDensity = 0.63
totalDeltaDensity = targetDensity - startDensity
density = startDensity
deltaDensity = totalDeltaDensity
decayFactor = 2.5
deltaDensity = 0.01
print "start approaching target density", targetDensity
while density < targetDensity:
#deltaDensity /= decayFactor
density += deltaDensity
print "current density", density
solver.setVolumeDensity(density)
solver.solve()
g = solver.getRDF()
solver.setStartValue(g)
#Direct calculation
print "Directly calculating RDF for target density", targetDensity
solver.setStartValue(np.zeros(solver.getNumberOfRadialSamplingPoints()) )
solver.setVolumeDensity(targetDensity)
solver.solve()
g_direct = solver.getRDF()
#Plot results
r = np.arange(solver.getNumberOfRadialSamplingPoints() ).astype('float') + 1.0
r *= solver.getDelta_r()/solver.getHardSphereRadius()
#s.setPotentialByName('LennardJones', 0.2)
s.setPotentialByName('Star', 20)
#Define the density range to scan
densityRange = np.arange(0.3, 0.4, 0.1)
#densityRange = np.asarray([0.3])
#densityRange = np.asarray([0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5])
densityRDFdictionary = {}
#Start loop over densities and measure wall clock time
t_start = time.time()
for d in densityRange:
s.setVolumeDensity(float(d))
s.solve()
g = s.getRDF()
densityRDFdictionary[d] = g
t_stop = time.time()
#Print out benchmark
print "time used for", densityRange.size, "density parameters:", t_stop - t_start, " sec"
print "time used for one OZ run:", (t_stop - t_start)/float(densityRange.size), "seconds"
#Plot results
r = np.arange(s.getNumberOfRadialSamplingPoints() ).astype('float') + 1.0
r *= s.getDelta_r()/s.getHardSphereRadius()
for densityKey in densityRDFdictionary:
'''
import numpy as np
from scipyAndersonOZsolver import ScipyAndersonOZsolver
#plot
import matplotlib.pyplot as plt
import pylab as pl
if __name__ == '__main__':
closureRDFdictionary = {}
solver = ScipyAndersonOZsolver(port=0)
solver.setPotentialByName('HardSphere')
solver.setVolumeDensity(0.4)
#Default is PY
print "PY closure.."
solver.solve()
closureRDFdictionary['PY'] = solver.getRDF()
print "HNC closure.."
solver.doHNCclosure()
solver.solve()
closureRDFdictionary['HNC'] = solver.getRDF()
print "RY closure, alpha -> 0.."
solver.doRYclosure(alpha=0.0001) #Not exactly zero...
solver.solve()
closureRDFdictionary['RY alpha -> 0'] = solver.getRDF()
The script calculates the OZ solution
of the HS + PY system with and without
the S_c(0) result.
'''
import numpy as np
from scipyAndersonOZsolver import ScipyAndersonOZsolver
#plot
import matplotlib.pyplot as plt
if __name__ == '__main__':
solver = ScipyAndersonOZsolver(port = 0)
solver.setPotentialByName('HardSphere')
volumeDensity = 0.5
solver.setVolumeDensity(volumeDensity)
solver.setConvergenceCriterion(1.0e-4*solver.getConvergenceCriterion())
#PY is default, so no explicit settings are needed in this regard
#so solver is in desired state.
solver.solve()
#Get reference structure factor
Sq_default = solver.getSq()
#now GCE limit version
solver.doEnforceGrandCanonicalZeroQlimit()
#solver is in desired state.
solver.solve()
#Get GCE structure factor
Sq_GCE = solver.getSq()
print "reference Sq(0)", Sq_default[0]
print "GCE Sq(0)", Sq_GCE[0]
print "Analytical Sq(0)", (1.0 - volumeDensity)**4/(1.0 + 2.0*volumeDensity)**2
So far for the naming)
The script calculates the OZ solution
of the HS + PY system with and without
the S_c(0) result.
'''
import numpy as np
from scipyAndersonOZsolver import ScipyAndersonOZsolver
#plot
import matplotlib.pyplot as plt
if __name__ == '__main__':
solver = ScipyAndersonOZsolver(port=0)
solver.setPotentialByName('HardSphere')
volumeDensity = 0.5
solver.setVolumeDensity(volumeDensity)
solver.setConvergenceCriterion(1.0e-4 * solver.getConvergenceCriterion())
#PY is default, so no explicit settings are needed in this regard
#so solver is in desired state.
solver.solve()
#Get reference structure factor
Sq_default = solver.getSq()
#now GCE limit version
solver.doEnforceGrandCanonicalZeroQlimit()
#solver is in desired state.
solver.solve()
#Get GCE structure factor
Sq_GCE = solver.getSq()
print "reference Sq(0)", Sq_default[0]
print "GCE Sq(0)", Sq_GCE[0]
print "Analytical Sq(0)", (1.0 - volumeDensity)**4 / (
