import pylab as plt
import SW
import RG
eta_conv = SW.sigma**3 * plt.pi / 6
n = plt.linspace(1e-8, 0.2, 10000)
### Low temp ###
T = 0.3
npart0 = 0.0462316928818
npart1 = 0.0776670124628
plt.figure()
plt.plot(n * eta_conv, RG.phi(T, n, npart0, 0), label='i=0')
plt.plot(n * eta_conv, RG.phi(T, n, npart1, 1), label='i=1')
plt.title('T = %0.2f' % T)
plt.ylabel(r'$\phi$')
plt.xlabel(r'$\eta$')
plt.ylim(-0.04, 0.1)
plt.xlim(0, 0.7)
plt.legend(loc=0)
plt.savefig('figs/phi-RG-lowT.pdf')
### High Temp ###
T = 1.32
npart0 = 0.0360850913603
import matplotlib, sys
if 'show' not in sys.argv:
matplotlib.use('Agg')
import pylab
import SW
import RG
eta_conv = SW.sigma**3*pylab.pi/6
n = pylab.linspace(0,0.2,10000)
T = 0.3
npart = 0.0462316928818
pylab.plot(n*eta_conv,SW.phi(T,n,npart),'g-',label='SW')
pylab.plot(n*eta_conv,RG.phi(T,n,npart,0),'r-',label='SW+RG; i=0')
pylab.plot(n*eta_conv,RG.phi(T,n,npart,1),'b--',label='SW+RG; i=1')
# pylab.plot(n*eta_conv,SW.f(T,n),'g-',label='SW')
# pylab.plot(n*eta_conv,RG.ftot(T,n,0),'r--',label='SW+RG; i=0')
# pylab.plot(n*eta_conv,RG.ftot(T,n,1),'b--',label='SW+RG; i=1')
pylab.title('T = %0.2f'%T)
pylab.ylabel(r'$\phi$')
# pylab.ylabel(r'$f$')
pylab.xlabel(r'$\eta$')
pylab.legend(loc=0)
pylab.savefig('figs/SW-RG-compare.pdf')
pylab.show()
def plotphi(T, n, npart, i):
plt.plot(n * RG.sigma ** 3 * np.pi / 6, RG.phi(T, n, npart, i))
plt.ylabel(r"$\phi$")
plt.xlabel(r"$\eta$")
import pylab as plt
import SW
import RG
eta_conv = SW.sigma**3*plt.pi/6
n = plt.linspace(1e-8,0.2,10000)
### Low temp ###
T = 0.3
npart0 = 0.0462316928818
npart1 = 0.0776670124628
plt.figure()
plt.plot(n*eta_conv,RG.phi(T,n,npart0,0),label='i=0')
plt.plot(n*eta_conv,RG.phi(T,n,npart1,1),label='i=1')
plt.title('T = %0.2f'%T)
plt.ylabel(r'$\phi$')
plt.xlabel(r'$\eta$')
plt.ylim(-0.04,0.1)
plt.xlim(0,0.7)
plt.legend(loc=0)
plt.savefig('figs/phi-RG-lowT.pdf')
### High Temp ###
T = 1.32
npart0 = 0.0360850913603
def npart(iterations):
# Initial conditions; dependent on you system
T = 0.1
nparticular = 0.08/(RG.sigma**3*np.pi/6) # using finite differences df_dn
# nparticular = 0.155/(RG.sigma**3*np.pi/6) # using analytic df_nd
# T = 0.68
# nparticular = 0.0414/(RG.sigma**3*np.pi/6)
N = 20 # For publication plots, make this bigger (40? 80? 100? You decide!)
Tc = 1.33
Tlow = T
# Bounds of minimization.
# Use range that works for many temperatures
# Left (vapor)
a_vap = 1e-10/(RG.sigma**3*np.pi/6)
c_vap = nparticular
# Right (liquid)
a_liq = nparticular
c_liq = 0.75/(RG.sigma**3*np.pi/6)
###############################
# Open file for output
fout = open('figs/npart_RG-i%d-out.dat'%iterations,'w')
# label the columns of the output
fout.write('#T nvapor nliquid phi(nvap) phi(nliq) nparticular\n')# phi_avg')
sys.stdout.flush()
# Do first temperature before the loop
nvapor,phi_vapor = minmax_RG.minimize(RG.phi,T,a_vap,c_vap,nparticular,iterations)
print 'initial nvap,phi_vap',nvapor,phi_vapor
nliquid,phi_liquid = minmax_RG.minimize(RG.phi,T,a_liq,c_liq,nparticular,iterations)
print 'initial nliq,phi_liq',nliquid,phi_liquid
print 'initial npart',nparticular*(RG.sigma**3*np.pi/6)
#while T < 1.4:
for j in xrange(0,N+1):
T = (Tc - Tlow)*(1 - ((N-j)/N)**4) + Tlow
fout.flush()
# Starting point for new nparticular is abscissa of max RG.phi with old nparticular
nparticular = minmax_RG.maximize(RG.phi,T,nvapor, nliquid, nparticular,iterations)
# I'm looking at the minima of RG.phi
c_vap = nparticular
a_liq = nparticular
nvapor,phi_vapor = minmax_RG.minimize(RG.phi,T,c_vap,a_vap,nparticular,iterations)
nliquid,phi_liquid = minmax_RG.minimize(RG.phi,T,a_liq,c_liq,nparticular,iterations)
tol = 1e-5
fnpart = RG.phi(T, nparticular, nparticular, iterations)
# Compare the two minima in RG.phi
while np.fabs(phi_vapor - phi_liquid)/np.fabs(fnpart) > tol:
delta_mu = (phi_liquid - phi_vapor)/(nliquid - nvapor)
def newphi(T, n, npart, i):
return RG.phi(T, n, npart, i) - delta_mu*n
nparticular = minmax_RG.maximize(newphi,T,nvapor,nliquid,nparticular,iterations)
fnpart = RG.phi(T, nparticular, nparticular, iterations)
nvapor,phi_vapor = minmax_RG.minimize(RG.phi,T,a_vap,c_vap,nparticular,iterations)
nliquid,phi_liquid = minmax_RG.minimize(RG.phi,T,a_liq,c_liq,nparticular,iterations)
fout.write(str(T))
fout.write(' ')
fout.write(str(nvapor))
fout.write(' ')
fout.write(str(nliquid))
fout.write(' ')
fout.write(str(phi_vapor))
fout.write(' ')
fout.write(str(phi_liquid))
fout.write(' ')
fout.write(str(nparticular))
fout.write('\n')
sys.stdout.flush();
print ' T, etaVap, etaLiq',T,nvapor/(RG.sigma**3*np.pi/6),nliquid/(RG.sigma**3*np.pi/6)
fout.close()
def newphi(T, n, npart, i):
return RG.phi(T, n, npart, i) - delta_mu*n
for i in xrange(0, N + 1):
T = (Tc - Tlow) * (1 - ((N - i) / N) ** 4) + Tlow
fout.flush()
# Starting point for new nparticular is abscissa of max RG.phi with old nparticular
nparticular = minmax_RG.maximize(RG.phi, T, nvapor, nliquid, nparticular, i)
# I'm looking at the minima of RG.phi
c_vap = nparticular
a_liq = nparticular
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, c_vap, a_vap, nparticular, i)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, a_liq, c_liq, nparticular, i)
tol = 1e-5
fnpart = RG.phi(T, nparticular, nparticular, i)
# Compare the two minima in RG.phi
while np.fabs(phi_vapor - phi_liquid) / np.fabs(fnpart) > tol:
delta_mu = (phi_liquid - phi_vapor) / (nliquid - nvapor)
def newphi(T, n, npart, i):
return RG.phi(T, n, npart, i) - delta_mu * n
nparticular = minmax_RG.maximize(newphi, T, nvapor, nliquid, nparticular, i)
fnpart = RG.phi(T, nparticular, nparticular, i)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, c_vap, nparticular, i)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, a_liq, c_liq, nparticular, i)
fout.write(str(T))
def plotphi_old(T, n, npart, i, label):
plt.plot(n * eta_conv, RG1.phi(T, n, npart, i), label=label)
def npart(iterations):
# Initial conditions; dependent on you system
T = 0.1
nparticular = 0.08 / (RG.sigma**3 * np.pi / 6
) # using finite differences df_dn
# nparticular = 0.155/(RG.sigma**3*np.pi/6) # using analytic df_nd
# T = 0.68
# nparticular = 0.0414/(RG.sigma**3*np.pi/6)
N = 20 # For publication plots, make this bigger (40? 80? 100? You decide!)
Tc = 1.33
Tlow = T
# Bounds of minimization.
# Use range that works for many temperatures
# Left (vapor)
a_vap = 1e-10 / (RG.sigma**3 * np.pi / 6)
c_vap = nparticular
# Right (liquid)
a_liq = nparticular
c_liq = 0.75 / (RG.sigma**3 * np.pi / 6)
###############################
# Open file for output
fout = open('figs/npart_RG-i%d-out.dat' % iterations, 'w')
# label the columns of the output
fout.write(
'#T nvapor nliquid phi(nvap) phi(nliq) nparticular\n'
) # phi_avg')
sys.stdout.flush()
# Do first temperature before the loop
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, c_vap,
nparticular, iterations)
print 'initial nvap,phi_vap', nvapor, phi_vapor
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, a_liq, c_liq,
nparticular, iterations)
print 'initial nliq,phi_liq', nliquid, phi_liquid
print 'initial npart', nparticular * (RG.sigma**3 * np.pi / 6)
#while T < 1.4:
for j in xrange(0, N + 1):
T = (Tc - Tlow) * (1 - ((N - j) / N)**4) + Tlow
fout.flush()
# Starting point for new nparticular is abscissa of max RG.phi with old nparticular
nparticular = minmax_RG.maximize(RG.phi, T, nvapor, nliquid,
nparticular, iterations)
# I'm looking at the minima of RG.phi
c_vap = nparticular
a_liq = nparticular
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, c_vap, a_vap,
nparticular, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, a_liq, c_liq,
nparticular, iterations)
tol = 1e-5
fnpart = RG.phi(T, nparticular, nparticular, iterations)
# Compare the two minima in RG.phi
while np.fabs(phi_vapor - phi_liquid) / np.fabs(fnpart) > tol:
delta_mu = (phi_liquid - phi_vapor) / (nliquid - nvapor)
def newphi(T, n, npart, i):
return RG.phi(T, n, npart, i) - delta_mu * n
nparticular = minmax_RG.maximize(newphi, T, nvapor, nliquid,
nparticular, iterations)
fnpart = RG.phi(T, nparticular, nparticular, iterations)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, c_vap,
nparticular, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, a_liq, c_liq,
nparticular, iterations)
fout.write(str(T))
fout.write(' ')
fout.write(str(nvapor))
fout.write(' ')
fout.write(str(nliquid))
fout.write(' ')
fout.write(str(phi_vapor))
fout.write(' ')
fout.write(str(phi_liquid))
fout.write(' ')
fout.write(str(nparticular))
fout.write('\n')
sys.stdout.flush()
print ' T, etaVap, etaLiq', T, nvapor / (
RG.sigma**3 * np.pi / 6), nliquid / (RG.sigma**3 * np.pi / 6)
fout.close()
def newphi(T, n, npart, i):
return RG.phi(T, n, npart, i) - delta_mu * n
def plotphi_old(T,n,npart,i,label): plt.plot(n*eta_conv,RG1.phi(T,n,npart,i),label=label)