def correction(Temp, num, chempot, i1, i2):
return RG.phi(Temp, num, chempot, i1) - RG.phi(Temp, num, chempot, i2)
def npart(iterations):
# Initial conditions; dependent on you system
T = 0.5
mu = -5.751 # I found this by plotting. It is good for T=0.5; i=0
nmid = 0.0439651327587 # I found this from running the code with the above mu
mu = -RG.df_dn(T, nmid, iterations)
Tc = 1.3295 # Rough estimate based on previous plots
Tlow = T
# Bounds of minimization.
# Use range that works for many temperatures
# Outside bounds
a_vap = 1e-10 / (RG.sigma ** 3 * np.pi / 6)
c_liq = 0.75 / (RG.sigma ** 3 * np.pi / 6)
# Use the central max as the inside bound
nmid = 0.2 / (RG.sigma ** 3 * np.pi / 6) # ad-hoc for now
# nmid = minmax_RG.maximize(RG.phi,T,a_vap,c_liq,mu,iterations)
###############################
# Open file for output
fout = open("figs/coexistence_RG-i%d-out.dat" % iterations, "w")
# label the columns of the output
fout.write("#T nvapor nmid nliquid phi(nvap) phi(nmid) phi(nliq) mu\n")
sys.stdout.flush()
# Do first temperature before the loop
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
print " initial nvap,phi_vap", nvapor, phi_vapor
print " initial nmid,phi_mid", nmid, RG.phi(T, nmid, mu, iterations)
print " initial nliq,phi_liq", nliquid, phi_liquid
print " initial mu", mu
# while T < 1.4:
for j in xrange(0, N + 1):
# Temp points get closer as we near the critical point
T = (Tc - Tlow) * (1 - ((N - j) / N) ** 4) + Tlow
print " T =", T
fout.flush()
# I'm looking at the minima of RG.phi
# Use the local max between vapor and liquid to set the boundary for each minimization
# nmid = minmax_RG.maximize(RG.phi,T,nvapor, nliquid, mu,iterations)
mu = -RG.df_dn(T, nmid, iterations)
# a_vap = max(nmid - 2.0*(nmid - nvapor), a_vap)
# c_liq = nmid + 2.0*(nliquid - nmid)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
phi_mid = RG.phi(T, nmid, mu, iterations)
tol = 1e-9
# Compare the two minima in RG.phi
# print ' entering while loop'
while np.fabs(phi_vapor - phi_liquid) / np.fabs(phi_mid) > tol: # np.fabs casts output as float
# print ' whilecond =',np.fabs(phi_vapor - phi_liquid)/np.fabs(phi_mid)
delta_mu = (phi_liquid - phi_vapor) / (nliquid - nvapor)
# print ' delta_mu=',delta_mu
# Change mu
mu += delta_mu
# find new values for nvap, nmid, nliq and phi_vap, phi_mid, phi_liq
nmid, phi_mid = (
minmax_RG.maximize(RG.phi, T, nvapor, nliquid, mu, iterations),
RG.phi(T, nmid, mu, iterations),
)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
# print ' nvap,phi(nvap)',nvapor,phi_vapor
# print ' etavap',nvapor*RG.sigma**3*np.pi/6
# print ' nmid,phi(nmid)',nmid,phi_mid
# print ' etamid',nmid*RG.sigma**3*np.pi/6
# print ' nliq,phi(nliq)',nliquid,phi_liquid
# print ' etaliq',nliquid*RG.sigma**3*np.pi/6
# print '\n'
# if j > N - 20:
# plt.figure()
# delta_n = nliquid - nvapor
# nvals = np.arange(max(nvapor - delta_n, a_vap), min(nliquid + delta_n, c_liq), 0.01*delta_n)
# phivals = np.zeros_like(nvals)
# for i in range(len(nvals)):
# phivals[i] = RG.phi(T,nvals[i],mu,iterations)
# plt.plot(nvals*np.pi*RG.sigma**3/6, phivals, 'b-')
# plt.plot(nliquid*np.pi*RG.sigma**3/6, RG.phi(T,nliquid,mu,iterations), 'o')
# plt.plot(nvapor*np.pi*RG.sigma**3/6, RG.phi(T,nvapor,mu,iterations), 'o')
# plt.plot(nmid*np.pi*RG.sigma**3/6, RG.phi(T,nmid,mu,iterations), '+')
# plt.title('T = %.14g' % T)
if nmid == nvapor or nmid == nliquid:
print "I have achieved silliness!"
print "This occurred at T =", T
# break
# print ' left while loop'
fout.write(str(T))
fout.write(" ")
fout.write(str(nvapor))
fout.write(" ")
fout.write(str(nmid))
fout.write(" ")
fout.write(str(nliquid))
fout.write(" ")
fout.write(str(phi_vapor))
fout.write(" ")
fout.write(str(phi_mid))
fout.write(" ")
fout.write(str(phi_liquid))
fout.write(" ")
fout.write(str(mu))
fout.write("\n")
sys.stdout.flush()
# print ' T, etaVap, etaLiq, mu',T,nvapor/(RG.sigma**3*np.pi/6),nliquid/(RG.sigma**3*np.pi/6),mu
# print '\n'
fout.close()
def npart(iterations):
# Initial conditions; dependent on you system
T = 0.5
mu = -5.751 # I found this by plotting. It is good for T=0.5; i=0
nmid = 0.0439651327587 # I found this from running the code with the above mu
mu = -RG.df_dn(T, nmid, iterations)
Tc = 1.3295 # Rough estimate based on previous plots
Tlow = T
# Bounds of minimization.
# Use range that works for many temperatures
# Outside bounds
a_vap = 1e-10/(RG.sigma**3*np.pi/6)
c_liq = 0.75/(RG.sigma**3*np.pi/6)
# Use the central max as the inside bound
nmid = 0.2/(RG.sigma**3*np.pi/6) # ad-hoc for now
# nmid = minmax_RG.maximize(RG.phi,T,a_vap,c_liq,mu,iterations)
###############################
# Open file for output
fout = open('figs/coexistence_RG-i%d-out.dat'%iterations, 'w')
# label the columns of the output
fout.write('#T nvapor nmid nliquid phi(nvap) phi(nmid) phi(nliq) mu\n')
sys.stdout.flush()
# Do first temperature before the loop
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
print(' initial nvap,phi_vap', nvapor, phi_vapor)
print(' initial nmid,phi_mid', nmid, RG.phi(T, nmid, mu, iterations))
print(' initial nliq,phi_liq', nliquid, phi_liquid)
print(' initial mu', mu)
#while T < 1.4:
for j in range(0, N+1):
# Temp points get closer as we near the critical point
T = (Tc - Tlow)*(1 - ((N-j)/N)**4) + Tlow
print(' T =', T)
fout.flush()
# I'm looking at the minima of RG.phi
# Use the local max between vapor and liquid to set the boundary for each minimization
#nmid = minmax_RG.maximize(RG.phi,T,nvapor, nliquid, mu,iterations)
mu = -RG.df_dn(T, nmid, iterations)
#a_vap = max(nmid - 2.0*(nmid - nvapor), a_vap)
#c_liq = nmid + 2.0*(nliquid - nmid)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
phi_mid = RG.phi(T, nmid, mu, iterations)
tol = 1e-9
# Compare the two minima in RG.phi
# print ' entering while loop'
while np.fabs(phi_vapor - phi_liquid)/np.fabs(phi_mid) > tol: # np.fabs casts output as float
# print ' whilecond =',np.fabs(phi_vapor - phi_liquid)/np.fabs(phi_mid)
delta_mu = (phi_liquid - phi_vapor)/(nliquid - nvapor)
# print ' delta_mu=',delta_mu
# Change mu
mu += delta_mu
# find new values for nvap, nmid, nliq and phi_vap, phi_mid, phi_liq
nmid, phi_mid = minmax_RG.maximize(RG.phi, T, nvapor, nliquid, mu, iterations), RG.phi(T, nmid, mu, iterations)
nvapor, phi_vapor = minmax_RG.minimize(RG.phi, T, a_vap, nmid, mu, iterations)
nliquid, phi_liquid = minmax_RG.minimize(RG.phi, T, nmid, c_liq, mu, iterations)
# print ' nvap,phi(nvap)',nvapor,phi_vapor
# print ' etavap',nvapor*RG.sigma**3*np.pi/6
# print ' nmid,phi(nmid)',nmid,phi_mid
# print ' etamid',nmid*RG.sigma**3*np.pi/6
# print ' nliq,phi(nliq)',nliquid,phi_liquid
# print ' etaliq',nliquid*RG.sigma**3*np.pi/6
# print '\n'
# if j > N - 20:
# plt.figure()
# delta_n = nliquid - nvapor
# nvals = np.arange(max(nvapor - delta_n, a_vap), min(nliquid + delta_n, c_liq), 0.01*delta_n)
# phivals = np.zeros_like(nvals)
# for i in range(len(nvals)):
# phivals[i] = RG.phi(T,nvals[i],mu,iterations)
# plt.plot(nvals*np.pi*RG.sigma**3/6, phivals, 'b-')
# plt.plot(nliquid*np.pi*RG.sigma**3/6, RG.phi(T,nliquid,mu,iterations), 'o')
# plt.plot(nvapor*np.pi*RG.sigma**3/6, RG.phi(T,nvapor,mu,iterations), 'o')
# plt.plot(nmid*np.pi*RG.sigma**3/6, RG.phi(T,nmid,mu,iterations), '+')
# plt.title('T = %.14g' % T)
if nmid == nvapor or nmid == nliquid:
print('I have achieved silliness!')
print('This occurred at T =', T)
#break
# print ' left while loop'
fout.write(str(T))
fout.write(' ')
fout.write(str(nvapor))
fout.write(' ')
fout.write(str(nmid))
fout.write(' ')
fout.write(str(nliquid))
fout.write(' ')
fout.write(str(phi_vapor))
fout.write(' ')
fout.write(str(phi_mid))
fout.write(' ')
fout.write(str(phi_liquid))
fout.write(' ')
fout.write(str(mu))
fout.write('\n')
sys.stdout.flush();
# print ' T, etaVap, etaLiq, mu',T,nvapor/(RG.sigma**3*np.pi/6),nliquid/(RG.sigma**3*np.pi/6),mu
# print '\n'
fout.close()
T = 1.31705231562
mu = -6.21486388264
T = 1.18142906562
mu = -6.02699427421
T = 1.2219968
mu = -6.08764244458
T = 0.5
mu = -5.75178857763
#plt.plot(ns*np.pi*RG.sigma**3/6, correction(T,ns,mu,1,0), label=r'$(T,\mu)=$ (%g,%g) difference'%(T,mu))
plt.plot(ns * np.pi * RG.sigma**3 / 6,
RG.phi(T, ns, mu, 0),
label=r'$\phi(%g,\eta,%g,0)$' % (T, mu))
plt.plot(ns * np.pi * RG.sigma**3 / 6,
RG.phi(T, ns, mu, 1),
label=r'$\phi(%g,\eta,%g,1)$' % (T, mu))
# The following is very slow, uncomment if you want to see the result.
# plt.plot(ns*np.pi*RG.sigma**3/6, RG.phi(T, ns, mu, 2), label=r'$\phi(%g,\eta,%g,2)$'%(T, mu))
plt.xlabel(r'$\eta$')
plt.ylabel(r'$\phi(T,\eta,\mu,i)$')
plt.legend(loc=0)
plt.savefig('figs/RG_comparison.pdf')
# plt.show()
def plotPress(T, n, i):
plt.plot(n * eta_conv, RG.P(T, n, i))
def plotphi(T, n, mu, i, label):
plt.plot(n * eta_conv, RG.phi(T, n, mu, i), label=label)
def plotphi(T,n,mu,i,label): plt.plot(n*eta_conv,RG.phi(T,n,mu,i),label=label)
def correction(Temp,num,chempot,i1,i2):
return RG.phi(Temp,num,chempot,i1) - RG.phi(Temp,num,chempot,i2)
def correction(Temp,num,chempot,i1,i2):
return RG.phi(Temp,num,chempot,i1) - RG.phi(Temp,num,chempot,i2)
ns = np.arange(1e-10,0.6/(np.pi*RG.sigma**3/6),1e-3/(np.pi*RG.sigma**3/6))
T = 1.31705231562
mu = -6.21486388264
T = 1.18142906562
mu = -6.02699427421
T = 1.2219968
mu = -6.08764244458
T = 0.5
mu = -5.75178857763
#plt.plot(ns*np.pi*RG.sigma**3/6, correction(T,ns,mu,1,0), label=r'$(T,\mu)=$ (%g,%g) difference'%(T,mu))
plt.plot(ns*np.pi*RG.sigma**3/6, RG.phi(T,ns,mu,0), label=r'$\phi(%g,\eta,%g,0)$'%(T,mu))
plt.plot(ns*np.pi*RG.sigma**3/6, RG.phi(T,ns,mu,1), label=r'$\phi(%g,\eta,%g,1)$'%(T,mu))
plt.plot(ns*np.pi*RG.sigma**3/6, RG.phi(T,ns,mu,2), label=r'$\phi(%g,\eta,%g,2)$'%(T,mu))
plt.xlabel(r'$\eta$')
plt.ylabel(r'$\phi(T,\eta,\mu,i)$')
plt.legend(loc=0)
plt.savefig('figs/RG_comparison.pdf')
# plt.show()