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_stick2(edge):
plot_mus = True # False #
#edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
data = np.empty(len(wis), dtype = 'object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F*1./(3*np.sqrt(3)*bond**2/4)*.4
a = .3
colors = ['blue', 'red', 'black', 'green', 'yellow']
#print fmax
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' %edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C = bond)
print width_f
def axplusb(x, a, b):
return a*x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f/2
def func(y,x):
return np.sqrt(x**2 + y**2)
return 2*f*dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2*2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
plot2 = []
plot3 = []
fit_vals = [[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],]
fit_vals = [[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:,0]/(np.pi/3.)
thetas = width_f[j]/(2*Rs)
mus = thetas*2./width_f[j]*360/(2*np.pi)*10
print thetas
'''
if plot_mus:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
else:
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
plt.scatter(mus, teor(thetas, width_f), marker = 'v', label = 'teor')
plt.plot([2,2], [0, .4], '--', color = 'black')
plt.plot([4,4], [0, .4], '--', color = 'black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05, 'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc = 2, frameon = False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
'''
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j]/(2*thetas)
plt.plot(mus, LbLt[:,1]/R_exp, '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
else:
plt.plot(thetas, LbLt[:,1], '-o', color = colors[j], alpha = .8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j]/.01*a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j]/theta*a + a**2) + Lt
return (1./6.*theta*k*width_f[j]**2 - Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp = 0)[0]**2
Lmax = 35
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .04, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:,1], p0 = [fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail([thts[i]], fmax ,a) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts*2/width_f[j]*3600/(2*np.pi)
Lbend_teor = np.pi/3*width_f[j]/(2*thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j]/(2*thts)
plt.plot(degs, teor_Lt/R_teor, '--', color = colors[j], label = 'width = %i' %wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp = 0)[0]
deg0 = theta0*2/width_f[j]*3600/(2*np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
plt.plot(thts, teor_Lt, '--', color = colors[j], label = 'width = %i' %wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
else:
plt.xlabel('Curve deg/Angst')
plt.ylabel('Ltail Angst')
plt.legend(loc = 2, frameon = False)
plt.title('Required tail length for pinning')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:,0], plot2[:,1], '-o')
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_stick2(edge):
plot_mus = True # False #
#edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
data = np.empty(len(wis), dtype='object')
width_f = np.zeros(len(wis))
F = .006 # eV/angst
fmax = F * 1. / (3 * np.sqrt(3) * bond**2 / 4) * .4
a = .3
colors = ['blue', 'red', 'black', 'green', 'yellow']
#print fmax
for i, wi in enumerate(wis):
data[i] = get_stick_data('KC', T, '%s_stickTaito' % edge, wi)
width_f[i] = int_toAngst(wi, edge, key='width', C_C=bond)
print width_f
def axplusb(x, a, b):
return a * x + b
def Mmax(Lt, width_f, f):
def gfun(x):
return 0
def hfun(x):
return width_f / 2
def func(y, x):
return np.sqrt(x**2 + y**2)
return 2 * f * dblquad(func, 0, Lt, gfun, hfun)[0]
#thetas = width_f/(2*360/mus*1./(2*np.pi)*10)
def teor(theta, W0):
#return 2*np.sqrt(3)/9*1000*bond**3/W0*k*(1- 2*tau/(k*W0))**2*theta**3
return 2 * 2 * np.sqrt(3) / 9 * 1000 * bond**3 / W0 * k * (
1 - 2 * tau / (k * W0))**2 * theta**3
plot2 = []
plot3 = []
fit_vals = [
[.0007, .46],
[.0008, .4],
[.00075, .64],
[.00084, .705],
[.00085, .868],
]
fit_vals = [
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
[.00077, .6],
]
for j, wi in enumerate(wis):
LbLt = data[j]
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
Rs = LbLt[:, 0] / (np.pi / 3.)
thetas = width_f[j] / (2 * Rs)
mus = thetas * 2. / width_f[j] * 360 / (2 * np.pi) * 10
print thetas
'''
if plot_mus:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
else:
plt.scatter(mus[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
plt.scatter(mus, teor(thetas, width_f), marker = 'v', label = 'teor')
plt.plot([2,2], [0, .4], '--', color = 'black')
plt.plot([4,4], [0, .4], '--', color = 'black')
plt.text(1.03, .4, 'experimetl stick below 2deg/angst')
plt.text(1.03, -.05, 'red squares only one unit cell \n enought to hold bend')
plt.text(3.7, .4, 'buckling')
plt.title('Reguired tail length for bend to stick ac, w=7')
plt.legend(loc = 2, frameon = False)
plt.xlabel('Deg/angst')
plt.ylabel('Ltail/Lbend')
plt.show()
else:
'''
if plot_mus:
#plt.plot(mus, LbLt[:,1], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#a,b = curve_fit(axplusb, mus, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
#plt.plot(mus, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
#plt.plot(mus, a*mus + b, '--', color = colors[j],
# alpha = .8)
#plot2.append([width_f[j], -b/a])
#plt.plot(mus, LbLt[:,1]/width_f[j], '-o', color = colors[j],
# alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
R_exp = width_f[j] / (2 * thetas)
plt.plot(mus,
LbLt[:, 1] / R_exp,
'-o',
color=colors[j],
alpha=.8,
label=r'width = %.2f\AA' % (width_f[j] + 2))
else:
plt.plot(thetas, LbLt[:, 1], '-o', color=colors[j], alpha=.8)
'''
a,b = curve_fit(axplusb, thetas, LbLt[:,1]/LbLt[:,0], p0 = [1.,11])[0][:2]
plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j],
alpha = .8, label = r'width = %.2f\AA' %(width_f[j] + 2))
plt.plot(thetas, a*thetas + b, '--', color = colors[j],
alpha = .8)
plot2.append([width_f[j], -b/a])
'''
#plt.plot(thetas, LbLt[:,1]/LbLt[:,0], '-o', color = colors[j], alpha = .8)
print np.sqrt(width_f[j] / .01 * a + a**2)
def gfunc(Lt, theta, f, a):
L = np.sqrt(width_f[j] / theta * a + a**2) + Lt
return (1. / 6. * theta * k * width_f[j]**2 -
Mmax(L, width_f[j], f))**2
def Ltail(thetas, f, a):
Lts = np.zeros(len(thetas))
print f, a
for i, theta in enumerate(thetas):
Lts[i] = fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]
return Lts
def Ltail2(theta, f, a):
return fmin(gfunc, 1, args=([theta, f, a]), disp=0)[0]**2
Lmax = 35
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .04, len(Lts))
teor_Lt = np.zeros(len(Lts))
if False:
fmax, a = curve_fit(Ltail, thetas, LbLt[:, 1], p0=[fmax, .2])[0]
else:
fmax, a = fit_vals[j]
print fmax, a
for i, Lt in enumerate(Lts):
#teor_theta[k] = 6*Mmax(Lt)/(k*width_f**2)
teor_Lt[i] = Ltail(
[thts[i]], fmax,
a) #fmin(gfunc, 1, args=([thts[i]]), disp = 0)[0]
#print thts[i], teor_Lt[i], 6*Mmax(teor_Lt[i], width_f[j])/(k*width_f[j]**2) - thts[i]
if plot_mus:
degs = thts * 2 / width_f[j] * 3600 / (2 * np.pi)
Lbend_teor = np.pi / 3 * width_f[j] / (2 * thts)
#plt.plot(degs, teor_Lt/Lbend_teor, '--', color = colors[j], label = 'width = %i' %wi)
#plt.plot(degs, teor_Lt/width_f[j], '--', color = colors[j], label = 'width = %i' %wi)
R_teor = width_f[j] / (2 * thts)
plt.plot(degs,
teor_Lt / R_teor,
'--',
color=colors[j],
label='width = %i' % wi)
theta0 = fmin(Ltail2, .001, args=([fmax, a]), disp=0)[0]
deg0 = theta0 * 2 / width_f[j] * 3600 / (2 * np.pi)
plot3.append([width_f[j], deg0, theta0])
else:
plt.plot(thts,
teor_Lt,
'--',
color=colors[j],
label='width = %i' % wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
else:
plt.xlabel('Curve deg/Angst')
plt.ylabel('Ltail Angst')
plt.legend(loc=2, frameon=False)
plt.title('Required tail length for pinning')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 1], '-o')
plt.show()
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 2], '-o')
plt.show()
plot2 = np.array(plot2)
plt.plot(plot2[:, 0], plot2[:, 1], '-o')
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()