def PVvsV_correlation():
global counter
ax1 = get_plot()
#ax1 = get_plot()
TP = []
NV = []
Z = []
Z_var = []
for i in range(len(Volume)):
TP = []
for j in range(len(temperature[i])):
TP.append(pressure[i][j]*Volume[i]/(temperature[i][j]*N))
NV.append(N/(Volume[i]))
Z.append(sum(TP)/len(TP))
var = 0
for i in range(len(TP)):
var += (TP[i]- Z[-1])**2/len(TP)
Z_var.append(var**2)
#print Z[-1], Z_var[-1], Z_var[-1]/Z[-1]*100
NV[0] = 0
Z[0] = 1
Z_var[0]=0
ax1.errorbar(NV,Z,yerr=Z_var,fmt='x%c'%colors[counter],label=title)
#peos.modifiedstarling_fit_all(ax1,np.array(Z),np.array(NV),colors[counter])
peos.viralexpansion_3(ax1,np.array(Z),np.array(NV),colors[counter],show=True)
#plt.semilogx()
#plt.semilogy()
ax1.set_xlabel(u'$\eta$')
ax1.set_ylabel('PV/NkT')
def ZvsZpot_gamma(pfit_fe_coef=[],fmin=9,fmax=-1, set_fe = True):
if set_fe:
if n == 6.25:
pfit_fe_coef =[-0.123471,3.112000,3.320848,0.083388]
if n == 7:
pfit_fe_coef = [-0.051930 ,2.703564 ,3.246362,0.379012]
if n == 8:
pfit_fe_coef = [-0.112304,2.741619 ,2.576233, 0.984856]
if n == 9:
pfit_fe_coef = [-0.282307, 3.300624 ,1.358420, 1.786398]
if n == 10:
pfit_fe_coef = [-0.626243, 4.208299, -0.225634, 2.708868]
if n == 11:
pfit_fe_coef = [-0.764629, 5.146447 ,-1.897390, 3.667005]
if n == 12:
pfit_fe_coef = [-0.951805, 6.005817, -3.441567, 4.552962]
if n == 13:
pfit_fe_coef = [-2.138254, 9.811643, -7.846507,6.339112]
if n == 14:
pfit_fe_coef = [-1.857837,9.347776,-8.089134,6.768926]
global counter
gamma=[]
NV = []
Z = []
Z_potential = []
r_cut = float(os.getcwd().split('/')[-1].split('_')[-2])
print 'N is ',N
Z_potential_no = []
for i in range(len(Volume)):
gamma.append(N/Volume[i]*temperature_avg[i]**(-3/n))
# rho
NV.append(N/(Volume[i]))
# (Z - 1) / rho
Z.append((pressure_avg[i]*Volume[i]/(N*temperature_avg[i])-1))
# (2 * Beta Phi_T / N ) / rho
DE = N*NV[-1]*2*math.pi/((n-3)*r_cut**(n-3))
#print 'Delta DE', DE/potential_avg[i]
Z_potential.append(n/3*((potential_avg[i]+DE)/(N*temperature_avg[i])))
Z_potential_no.append(n/3*((potential_avg[i])/(N*temperature_avg[i])))
fit_Z = []
fit_ZFE = []
ax1 = get_plot()
print "potential"
fit_Z_potential = peos.viralexpansion_3(ax1, Z_potential[fmin:fmax], np.array(gamma[fmin:fmax]),'r',show=True)
print "potential w/o correction"
fit_Z_potential_no = peos.viralexpansion_3(ax1,
Z_potential_no[fmin:fmax],
np.array(gamma[fmin:fmax]),'r',show=False)
ax1.set_ylabel(r'Z-1')
ax1.set_xlabel(r'$\gamma$')
plt.show()
print "Free Energy"
print 'a=%f,c1=%f,c2=%f,c3=%f'%(pfit_fe_coef[0],pfit_fe_coef[1],pfit_fe_coef[2],pfit_fe_coef[3])
#fit_Z_pressure = peos.viralexpansion_3(ax1, Z[fmin:fmax], np.array(gamma[fmin:fmax]),'r',show=True)
PvsV(fit_Z_potential,fit_Z_potential_no,pfit_fe_coef,fmin=fmin)
def Z_gamma():
global counter
ax1 = get_plot()
ax1.set_xlabel(r'$\gamma$')
ax1.set_ylabel('Z-1')
r_cut = float(os.getcwd().split('/')[-1].split('_')[-2])
NV = [0]
Z_potential = [0]
Z_potentialm = [0]
for i in range(len(Volume)):
# rho
NV.append(N/(Volume[i]))
# Z - 1
#Z.append((pressure_avg[i]*Volume[i]/(N*temperature_avg[i])-1)/NV[-1])
# 2 * Beta Phi_T / N
DE = N*NV[-1]*2*math.pi/((n-3)*r_cut**(n-3))
Z_potential.append(n/3*((potential_avg[i]+DE)/(N*temperature_avg[i]*NV[-1])))
Z_potentialm.append(n/3*((potential_avg[i]+DE)/(N*temperature_avg[i])))
#ax1.errorbar(NV,Z,yerr=Z_var,fmt='x%c'%colors[counter],label=title)
#peos.modifiedstarling_fit_all(ax1,np.array(Z_potential),np.array(NV),colors[counter],show=True)
#peos.viralexpansion_3(ax1,np.array(Z_potential),np.array(NV),colors[counter],show=True)
A = peos.viralexpansion_3(ax1,np.array(Z_potentialm),np.array(NV),colors[counter],show=True)
#peos.viralexpansion_3(ax1,np.array(Z_potentialm),np.array(NV),colors[counter],show=True)
g=.1
init =A[1]*g+.5*A[2]*g**2+A[3]*g**3/3.
print init
def FreeEnergy():
global counter
global n
# Fit to Z-1 from N/V = 0 to g
#if n==6.:
# c1=3.586511
# c2=6.1187979
# c1= 3.630785
# c2=5.919866
# g=.1
#if n==7.:
# c1= 3.139660
# c2 = 6.038275
# g=.1
#if n==8:
# c1 = 2.889490
# c2=5.810482
# g=.1
#if n==9:
# c1= 2.748766
# c2=5.428522
# g=.1
#if n ==10:
# c1= 2.098992
# c2=7.387928
# g=.1
#if n ==11.:
# c1= 2.434736
# c2=5.788083
# g=.1
#if n ==12.:
# a=2.549678
# c1= 3.993234
# c2=2.712819
# c3=3.469902
# g=.1
#if n ==13.:
# a=1.000000
# c1= 2.532850
# c2=3.437891
# c3=4.843509
# g=.1
#if n ==14.:
# a = 1.000000
# c1 = 2.482896
# c2 = 3.367217
# c3 = 4.901456
# g = .1
#if n == 6.25:
# a = 1.000000
# c1 = 3.525116
# c2 = 5.409153
# c3 = 1.469899
# g = .1
#try:
# init =a*g+.5*c1*g**2+c2/3.*g**3+c3/4.*g**4
#except:
# init =c1*g+c2/2.*g**2
if n==6.:
init = .398
g=.1
if n == 6.25:
init = .385
g = .1
if n==7.:
init = .352
g=.1
if n==8:
init = .324
g=.1
if n==9:
init = .306
g=.1
if n ==10:
init = 0.293
g = .1
if n ==11.:
init = 0.283
g = .1
if n ==12.:
init = 0.276
g = .1
if n ==13.:
init=.271
g=.1
if n ==14.:
init=.265
g = .1
print 'free energy from fit',init
r_cut = float(os.getcwd().split('/')[-1].split('_')[-2])
NV = []
Z = []
Z_potential = []
Z_potential_no = []
gamma2 = []
for i in range(len(temperature_avg)):
temperature_avg[i]=1.0
for i in range(len(Volume)):
# rho
NV.append(N/(Volume[i]))
# Z - 1
Z.append((pressure_avg[i]*Volume[i]/(N*temperature_avg[i])-1)/NV[-1])
# 2 * Beta Phi_T / N
DE = N*NV[-1]*2*math.pi/((n-3)*r_cut**(n-3))
Z_potential.append(n/3*((potential_avg[i]+DE)/(N*temperature_avg[i]*NV[-1])))
Z_potential_no.append(n/3*((potential_avg[i])/(N*temperature_avg[i]*NV[-1])))
##
gamma2.append(NV[-1]/2**0.5*(1/temperature_avg[i])**0.5)
#peos.viralexpansion(ax1,np.array(Z_potential[0:5]),np.array(NV[0:5]),colors[counter],show=True)
#peos.modifiedstarling_fit_all(ax1,np.array(Z_potential),np.array(NV),colors[counter])
ax1 = get_plot()
print NV[:4]
#Integrate To get the Free Energy
#F_excess_Z, gamma = simpson_integration_min(Z, NV,
# initial=init,int_min=g)
F_excess_potential, NV = simpson_integration_min(Z_potential, NV,
initial=init,int_min=g)
print NV[:4]
print F_excess_potential[:4]
gamma = []
for i in NV:
gamma.append(i*(sum(temperature_avg)/len(temperature_avg))**(-3/6.))
gamma = np.array(gamma)
ax1.plot(gamma,F_excess_potential, '-',label=title+' FE Potential')
#FIT OF Free Energy
print len(NV)
fmin= delta # Min Cutoff of fit
print 'fmin =',fmin, 'fit range', NV[fmin],'-',NV[-1]
fitted = peos.viralexpansion_3(ax1, F_excess_potential[fmin:],
np.array(gamma[fmin:]),'r',show=False)
## fitted function ##
fit_FE = []
for g in gamma:
fit_FE.append(fitted[0]+fitted[1]*g+fitted[2]*g**2+fitted[3]*g**3)
ax1.plot(gamma,fit_FE, '-x',label=title+' fit')
#fcc calculated trvsst
fcc_excess = np.zeros((gamma.shape[0]))
energy_excess = np.zeros((gamma.shape[0]))
if n == 6:
a_fcc = 3.6131
b_fcc = 3.6982
g_L = 2.36
g_fcc = 2.39
if n == 6.25:
a_fcc = 3.4247505
b_fcc = 3.7851997
g_L = 2.36
g_fcc = 2.39
if n == 7:
a_fcc = 2.9754654
b_fcc = 4.0185839
g_L = 2.05
g_fcc = 2.08
if n == 8:
a_fcc = 2.5402261
b_fcc = 4.2753817
g_L = 1.7
g_fcc = 1.73
if n == 9:
a_fcc = 2.2083911
b_fcc = 4.4821760
g_L = 1.49
g_fcc = 1.52
if n == 10:
a_fcc = 1.9388997
b_fcc = 4.6487343
g_L = 1.4
g_fcc = 1.43
if n == 11:
a_fcc = 1.7118338
b_fcc = 4.7823161
g_L = 1.25
g_fcc = 1.28
if n == 12:
a_fcc = 1.5164850
b_fcc = 4.8884526
g_L = 1.16
g_fcc = 1.19
if n == 13:
a_fcc = 1.3461175
b_fcc = 4.9714449
g_L = 1.10
g_fcc = 1.13
if n == 14:
a_fcc = 1.1964035
b_fcc = 5.0346944
g_L = 1.0
g_fcc = 1.03
for i,g in enumerate(gamma):
fcc_excess[i] = a_fcc*g**(n/3.) + b_fcc + (n/2.)*math.log(g)
energy_excess[i] = a_fcc*g**(n/3.) + 3
ax1.plot(gamma, fcc_excess, '-',label='fcc phonon')
ax1.set_xlabel(u'$\gamma_{%i}$'%int(n))
ax1.set_ylabel('Excess Free Energy of Liquid')
coex_fcc = a_fcc*g_fcc**(n/3.) + b_fcc + (n/2.)*math.log(g_fcc)
coex_liq = fitted[0]+fitted[1]*g_L+fitted[2]*g_L**2+fitted[3]*g_L**3
print 'Df = ', - coex_fcc + coex_liq
ax1.set_xlim([g_L-.2,g_fcc+.02])
ax1.set_ylim([coex_fcc-4,coex_liq+2])
plt.legend(loc=2)
plt.show()
ZvsZpot_gamma(pfit_fe_coef=fitted,fmin=fmin*2, set_fe = False)
