def get_data(data, edge):
W,L = data[0], data[1]
Dy = data[2]
R = data[3]
Wf = int_toAngst(W, edge, key = 'width', C_C = 1.42)
Lf = int_toAngst(L, edge, key = 'length', C_C = 1.42)
theta = Wf / (2 * R) # new journal of physics Bending and buckling -> theta ~ 0.013 (7-ac ribbon).
print Lf/Wf, Wf, R, theta, L
return [Wf, Lf, Dy, R, theta]
def get_data(data, edge):
W, L = data[0], data[1]
Dy = data[2]
R = data[3]
Wf = int_toAngst(W, edge, key='width', C_C=1.42)
Lf = int_toAngst(L, edge, key='length', C_C=1.42)
theta = Wf / (
2 * R
) # new journal of physics Bending and buckling -> theta ~ 0.013 (7-ac ribbon).
print Lf / Wf, Wf, R, theta, L
return [Wf, Lf, Dy, R, theta]
def plot_fig3c():
plot_mus = True # False #
edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
_, axs = get_axes(1, 1, .8)
deva = .6
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 = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
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 wi == 5: m = 0
if wi == 7: m = 1
if wi == 9: m = 2
if wi == 11: m = 3
if wi == 13: m = 4
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)
add_L = np.sqrt(2 * R_exp * deva + deva**2) / 10.
axs[0].scatter(LbLt[:, 1] / 10 + add_L, mus, color=colors[m])
axs[0].text(3 + 1.5 / 4 * m,
11 - 7. / 4 * m,
r'w=%i' % wi,
color=colors[m])
else:
axs[0].plot(thetas, LbLt[:, 1], '-o', color=colors[m], 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 = 55
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .045, 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) + np.sqrt(
width_f[j] / thts[i] * deva +
deva**2) #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)
axs[0].plot(teor_Lt / 10,
degs,
'--',
color=colors[m],
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:
axs[0].plot(teor_Lt / 10,
thts,
'--',
color=colors[m],
label='width = %i' % wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
axs[0].set_ylabel(r'$\Theta$')
axs[0].set_xlabel(r'$L (nm)$')
else:
axs[0].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[0].set_xlabel(r'$L$ (nm)')
#axs[0].legend(loc = 2, frameon = False)
#axs[0].set_title('Required tail length for pinning')
axs[0].set_ylim([0, 13])
axs[0].set_xlim([1, 6])
axs[0].set_xticks(np.linspace(0, 7, 8))
a = plt.axes([.3, .675, .27, .23])
plot3 = np.array(plot3)
plt.plot(plot3[:, 0], plot3[:, 1], '--', color='black', alpha=.5)
for i in range(5):
plt.scatter(plot3[i, 0], plot3[i, 1], color=colors[i])
plt.yticks(np.linspace(.6, 2.2, 5))
plt.xticks(np.linspace(4, 16, 4))
plt.xlabel(r'Width (\AA)')
plt.ylabel(r'$\kappa$ (deg/nm)')
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_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_fig3c():
plot_mus = True # False #
edge = 'ac'
T, wis = 10, [5, 7, 9, 11, 13]
_, axs = get_axes(1,1, .8)
deva = .6
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 = ['red', 'blue', 'green', 'black', 'cyan', 'yellow']
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 wi == 5: m = 0
if wi == 7: m = 1
if wi == 9: m = 2
if wi == 11: m = 3
if wi == 13: m = 4
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)
add_L = np.sqrt(2*R_exp*deva + deva**2)/10.
axs[0].scatter(LbLt[:,1]/10 + add_L, mus, color = colors[m])
axs[0].text(3 + 1.5/4*m, 11 - 7./4*m, r'w=%i' %wi, color = colors[m])
else:
axs[0].plot(thetas, LbLt[:,1], '-o', color = colors[m], 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 = 55
Lts = np.linspace(0, Lmax, 15)
thts = np.linspace(0.005, .045, 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) + np.sqrt(width_f[j]/thts[i]*deva + deva**2) #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)
axs[0].plot(teor_Lt/10, degs, '--', color = colors[m], 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:
axs[0].plot(teor_Lt/10, thts, '--', color = colors[m], label = 'width = %i' %wi)
#plt.legend(loc = 2, frameon = False)
if not plot_mus:
axs[0].set_ylabel(r'$\Theta$')
axs[0].set_xlabel(r'$L (nm)$')
else:
axs[0].set_ylabel(r'Curvature $\kappa$ (deg/nm)')
axs[0].set_xlabel(r'$L$ (nm)')
#axs[0].legend(loc = 2, frameon = False)
#axs[0].set_title('Required tail length for pinning')
axs[0].set_ylim([0,13])
axs[0].set_xlim([1,6])
axs[0].set_xticks(np.linspace(0, 7, 8))
a = plt.axes([.3, .675, .27, .23])
plot3 = np.array(plot3)
plt.plot(plot3[:,0], plot3[:,1], '--', color = 'black', alpha = .5)
for i in range(5):
plt.scatter(plot3[i,0], plot3[i,1], color = colors[i])
plt.yticks(np.linspace(.6, 2.2, 5))
plt.xticks(np.linspace(4, 16, 4))
plt.xlabel(r'Width (\AA)')
plt.ylabel(r'$\kappa$ (deg/nm)')
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_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_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_stick():
#width_f = 7.5
#print 4./360*2*np.pi*width_f/10/2.
#exit()
plot_mus = False
edge = 'ac'
T, wi = 10, 11
LbLt = get_stick_data('KC', T, '%s_stickTaito' %edge, wi)
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
width_f = int_toAngst(wi, edge, key='width', C_C = bond)
Rs = LbLt[:,0]/(np.pi/3.)
thetas = width_f/(2*Rs)
mus = thetas*2./width_f*360/(2*np.pi)*10
#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
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:
for i in range(len(mus)):
if LbLt[i,1] < 3:
print 'hoos'
plt.scatter(thetas[i], LbLt[i,1]/LbLt[i,0], marker = 'D',color = 'red')
#plt.scatter(thetas[i], LbLt[i,1], marker = 'D',color = 'red')
else:
plt.scatter(thetas[i], LbLt[i,1]/LbLt[i,0], color = 'blue')
#plt.scatter(thetas[i], LbLt[i,1], color = 'blue')
print LbLt[i,1]/(np.pi/3)*2*thetas[i]/width_f, LbLt[i,1], 1/(np.pi/3)*2*thetas[i]/width_f, LbLt[i,0]
#plt.scatter(thetas, teor(thetas, width_f), marker = 'v', label = 'teor')
#plt.scatter(thetas, teor(thetas, width_f)*LbLt[:,0], marker = 'v', label = 'teor')
plt.twinx()
plt.scatter(thetas, LbLt[:,0])
plt.scatter(thetas, LbLt[:,1])
plt.legend(loc = 2, frameon = False)
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
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_stick():
#width_f = 7.5
#print 4./360*2*np.pi*width_f/10/2.
#exit()
plot_mus = False
edge = 'ac'
T, wi = 10, 11
LbLt = get_stick_data('KC', T, '%s_stickTaito' % edge, wi)
LbLt.view('i8,i8').sort(order=['f0'], axis=0)
width_f = int_toAngst(wi, edge, key='width', C_C=bond)
Rs = LbLt[:, 0] / (np.pi / 3.)
thetas = width_f / (2 * Rs)
mus = thetas * 2. / width_f * 360 / (2 * np.pi) * 10
#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
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:
for i in range(len(mus)):
if LbLt[i, 1] < 3:
print 'hoos'
plt.scatter(thetas[i],
LbLt[i, 1] / LbLt[i, 0],
marker='D',
color='red')
#plt.scatter(thetas[i], LbLt[i,1], marker = 'D',color = 'red')
else:
plt.scatter(thetas[i], LbLt[i, 1] / LbLt[i, 0], color='blue')
#plt.scatter(thetas[i], LbLt[i,1], color = 'blue')
print LbLt[i, 1] / (np.pi / 3) * 2 * thetas[i] / width_f, LbLt[
i, 1], 1 / (np.pi / 3) * 2 * thetas[i] / width_f, LbLt[i, 0]
#plt.scatter(thetas, teor(thetas, width_f), marker = 'v', label = 'teor')
#plt.scatter(thetas, teor(thetas, width_f)*LbLt[:,0], marker = 'v', label = 'teor')
plt.twinx()
plt.scatter(thetas, LbLt[:, 0])
plt.scatter(thetas, LbLt[:, 1])
plt.legend(loc=2, frameon=False)
plt.xlabel('Theta')
plt.ylabel('Ltail Angst')
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()
