def plot_fig2():
Wis = [5, 7, 9, 11, 13] #,9,11,13]
datas = get_log_data('LJ', T, '%s_twistTaito' % edge, Wis)
wili_used = []
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
W0s = []
offset = .4
thresz = 5
coll_data_ac = np.zeros((len(datas), 7))
vmax = -1
fig, axs = get_axes(1, 3, 1.5)
def shear_eDens(W0, theta):
return 1. / 6 * k * theta**2 * (1. - 2 * tau /
(k * W0))**2 #- 2*tau**2/(k*W0)*L0
for i, data in enumerate(datas):
Wi, Li, W, L = data[:4]
energy_table = data[6]
natoms = data[4]
v = data[5]
phi = energy_table[:, 3]
z = energy_table[:, 4]
epot = (energy_table[:, 5] - energy_table[-1, 5]) * 1000
cutn = int(len(epot) / 2)
if Wi == 5: m = 0
if Wi == 7: m = 1
if Wi == 9: m = 2
if Wi == 11: m = 3
if Wi == 13: m = 4
epot = epot[cutn:]
if edge == 'ac':
W0 = (Wi - 1) * np.sqrt(3) / 2 * bond
L0 = Li * 3. * bond - 1. * bond
Area = W0 * L0
else:
raise
#print W0
thetash = W / (2 * (L / phi))
thetas = thetash[cutn:]
heights = energy_table[:, 4]
inds = np.where(thresz < heights)[0]
indv = max(inds)
indb = min(inds)
W = int_toAngst(Wi, 'ac', key='width', C_C=bond)
mus = thetash * 2. / W * 360 / (2 * np.pi) * 10
coll_data_ac[i] = [
W, v, thetash[indv], thetash[indb], mus[indv], mus[indb], Wi
]
if v > vmax:
vmax = v
if [Wi, Li] not in wili_used:
wili_used.append([Wi, Li])
epot_tDens = shear_eDens(W0, thetas) * 1000
axs[0].plot(thetas,
epot_tDens + m * offset,
'-',
color=colors[m],
alpha=1) #, label = 'Epot teor')
W0s.append(W0)
axs[0].text(.01 - (m + 1) * .0017,
(m + 1) * offset * .85 + offset / 10,
r'N=%i' % Wi,
color=colors[m])
axs[1].text(.08 - float(m) / 4 * .04,
float(m) / 4 * 6. + 9,
r'N=%i' % Wi,
color=colors[m])
axs[0].plot(thetas,
epot / Area + m * offset,
color=colors[m],
alpha=.05) #, label = 'Epot')
axs[1].plot(thetash, heights, color=colors[m],
alpha=.15) #, label = 'Epot')
axs[0].set_xlim([0, .03])
axs[0].set_ylim([-.2, 3.5])
axs[0].set_xlabel(r'$\Theta$')
axs[0].set_ylabel(r'Energy density (m$eV/$\AA$^2$)')
axs[1].set_ylim([2, 17])
axs[1].set_xlabel(r'$\Theta$')
axs[1].set_ylabel(r'Max Height (\AA)')
axs[0].legend(loc=2)
# KINK
magic_par = 0.0228171
class alpha():
def __init__(self):
pass
def set_s(self, s):
self.s = s
def set_t(self, t):
self.t = t
def set_pot(self, pot):
self.pot = pot
def set_params(self, s, t, pot):
self.set_s(s)
self.set_t(t)
self.set_pot(pot)
def get_alpha(self, w):
return magic_par / (self.s / w**self.pot + self.t)
alpha = alpha()
def theta_teorFitPar(W, *args):
if len(args) == 1:
s = args[:1]
alpha.set_s(s)
if len(args) == 2:
s, t = args[:2]
alpha.set_s(s)
alpha.set_t(t)
if len(args) == 3:
s, t, pot = args[:3]
alpha.set_s(s)
alpha.set_t(t)
alpha.set_pot(pot)
return magic_par / alpha.get_alpha(W)
ac_curvature = np.zeros(5)
amount = np.zeros(5)
for i in range(len(coll_data_ac)):
Wi = coll_data_ac[i, -1]
if Wi == 5:
m = 0
ac_curvature[0] += coll_data_ac[i, 4]
amount[0] += 1
if Wi == 7:
m = 1
ac_curvature[1] += coll_data_ac[i, 4]
amount[1] += 1
if Wi == 9:
m = 2
ac_curvature[2] += coll_data_ac[i, 4]
amount[2] += 1
if Wi == 11:
m = 3
ac_curvature[3] += coll_data_ac[i, 4]
amount[3] += 1
if Wi == 13:
m = 4
ac_curvature[4] += coll_data_ac[i, 4]
amount[4] += 1
axs[2].scatter(coll_data_ac[i, 0],
coll_data_ac[i, 4],
alpha=coll_data_ac[i, 1] / vmax,
color=colors[m])
axs[2].scatter(coll_data_ac[i, 0],
coll_data_ac[i, 5],
alpha=coll_data_ac[i, 1] / vmax,
marker='D',
color=colors[m])
for i in range(5):
print 'average curvature %i-ac = %.4f deg/nm' % (
Wis[i], ac_curvature[i] / amount[i])
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1_ac = curve_fit(theta_teorFitPar,
coll_data_ac[:, 0],
coll_data_ac[:, 2],
p0=[1.])[0][:1]
plot_widths = np.linspace(
np.min(coll_data_ac[:, 0]) - .5,
np.max(coll_data_ac[:, 0]) + 2, 50)
axs[2].plot(plot_widths,
2 / plot_widths * 3600 / (2 * np.pi) *
theta_teorFitPar(plot_widths, sopm1_ac, magic_par, 1.),
'--',
label=r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %
(sopm1_ac, magic_par),
color='black')
#axs[2].legend(loc = 1, frameon = False)
axs[2].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[2].set_xlabel(r'Width (\AA)')
#xticks = (np.array(Wis) - 1)*np.sqrt(3)/2*1.4
#xticklabels = Wis
#axs[2].set_xticks(xticks)
#axs[2].set_xticklabels(xticklabels)
plt.show()
def plot_fig2():
Wis = [5,7,9,11,13] #,9,11,13]
datas = get_log_data('LJ', T, '%s_twistTaito' %edge, Wis)
wili_used = []
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
W0s = []
offset = .4
thresz = 5
coll_data_ac= np.zeros((len(datas), 7))
vmax = -1
fig, axs = get_axes(1,3, 1.5)
def shear_eDens(W0, theta):
return 1./6*k*theta**2*(1. - 2*tau/(k*W0))**2 #- 2*tau**2/(k*W0)*L0
for i, data in enumerate(datas):
Wi, Li, W, L= data[:4]
energy_table= data[6]
natoms = data[4]
v = data[5]
phi = energy_table[:,3]
z = energy_table[:,4]
epot = (energy_table[:,5] - energy_table[-1,5])*1000
cutn = int(len(epot)/2)
if Wi == 5: m = 0
if Wi == 7: m = 1
if Wi == 9: m = 2
if Wi == 11: m = 3
if Wi == 13: m = 4
epot = epot[cutn:]
if edge == 'ac':
W0 = (Wi - 1)*np.sqrt(3)/2*bond
L0 = Li*3.*bond - 1.*bond
Area = W0 * L0
else: raise
#print W0
thetash = W/(2*(L/phi))
thetas = thetash[cutn:]
heights = energy_table[:,4]
inds = np.where(thresz < heights)[0]
indv = max(inds)
indb = min(inds)
W = int_toAngst(Wi, 'ac', key='width', C_C = bond)
mus = thetash*2./W*360/(2*np.pi)*10
coll_data_ac[i] = [W, v, thetash[indv], thetash[indb], mus[indv], mus[indb], Wi]
if v > vmax:
vmax = v
if [Wi, Li] not in wili_used:
wili_used.append([Wi, Li])
epot_tDens = shear_eDens(W0, thetas)*1000
axs[0].plot(thetas, epot_tDens + m*offset, '-', color = colors[m], alpha = 1) #, label = 'Epot teor')
W0s.append(W0)
axs[0].text(.01 - (m+1)*.0017, (m+1)*offset*.85 + offset/10, r'N=%i' %Wi,
color = colors[m])
axs[1].text(.08 - float(m)/4*.04, float(m)/4*6. + 9, r'N=%i' %Wi,
color = colors[m])
axs[0].plot(thetas, epot/Area + m*offset, color = colors[m], alpha = .05) #, label = 'Epot')
axs[1].plot(thetash, heights, color = colors[m], alpha = .15) #, label = 'Epot')
axs[0].set_xlim([0, .03])
axs[0].set_ylim([-.2, 3.5])
axs[0].set_xlabel(r'$\Theta$')
axs[0].set_ylabel(r'Energy density (m$eV/$\AA$^2$)')
axs[1].set_ylim([2, 17])
axs[1].set_xlabel(r'$\Theta$')
axs[1].set_ylabel(r'Max Height (\AA)')
axs[0].legend(loc = 2)
# KINK
magic_par = 0.0228171
class alpha():
def __init__(self):
pass
def set_s(self, s):
self.s = s
def set_t(self, t):
self.t = t
def set_pot(self, pot):
self.pot= pot
def set_params(self, s,t, pot):
self.set_s(s)
self.set_t(t)
self.set_pot(pot)
def get_alpha(self, w):
return magic_par/(self.s/w**self.pot + self.t)
alpha = alpha()
def theta_teorFitPar(W, *args):
if len(args) == 1:
s = args[:1]
alpha.set_s(s)
if len(args) == 2:
s,t = args[:2]
alpha.set_s(s)
alpha.set_t(t)
if len(args) == 3:
s,t,pot = args[:3]
alpha.set_s(s)
alpha.set_t(t)
alpha.set_pot(pot)
return magic_par/alpha.get_alpha(W)
ac_curvature = np.zeros(5)
amount = np.zeros(5)
for i in range(len(coll_data_ac)):
Wi = coll_data_ac[i, -1]
if Wi == 5:
m = 0
ac_curvature[0] += coll_data_ac[i,4]
amount[0] += 1
if Wi == 7:
m = 1
ac_curvature[1] += coll_data_ac[i,4]
amount[1] += 1
if Wi == 9:
m = 2
ac_curvature[2] += coll_data_ac[i,4]
amount[2] += 1
if Wi == 11:
m = 3
ac_curvature[3] += coll_data_ac[i,4]
amount[3] += 1
if Wi == 13:
m = 4
ac_curvature[4] += coll_data_ac[i,4]
amount[4] += 1
axs[2].scatter(coll_data_ac[i,0], coll_data_ac[i,4],
alpha = coll_data_ac[i,1]/vmax, color = colors[m])
axs[2].scatter(coll_data_ac[i,0], coll_data_ac[i,5],
alpha = coll_data_ac[i,1]/vmax, marker = 'D',
color = colors[m])
for i in range(5):
print 'average curvature %i-ac = %.4f deg/nm' %(Wis[i], ac_curvature[i]/amount[i])
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1_ac = curve_fit(theta_teorFitPar, coll_data_ac[:,0], coll_data_ac[:,2],
p0 = [1.])[0][:1]
plot_widths = np.linspace(np.min(coll_data_ac[:,0]) - .5, np.max(coll_data_ac[:,0]) + 2, 50)
axs[2].plot(plot_widths, 2/plot_widths*3600/(2*np.pi)*theta_teorFitPar(plot_widths, sopm1_ac, magic_par, 1.),
'--', label = r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %(sopm1_ac, magic_par),
color = 'black')
#axs[2].legend(loc = 1, frameon = False)
axs[2].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[2].set_xlabel(r'Width (\AA)')
#xticks = (np.array(Wis) - 1)*np.sqrt(3)/2*1.4
#xticklabels = Wis
#axs[2].set_xticks(xticks)
#axs[2].set_xticklabels(xticklabels)
plt.show()
def plot_kinkOfBend_deg(edge):
plot_mus = True #False #
magic_par = 0.0228171 #0.0203724
datas_ac = get_log_data('LJ', T, '%s_twistTaito' %'ac')
datas_zz = get_log_data('LJ', T, '%s_twistTaito' %'zz')
coll_data_ac= np.zeros((len(datas_ac), 6))
coll_data_zz= np.zeros((len(datas_zz), 6))
thresz = 5
vmax = -1.
eps = 0.002843732471143 #[eV]
kappa = .95 #[eV]
n = 1/(3*np.sqrt(3)*bond**2/4)
pot = 1
def theta_teor(W):
Y = 11.43/W + 19.88
return 24./Y*np.sqrt(eps*kappa*np.pi)*n
class alpha():
def __init__(self):
pass
def set_s(self, s):
self.s = s
def set_t(self, t):
self.t = t
def set_pot(self, pot):
self.pot= pot
def set_params(self, s,t, pot):
self.set_s(s)
self.set_t(t)
self.set_pot(pot)
def get_alpha(self, w):
#Y = 11.43/W + 19.88
#A, B = 48.7, .0055
#Length = 12.8
#B = 4/(Y*np.pi**2)*(A/Length**2 + B*Length**2)
return magic_par/(self.s/w**self.pot + self.t)
#return self.s/w**self.pot + self.t
alpha = alpha()
def theta_teorFitPar(W, *args):
if len(args) == 1:
s = args[:1]
alpha.set_s(s)
if len(args) == 2:
s,t = args[:2]
alpha.set_s(s)
alpha.set_t(t)
if len(args) == 3:
s,t,pot = args[:3]
alpha.set_s(s)
alpha.set_t(t)
alpha.set_pot(pot)
#Y = 11.43/W + 19.88
#A, B = 48.7, .0055
#Length = 12.8
#print np.average(4/(Y*np.pi**2)*(A/Length**2 + B*Length**2))
return magic_par/alpha.get_alpha(W)
#return 4/(Y*np.pi**2*alpha.get_alpha(W))*(A/Length**2 + B*Length**2)
def overR(W, a1, a2):
return a1/W + a2
def overRandconst(W, a1, a2):
return a1/(W + a2)
def overR2(W, a1, a2):
return a1/W**2 + a2
for i, data in enumerate(datas_ac):
energy_table = data[6]
v = data[5]
natoms = data[4]
Wi, Li, W, L = data[:4]
phi = energy_table[:,3]
epot = (energy_table[:,5] - energy_table[-1,5])/natoms
heights = energy_table[:,4]
inds = np.where(thresz < heights)[0]
indv = max(inds)
indb = min(inds)
W = int_toAngst(Wi, 'ac', key='width', C_C = bond)
thetas = W/(2*(L/phi))
mus = thetas*2./W*360/(2*np.pi)*10
coll_data_ac[i] = [W, v, thetas[indv], thetas[indb], mus[indv], mus[indb]]
if v > vmax:
vmax = v
for i, data in enumerate(datas_zz):
energy_table = data[6]
v = data[5]
natoms = data[4]
Wi, Li, W, L = data[:4]
phi = energy_table[:,3]
epot = (energy_table[:,5] - energy_table[-1,5])/natoms
heights = energy_table[:,4]
inds = np.where(thresz < heights)[0]
indv = max(inds)
indb = min(inds)
W = int_toAngst(Wi, 'zz', key='width', C_C = bond)
thetas = W/(2*(L/phi))
mus = thetas*2./W*360/(2*np.pi)*10
coll_data_zz[i] = [W, v, thetas[indv], thetas[indb], mus[indv], mus[indb]]
if v > vmax:
vmax = v
if plot_mus:
for i in range(len(coll_data_ac)):
plt.scatter(coll_data_ac[i,0], coll_data_ac[i,4],
alpha = coll_data_ac[i,1]/vmax, color = 'red')
plt.scatter(coll_data_ac[i,0], coll_data_ac[i,5],
alpha = coll_data_ac[i,1]/vmax, color = 'blue')
#for i in range(len(coll_data_zz)):
# plt.scatter(coll_data_zz[i,0], coll_data_zz[i,4],
# alpha = coll_data_zz[i,1]/vmax, color = 'red')
# plt.scatter(coll_data_zz[i,0], coll_data_zz[i,5],
# alpha = coll_data_zz[i,1]/vmax, color = 'blue')
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1_ac = curve_fit(theta_teorFitPar, coll_data_ac[:,0], coll_data_ac[:,2],
p0 = [1.])[0][:1]
plot_widths = np.linspace(np.min(coll_data_ac[:,0]) - .5, np.max(coll_data_ac[:,0]) + 2, 50)
plt.plot(plot_widths, 2/plot_widths*3600/(2*np.pi)*theta_teorFitPar(plot_widths, sopm1_ac, magic_par, 1.), '--',
label = r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %(sopm1_ac, magic_par),
color = 'green')
plt.legend(loc = 2, frameon = False)
plt.ylabel(r'$^{\circ}/$\AA')
plt.xlabel(r'Width \AA')
#plt.twinx()
#
#alpha.set_params(sopm1_ac, magic_par, 1)
#plt.plot(plot_widths, alpha.get_alpha(plot_widths),
# label = r'$\alpha = \frac{%.3f}{%.2f/w + %.3f} \rightarrow %.3f$'
# %(magic_par, sopm1_ac, magic_par, 1),
# color = 'green')
#plt.legend(loc = 1, frameon = False)
#plt.ylabel(r'$\alpha$')
plt.show()
else:
for i in range(len(coll_data_ac)):
plt.scatter(coll_data_ac[i,0], coll_data_ac[i,2],
alpha = coll_data_ac[i,1]/vmax, color = 'red')
plt.scatter(coll_data_ac[i,0], coll_data_ac[i,3],
alpha = coll_data_ac[i,1]/vmax, color = 'blue')
#pot = 1.5
#alpha.set_pot(pot)
#sopm15, topm15 = curve_fit(theta_teorFitPar, coll_data[:,0], coll_data[:,2], p0 = [1., 1])[0][:2]
pot = 2.
alpha.set_pot(pot)
sopm2, topm2 = curve_fit(theta_teorFitPar, coll_data_ac[:,0], coll_data_ac[:,2], p0 = [1., 1])[0][:2]
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1 = curve_fit(theta_teorFitPar, coll_data_ac[:,0], coll_data_ac[:,2], p0 = [1.])[0][:1]
sopm3, topm3, potopm = curve_fit(theta_teorFitPar, coll_data_ac[:,0], coll_data_ac[:,2], p0 = [1., 1, 1])[0][:3]
#plt.plot(coll_data[:,0], np.ones(len(coll_data[:,0]))*.04, '-.', color = 'black')
#plt.text(np.min(coll_data[:,0]), .041, 'teor')
#plt.scatter(coll_data[:,0], theta_teor(coll_data[:,0]))
#plt.text(np.min(coll_data[:,0]), .041, 'teor')
plot_widths = np.linspace(np.min(coll_data_ac[:,0]) - .5, np.max(coll_data_ac[:,0]) + 2, 50)
#plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm15, topm15, 1.5), '--',
# label = 'alpha = %.2f/w**%.1f + %.3f' %(sopm15, 1.5, topm15))
'''
plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm2, topm2, 2.), '--',
label = r'$\Theta \approx \frac{%.2f}{w^2} + %.3f$' %(sopm2, topm2),
color = 'red')
'''
plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm1, magic_par, 1.), '--',
label = r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %(sopm1, magic_par),
color = 'green')
#plt.plot(plot_widths, overR2(plot_widths, sopm2a, topm2a),
# label = r'$\Theta \approx \frac{1}{%.2fw^2} + %.3f$' %(sopm2a, topm2a), )
'''
plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm3, topm3, potopm), '.-',
label = r'$\Theta \approx \frac{%.2f}{w^{%.2f}} + %.3f$' %(sopm3, potopm, topm3),
color = 'red')
'''
plt.scatter(8.46, .026, marker = 'D', color = 'black')
plt.text(np.min(coll_data_ac[:,0]), .028, r'Experim. $\Theta \approx 0.026 = 4deg/nm$')
plt.legend(frameon = False, loc = 2)
plt.xlabel('width Angst')
plt.ylabel(r'$\Theta$')
plt.twinx()
#alpha.set_params(sopm15, topm15, 1.5)
#plt.plot(plot_widths, alpha.get_alpha(plot_widths),
# label = 'alpha -> %.3f' %alpha.get_alpha(10000))
'''
alpha.set_params(sopm2, topm2, 2)
plt.plot(plot_widths, alpha.get_alpha(plot_widths),
label = r'$\alpha = \frac{%.3f}{%.2f/w^2 + %.3f} \rightarrow %.3f$'
%(magic_par, sopm2, topm2, magic_par/topm2),
color = 'red')
'''
alpha.set_params(sopm1, magic_par, 1)
plt.plot(plot_widths, alpha.get_alpha(plot_widths),
label = r'$\alpha = \frac{%.3f}{%.2f/w + %.3f} \rightarrow %.3f$'
%(magic_par, sopm1, magic_par, 1),
color = 'green')
'''
print sopm1/magic_par, sopm1, magic_par
plt.plot(plot_widths, plot_widths/(sopm1/magic_par + plot_widths), '-o',
color = 'green')
alpha.set_params(sopm3, topm3, potopm)
plt.plot(plot_widths, alpha.get_alpha(plot_widths), '.-',
label = r'$\alpha = \frac{%.3f}{%.2f/w^{%.2f} + %.3f} \rightarrow %.3f$'
%(magic_par, sopm3, potopm, topm3, magic_par/topm3),
color = 'red')
'''
plt.ylabel(r'$\alpha$')
plt.legend(frameon = False)
plt.show()
def plot_energy(edge):
Wis = [5,7,9,11,13]
datas = get_log_data('LJ', T, '%s_twistTaito' %edge, Wis)
wili_used = []
n = 0
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
aopms = []
teor_aopms = []
W0s = []
def shear_e(W0, L0, theta):
#return k*L*(W/R)**2*W/24
tau = 1.54 #-.13 # -.064/W0 - .13 #- .13
Y = 18.75 #19.89 # 11.43/W0 + 19.89 # 19.89 #
return 1./6*Y*L0*W0*theta**2*(1. - 2*tau/(k*W0))**2 #- 2*tau**2/(k*W0)*L0
def shear_eNoedge(W0, L0, theta):
return 1./6*k*L0*W0*theta**2
def x2(thetas, a):
return a*thetas**2
ang_vs = np.zeros(len(datas))
for i, dat in enumerate(datas):
ang_vs[i] = dat[5]
ang_vs = np.max(ang_vs)
for data in datas:
Wi, Li, W, L= data[:4]
energy_table= data[6]
natoms = data[4]
v = data[5]
phi = energy_table[:,3]
z = energy_table[:,4]
epot = (energy_table[:,5] - energy_table[-1,5])
heights = energy_table[:,4]
inds = np.where(5 < heights)[0]
indv = max(inds)
indb = min(inds)
thetas = W/(2*(L/phi))
if edge == 'ac':
W0 = (Wi - 1)*np.sqrt(3)/2*bond
L0 = Li*3.*bond - 1.*bond
Area = W0 * L0
natoms2 = W0 * L0 / (3*np.sqrt(3)/4*bond**2)
else: raise
if [Wi, Li] not in wili_used:
wili_used.append([Wi, Li])
weff = 1 * W0 #- (bond*np.sqrt(3))*.3 # .02/(.16/W0 + .02)*W0 #
epot_t = shear_e(weff, L0, thetas)
plt.plot(thetas, epot_t/Area, '.-', color = colors[n], alpha = .4) #, label = 'Epot teor')
W0s.append(W0)
teor_aopms.append(shear_e(weff, L0, 1)/Area)
n += 1
#epot_t2 = shear_eNoedge(W0, L0, thetas)
ind_last = np.where(.02 < thetas)[0][-1]
aopm = curve_fit(x2, thetas[ind_last:], epot[ind_last:]/Area, 1)[0][0]
#aopm = curve_fit(x2, thetas[:indb], epot[:indb]/Area, 1)[0][0]
if len(aopms) < n:
aopms.append([])
aopms[n - 1].append(aopm)
erange = np.max(epot/Area)
#plt.plot(thetas, x2(thetas, aopm), color = colors[n -1], alpha = .4) #, label = 'Epot')
plt.plot(thetas, epot/Area, color = colors[n -1], alpha = .1) #, label = 'Epot')
'''
plt.plot([thetas[indv], thetas[indv]], [epot[indv]/Area - erange/7, epot[indv]/Area + erange/7],
'--', color = colors[n -1], alpha = .3)
plt.plot([thetas[indb], thetas[indb]], [epot[indb]/Area - erange/7, epot[indb]/Area + erange/7],
'--', color = colors[n -1], alpha = .3)
'''
#plt.plot(thetas, z, color = colors[n -1], alpha = v/ang_vs) #, label = 'maxH')
#plt.scatter(thetas[indv], heights[indv], color = colors[n -1], alpha = .5)
#plt.scatter(thetas[indb], heights[indb], color = colors[n -1], alpha = .5)
#plt.plot(thetas, epot_t2, label = 'Epot teor2')
plt.xlabel('Theta w/(2R)')
plt.legend(loc = 1)
#plt.ylabel('tot Edens eV/angst2')
#plt.title('width = %.2fAngst, edge = %s' %(W, edge))
plt.legend(loc = 2)
plt.ylabel('height max Angst')
plt.show()
aopm_av = np.zeros(len(aopms))
for i in range(n):
aopm_av[i] = np.average(aopms[i])
plt.scatter(W0s, aopm_av, color = 'red')
plt.scatter(W0s, teor_aopms, color = 'green', label = 'teor')
plt.ylabel('aopm')
plt.xlabel('width')
plt.legend(loc = 2, frameon = False)
plt.twinx()
plt.scatter(W0s, np.array(aopm_av)/np.array(teor_aopms),
color = 'black', label = 'teor/expr')
plt.ylabel('aopm teor over aopm expr')
plt.legend(loc = 4, frameon = False)
plt.show()
def plot_energy(edge):
Wis = [5, 7, 9, 11, 13]
datas = get_log_data('LJ', T, '%s_twistTaito' % edge, Wis)
wili_used = []
n = 0
colors = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
aopms = []
teor_aopms = []
W0s = []
def shear_e(W0, L0, theta):
#return k*L*(W/R)**2*W/24
tau = 1.54 #-.13 # -.064/W0 - .13 #- .13
Y = 18.75 #19.89 # 11.43/W0 + 19.89 # 19.89 #
return 1. / 6 * Y * L0 * W0 * theta**2 * (
1. - 2 * tau / (k * W0))**2 #- 2*tau**2/(k*W0)*L0
def shear_eNoedge(W0, L0, theta):
return 1. / 6 * k * L0 * W0 * theta**2
def x2(thetas, a):
return a * thetas**2
ang_vs = np.zeros(len(datas))
for i, dat in enumerate(datas):
ang_vs[i] = dat[5]
ang_vs = np.max(ang_vs)
for data in datas:
Wi, Li, W, L = data[:4]
energy_table = data[6]
natoms = data[4]
v = data[5]
phi = energy_table[:, 3]
z = energy_table[:, 4]
epot = (energy_table[:, 5] - energy_table[-1, 5])
heights = energy_table[:, 4]
inds = np.where(5 < heights)[0]
indv = max(inds)
indb = min(inds)
thetas = W / (2 * (L / phi))
if edge == 'ac':
W0 = (Wi - 1) * np.sqrt(3) / 2 * bond
L0 = Li * 3. * bond - 1. * bond
Area = W0 * L0
natoms2 = W0 * L0 / (3 * np.sqrt(3) / 4 * bond**2)
else:
raise
if [Wi, Li] not in wili_used:
wili_used.append([Wi, Li])
weff = 1 * W0 #- (bond*np.sqrt(3))*.3 # .02/(.16/W0 + .02)*W0 #
epot_t = shear_e(weff, L0, thetas)
plt.plot(thetas, epot_t / Area, '.-', color=colors[n],
alpha=.4) #, label = 'Epot teor')
W0s.append(W0)
teor_aopms.append(shear_e(weff, L0, 1) / Area)
n += 1
#epot_t2 = shear_eNoedge(W0, L0, thetas)
ind_last = np.where(.02 < thetas)[0][-1]
aopm = curve_fit(x2, thetas[ind_last:], epot[ind_last:] / Area,
1)[0][0]
#aopm = curve_fit(x2, thetas[:indb], epot[:indb]/Area, 1)[0][0]
if len(aopms) < n:
aopms.append([])
aopms[n - 1].append(aopm)
erange = np.max(epot / Area)
#plt.plot(thetas, x2(thetas, aopm), color = colors[n -1], alpha = .4) #, label = 'Epot')
plt.plot(thetas, epot / Area, color=colors[n - 1],
alpha=.1) #, label = 'Epot')
'''
plt.plot([thetas[indv], thetas[indv]], [epot[indv]/Area - erange/7, epot[indv]/Area + erange/7],
'--', color = colors[n -1], alpha = .3)
plt.plot([thetas[indb], thetas[indb]], [epot[indb]/Area - erange/7, epot[indb]/Area + erange/7],
'--', color = colors[n -1], alpha = .3)
'''
#plt.plot(thetas, z, color = colors[n -1], alpha = v/ang_vs) #, label = 'maxH')
#plt.scatter(thetas[indv], heights[indv], color = colors[n -1], alpha = .5)
#plt.scatter(thetas[indb], heights[indb], color = colors[n -1], alpha = .5)
#plt.plot(thetas, epot_t2, label = 'Epot teor2')
plt.xlabel('Theta w/(2R)')
plt.legend(loc=1)
#plt.ylabel('tot Edens eV/angst2')
#plt.title('width = %.2fAngst, edge = %s' %(W, edge))
plt.legend(loc=2)
plt.ylabel('height max Angst')
plt.show()
aopm_av = np.zeros(len(aopms))
for i in range(n):
aopm_av[i] = np.average(aopms[i])
plt.scatter(W0s, aopm_av, color='red')
plt.scatter(W0s, teor_aopms, color='green', label='teor')
plt.ylabel('aopm')
plt.xlabel('width')
plt.legend(loc=2, frameon=False)
plt.twinx()
plt.scatter(W0s,
np.array(aopm_av) / np.array(teor_aopms),
color='black',
label='teor/expr')
plt.ylabel('aopm teor over aopm expr')
plt.legend(loc=4, frameon=False)
plt.show()
def plot_kinkOfBend3(edge):
plot_mus = False
magic_par = 0.0203724
datas = get_log_data('LJ', T, '%s_twistTaito' % edge)
coll_data = np.zeros((len(datas), 6))
thresz = 5
vmax = -1.
eps = 0.002843732471143 #[eV]
kappa = .95 #[eV]
n = 1 / (3 * np.sqrt(3) * bond**2 / 4)
pot = 1
def theta_teor(W):
Y = 11.43 / W + 19.88
return 24. / Y * np.sqrt(eps * kappa * np.pi) * n
class alpha():
def __init__(self):
pass
def set_s(self, s):
self.s = s
def set_t(self, t):
self.t = t
def set_pot(self, pot):
self.pot = pot
def set_params(self, s, t, pot):
self.set_s(s)
self.set_t(t)
self.set_pot(pot)
def get_alpha(self, w):
#Y = 11.43/W + 19.88
#A, B = 48.7, .0055
#Length = 12.8
#B = 4/(Y*np.pi**2)*(A/Length**2 + B*Length**2)
return self.s / w**self.pot + self.t
#return self.s/w**self.pot + self.t
alpha = alpha()
def theta_teorFitPar(W, *args):
if len(args) == 1:
s = args[:1]
alpha.set_s(s)
if len(args) == 2:
s, t = args[:2]
alpha.set_s(s)
alpha.set_t(t)
if len(args) == 3:
s, t, pot = args[:3]
alpha.set_s(s)
alpha.set_t(t)
alpha.set_pot(pot)
#Y = 11.43/W + 19.88
#A, B = 48.7, .0055
#Length = 12.8
#print np.average(4/(Y*np.pi**2)*(A/Length**2 + B*Length**2))
return magic_par / alpha.get_alpha(W)
#return 4/(Y*np.pi**2*alpha.get_alpha(W))*(A/Length**2 + B*Length**2)
def overR(W, a1, a2):
return a1 / W + a2
def overRandconst(W, a1, a2):
return a1 / (W + a2)
def overR2(W, a1, a2):
return a1 / W**2 + a2
for i, data in enumerate(datas):
energy_table = data[6]
v = data[5]
natoms = data[4]
Wi, Li, Wd, L = data[:4]
phi = energy_table[:, 3]
epot = (energy_table[:, 5] - energy_table[-1, 5]) / natoms
heights = energy_table[:, 4]
inds = np.where(thresz < heights)[0]
indv = max(inds)
indb = min(inds)
W = Wd #int_toAngst(Wi, edge, key='width', C_C = bond) + 1.2
print W, Wd, Wd - W
thetas = W / (2 * (L / phi))
mus = thetas * 2. / W * 360 / (2 * np.pi) * 10
coll_data[i] = [W, v, thetas[indv], thetas[indb], mus[indv], mus[indb]]
if v > vmax:
vmax = v
if plot_mus:
for i in range(len(coll_data)):
plt.scatter(coll_data[i, 0],
coll_data[i, 4],
alpha=coll_data[i, 1] / vmax,
color='red')
plt.scatter(coll_data[i, 0],
coll_data[i, 5],
alpha=coll_data[i, 1] / vmax,
color='blue')
pot = 2.
alpha.set_pot(pot)
sopm2, topm2 = curve_fit(theta_teorFitPar,
coll_data[:, 0],
coll_data[:, 2],
p0=[1., 1])[0][:2]
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1 = curve_fit(theta_teorFitPar,
coll_data[:, 0],
coll_data[:, 2],
p0=[1.])[0][:1]
print sopm2, topm2
print sopm1
plot_widths = np.linspace(
np.min(coll_data[:, 0]) - .5,
np.max(coll_data[:, 0]) + 2, 50)
plt.plot(plot_widths,
2 / plot_widths * 3600 / (2 * np.pi) *
theta_teorFitPar(plot_widths, sopm2, topm2, 2.),
'--',
label=r'$\Theta \approx \frac{%.2f}{w^2} + %.3f$' %
(sopm2, topm2),
color='red')
plt.plot(plot_widths,
2 / plot_widths * 3600 / (2 * np.pi) *
theta_teorFitPar(plot_widths, sopm1, magic_par, 1.),
'--',
label=r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %
(sopm1, magic_par),
color='green')
plt.scatter(8.46, 4, marker='D', color='black')
plt.text(np.min(coll_data[:, 0]), 4.1,
r'Experim. $\Theta \approx 0.026 = 4deg/nm$')
plt.legend(frameon=False, loc=2)
plt.xlabel('width Angst')
plt.ylabel(r'$\Theta$')
plt.twinx()
alpha.set_params(sopm2, topm2, 2)
plt.plot(
plot_widths,
alpha.get_alpha(plot_widths),
label=r'$\alpha = \frac{%.3f}{%.2f/w^2 + %.3f} \rightarrow %.3f$' %
(magic_par, sopm2, topm2, magic_par / topm2),
color='red')
alpha.set_params(sopm1, magic_par, 1)
plt.plot(
plot_widths,
alpha.get_alpha(plot_widths),
label=r'$\alpha = \frac{%.3f}{%.2f/w + %.3f} \rightarrow %.3f$' %
(magic_par, sopm1, magic_par, 1),
color='green')
plt.ylabel(r'$\alpha$')
plt.legend(frameon=False)
plt.show()
else:
for i in range(len(coll_data)):
plt.scatter(coll_data[i, 0],
coll_data[i, 2],
alpha=coll_data[i, 1] / vmax,
color='red')
plt.scatter(coll_data[i, 0],
coll_data[i, 3],
alpha=coll_data[i, 1] / vmax,
color='blue')
#pot = 1.5
#alpha.set_pot(pot)
#sopm15, topm15 = curve_fit(theta_teorFitPar, coll_data[:,0], coll_data[:,2], p0 = [1., 1])[0][:2]
pot = 2.
alpha.set_pot(pot)
sopm2, topm2 = curve_fit(theta_teorFitPar,
coll_data[:, 0],
coll_data[:, 2],
p0=[1., 1])[0][:2]
alpha.set_pot(1)
alpha.set_t(magic_par)
sopm1 = curve_fit(theta_teorFitPar,
coll_data[:, 0],
coll_data[:, 2],
p0=[1.])[0][:1]
sopm1 = .16
#sopm3, topm3, potopm = curve_fit(theta_teorFitPar, coll_data[:,0], coll_data[:,2], p0 = [1., 1, 1])[0][:3]
print sopm2, topm2
print sopm1
#plt.plot(coll_data[:,0], np.ones(len(coll_data[:,0]))*.04, '-.', color = 'black')
#plt.text(np.min(coll_data[:,0]), .041, 'teor')
#plt.scatter(coll_data[:,0], theta_teor(coll_data[:,0]))
#plt.text(np.min(coll_data[:,0]), .041, 'teor')
plot_widths = np.linspace(
np.min(coll_data[:, 0]) - .5,
np.max(coll_data[:, 0]) + 2, 50)
#plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm15, topm15, 1.5), '--',
# label = 'alpha = %.2f/w**%.1f + %.3f' %(sopm15, 1.5, topm15))
plt.plot(plot_widths,
theta_teorFitPar(plot_widths, sopm2, topm2, 2.),
'--',
label=r'$\Theta \approx \frac{%.2f}{w^2} + %.3f$' %
(sopm2, topm2),
color='red')
plt.plot(plot_widths,
theta_teorFitPar(plot_widths, sopm1, magic_par, 1.),
'--',
label=r'$\Theta \approx \frac{%.2f}{w} + %.3f$' %
(sopm1, magic_par),
color='green')
#plt.plot(plot_widths, overR2(plot_widths, sopm2a, topm2a),
# label = r'$\Theta \approx \frac{1}{%.2fw^2} + %.3f$' %(sopm2a, topm2a), )
#plt.plot(plot_widths, theta_teorFitPar(plot_widths, sopm3, topm3, potopm), '.-',
# label = r'$\Theta \approx \frac{%.2f}{w^{%.2f}} + %.3f$' %(sopm3, potopm, topm3),
# color = 'red')
plt.scatter(8.46, .026, marker='D', color='black')
plt.text(np.min(coll_data[:, 0]), .028,
r'Experim. $\Theta \approx 0.026 = 4deg/nm$')
plt.legend(frameon=False, loc=2)
plt.xlabel('width Angst')
plt.ylabel(r'$\Theta$')
plt.twinx()
#alpha.set_params(sopm15, topm15, 1.5)
#plt.plot(plot_widths, alpha.get_alpha(plot_widths),
# label = 'alpha -> %.3f' %alpha.get_alpha(10000))
alpha.set_params(sopm2, topm2, 2)
plt.plot(
plot_widths,
alpha.get_alpha(plot_widths),
label=r'$\alpha = \frac{%.3f}{%.2f/w^2 + %.3f} \rightarrow %.3f$' %
(magic_par, sopm2, topm2, magic_par / topm2),
color='red')
alpha.set_params(sopm1, magic_par, 1)
plt.plot(
plot_widths,
alpha.get_alpha(plot_widths),
label=r'$\alpha = \frac{%.3f}{%.2f/w + %.3f} \rightarrow %.3f$' %
(magic_par, sopm1, magic_par, 1),
color='green')
#alpha.set_params(sopm3, topm3, potopm)
#plt.plot(plot_widths, alpha.get_alpha(plot_widths), '.-',
# label = r'$\alpha = \frac{%.3f}{%.2f/w^{%.2f} + %.3f} \rightarrow %.3f$'
# %(magic_par, sopm3, potopm, topm3, magic_par/topm3),
# color = 'red')
plt.ylabel(r'$\alpha$')
plt.legend(frameon=False)
plt.show()