some stuff done
This commit is contained in:
Dominik Demuth
parent
996b0b2ae2
commit
bc215ce32b
@ -1,41 +1,26 @@
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# Tool-Naranayaswamy-Moynihan-Hodge model
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# by Florian Pabst 2020
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import re
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import os
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import sys
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import time
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import numpy as np
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import matplotlib.pyplot as plt
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from scipy.integrate import quad, cumulative_trapezoid
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from scipy.integrate import cumulative_trapezoid
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from scipy.optimize import curve_fit, fsolve
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from scipy.stats import linregress
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from nmreval.data import Points
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def slope(x, t, m):
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return t+x*m
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def tau_k(tau_0, deltaE, temp_k, xx, T_f_km1):
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return tau_0 * np.exp(xx*deltaE / (R*temp_k) + (1-xx) * deltaE / (R*T_f_km1))
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# Read data
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dataName = sys.argv[1]
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try:
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data = np.loadtxt(dataName, skiprows=0).T
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# print("Loading")
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temp = data[0]
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heat_capacity = data[1]
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except IndexError:
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# print("File not found")
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exit()
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print(np.round(temp, decimals=3)[:30])
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def get_fictive_temperature(pts: Points, glass: tuple[float, float], liquid: tuple[float, float]):
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min_glass, max_glass = min(glass), max(glass)
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@ -51,8 +36,8 @@ def get_fictive_temperature(pts: Points, glass: tuple[float, float], liquid: tup
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region.y -= glass_extrapolation
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liquid_regime = (min_liquid < region.x) & (region.x < max_liquid)
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regress = linregress(region.x[liquid_regime], region.y[liquid_regime])
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liquid_extrapolation = regress.slope * region.x + regress.intercept
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regress2 = linregress(region.x[liquid_regime], region.y[liquid_regime])
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liquid_extrapolation = regress2.slope * region.x + regress2.intercept
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real_area = -cumulative_trapezoid(region.y, region.x, initial=0)
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real_area -= real_area[-1]
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@ -60,10 +45,12 @@ def get_fictive_temperature(pts: Points, glass: tuple[float, float], liquid: tup
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equivalent_area -= equivalent_area[-1]
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equivalent_area *= -1
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return region.x, region.x[np.argmin(np.abs(real_area[:, None] - equivalent_area[None, :]), axis=1)]
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return region.x, np.round(region.x[np.argmin(np.abs(real_area[:, None] - equivalent_area[None, :]), axis=1)], decimals=4)
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curve = Points(x=temp, y=heat_capacity, name=dataName)
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# plt.plot(curve.x, curve.y)
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# plt.show()
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# First step: Calculate fictive Temperature T_f(T) from Cp data, then dT_f/dT
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@ -75,21 +62,19 @@ initial_Tf = np.mean(fictiveTemp[:20])
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rate = curve.value
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# Calculate dTf/dT
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with np.errstate(all='ignore'):
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dTfdT = np.gradient(fictiveTemp, temperatures)
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nan_filter = ~np.isnan(dTfdT)
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temperatures = np.array(temperatures)[nan_filter]
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dTfdT = dTfdT[nan_filter]
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# with np.errstate(all='ignore'):
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# dTfdT = np.diff(fictiveTemp)/np.diff(temperatures) # np.gradient(fictiveTemp, temperatures)
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# nan_filter = ~np.isnan(dTfdT)
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# temperatures = 0.5 * (temperatures[:-1] + temperatures[1:])[nan_filter]
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# # fictiveTemp = fictiveTemp[nan_filter]
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# dTfdT = dTfdT[nan_filter]
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print(fictiveTemp[:30])
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exponents = []
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taus = []
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temps = [0]
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T_f_ns = []
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R = 8.314
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def tnmfunc(temperature, tau_g, x, beta, deltaE):
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def tnm_function(temperature, tau_g, x, beta, energy, tg):
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step = len(temperature)
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Tf = np.empty(step)
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@ -103,7 +88,7 @@ def tnmfunc(temperature, tau_g, x, beta, deltaE):
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temp_0 = temperature[0]
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for i in range(0, step-1):
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tau[i] = relax(temperature[i+1], Tf[i], tau_g, T_g, deltaE, x)
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tau[i] = relax(temperature[i+1], Tf[i], tau_g, tg, energy, x)
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dttau[:i] += delt[i] / tau[i]
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Tf[i+1] = np.sum(delT[:i] * (1-np.exp(-dttau[:i]**beta))) + temp_0
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@ -115,147 +100,6 @@ def relax(t, tf, tau_g, t_glass, ea, x):
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return tau_g * np.exp((x*h / t) + ((1 - x) * h / tf) - h / t_glass)
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# TNMH Code (adapted from Badrinarayanan's PhD Thesis):
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def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
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delhR = deltaE/8.314
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T = []
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Tf = []
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t = []
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delt = []
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tau = []
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dttau = []
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delT = []
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step = len(xdata)
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for k in range(0, step):
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dttau.append(0)
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T.append(240)
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Tf.append(240)
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t.append(0)
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delt.append(0)
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tau.append(0)
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dttau.append(0)
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delT.append(0)
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T[1] = xdata[1]
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Tf[1] = T[1]
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t[1] = 0
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delt[1] = 0
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tau[1] = tau_0 * np.exp((xx*delhR / T[1]) + ((1 - xx)*delhR / Tf[1])-delhR/T_g)
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dttau[1] = delt[1] / tau[1]
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delT[1] = 0
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Tfinit = T[1]
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T_f_ns = [xdata[0]]
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for i in range(1, step):
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T[i] = xdata[i]
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delT[i] = xdata[i] - xdata[i-1]
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delt[i] = abs(delT[i]) / (rate/60)
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t[i] = t[i-1] + delt[i]
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tau[i] = tau_0 * np.exp((delhR*xx / T[i]) + ((1 - xx)*delhR / Tf[i-1])-delhR/T_g)
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# print(tau[i], T[i], Tf[i-1], dttau)
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for j in np.arange(2, i).reshape(-1):
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dttau[j] = dttau[j] + (delt[i] / tau[i])
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Tfinit = Tfinit + (delT[j] * (1 - np.exp(- (dttau[j] ** beta))))
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Tf[i] = Tfinit
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T_f_ns.append(Tfinit)
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Tfinit = Tf[1]
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return T_f_ns
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def tnmfunc3(xdata, tau_0, xx, beta, deltaE):
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delhR = deltaE/8.314
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step = len(xdata)
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dttau = []
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T = []
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Tf = []
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t = []
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delT = []
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delt = []
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tau = []
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for _ in range(step):
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T.append(np.nan)
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Tf.append(np.nan)
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t.append(np.nan)
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delT.append(np.nan)
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delt.append(np.nan)
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tau.append(np.nan)
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dttau.append(0)
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T[0] = xdata[0]
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Tf[0] = T[0]
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t[0] = 0
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delT[0] = 0
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delt[0] = 0
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tau[0] = tau_0 * np.exp(xx * delhR/T[0] + (1-xx)*delhR/Tf[0] - delhR/T_g)
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dttau[0] = delt[0]/tau[0]
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Tfinit = T[0]
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for i in range(1, step):
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T[i] = xdata[i]
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delT[i] = xdata[i] - xdata[i-1]
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delt[i] = abs(delT[i]) * 60 / rate
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t[i] = t[i-1] + delt[i]
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tau[i] = tau_0 * np.exp(xx * delhR/T[i] + (1-xx)*delhR/Tf[i-1] - delhR/T_g)
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for j in range(1, i):
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dttau[j] += delt[i]/tau[i]
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Tfinit += delT[j] * (1-np.exp(-dttau[j]**beta))
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Tf[i] = Tfinit
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Tfinit = T[0]
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return Tf
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def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
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delhR = deltaE/8.314
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T = []
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Tf = []
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t = []
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delt = []
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tau = []
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dttau = []
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delT = []
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step = len(xdata)
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for k in range(0, step):
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dttau.append(0)
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T.append(240)
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Tf.append(240)
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t.append(0)
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delt.append(0)
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tau.append(0)
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dttau.append(0)
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delT.append(0)
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T[1] = xdata[1]
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Tf[1] = T[1]
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t[1] = 0
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delt[1] = 0
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tau[1] = tau_0 * np.exp((xx*delhR / T[1]) + ((1 - xx)*delhR / Tf[1])-delhR/T_g)
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dttau[1] = delt[1] / tau[1]
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delT[1] = 0
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Tfinit = T[1]
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T_f_ns = [xdata[0]]
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for i in range(1, step):
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T[i] = xdata[i]
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delT[i] = xdata[i] - xdata[i-1]
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delt[i] = abs(delT[i]) / (rate/60)
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t[i] = t[i-1] + delt[i]
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tau[i] = tau_0 * np.exp((delhR*xx / T[i]) + ((1 - xx)*delhR / Tf[i-1])-delhR/T_g)
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# print(tau[i], T[i], Tf[i-1], dttau)
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for j in np.arange(2, i).reshape(-1):
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dttau[j] = dttau[j] + (delt[i] / tau[i])
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Tfinit = Tfinit + (delT[j] * (1 - np.exp(- (dttau[j] ** beta))))
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Tf[i] = Tfinit
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T_f_ns.append(Tfinit)
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Tfinit = Tf[1]
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return T_f_ns
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# Use T_g = T_fictive for tau determination
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T_g = initial_Tf
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@ -263,48 +107,26 @@ T_g = initial_Tf
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p0 = [10, 0.5, 0.4, 225085]
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def fitTNMH(x, tau_0, xx, beta, deltaE):
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dTNMHdT = []
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modelTemp = np.append(x[::-1], x[1:])
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def tnmh_fit(tg):
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def wrap(x, tau_0, xx, beta, energy):
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modelTemp = np.r_[x[::-1], x[1:]]
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TNMH = tnmfunc2(modelTemp, tau_0, xx, beta, deltaE)
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for i in range(len(modelTemp)-1):
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dTNMHdT.append((TNMH[i+1]-TNMH[i]) / (modelTemp[i+1]-modelTemp[i]))
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res = dTNMHdT[len(modelTemp)//2-1:]
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TNMH = tnm_function(modelTemp, tau_0, xx, beta, energy, tg)
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res = np.gradient(TNMH, modelTemp)
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plt.plot(x, res)
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plt.show()
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return res[len(x)-1:]
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return np.array(res)
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return wrap
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# Use only every 20th data point to reduce fitting time
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temperaturesInterpol = np.linspace(temperatures[0], temperatures[-1], 20)
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temperaturesInterpol = np.linspace(150, 200, 51)
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temperaturesInterpol = np.append(temperaturesInterpol[::-1], temperaturesInterpol[1:])
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start = time.time()
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tnmfunc2(temperaturesInterpol, *p0)
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print('Flo', time.time()-start)
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start = time.time()
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tnmfunc3(temperaturesInterpol, *p0)
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print('list', time.time()-start)
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start = time.time()
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tnmfunc(temperaturesInterpol, *p0)
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print('Array', time.time()-start)
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temperaturesInterpol = np.linspace(temperatures[0], temperatures[-1], 200)
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dTfdTInterpol = np.interp(temperaturesInterpol, temperatures, dTfdT)
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plt.plot(tnmfunc2(temperaturesInterpol, *p0), label='Flo')
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plt.plot(tnmfunc3(temperaturesInterpol, *p0), label='List')
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plt.plot(tnmfunc(temperaturesInterpol, *p0), label='array')
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plt.legend()
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plt.show()
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res = curve_fit(tnmh_fit(T_g), temperaturesInterpol, dTfdTInterpol, p0)
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plt.plot(np.diff(tnmfunc2(temperaturesInterpol, *p0)), label='Flo')
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plt.plot(np.diff(tnmfunc3(temperaturesInterpol, *p0)), label='List')
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plt.plot(np.diff(tnmfunc(temperaturesInterpol, *p0)), label='array')
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plt.plot(temperatures, dTfdT, label='dTf/dT')
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plt.plot(temperaturesInterpol, tnmh_fit(T_g)(temperaturesInterpol, *res[0]), label='fit')
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plt.legend()
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plt.show()
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# print(fitTNMH(temperaturesInterpol, *p0))
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@ -26,7 +26,6 @@ except IndexError:
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dataOutName = os.path.splitext(str(dataName))[0] + "_Tfict+TNMH.dat"
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# First step: Calculate fictive Temperature T_f(T) from Cp data, then dT_f/dT
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# Find start and end point for glass Cp linear fit
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@ -172,20 +171,15 @@ for i in range(len(temperatures)-1):
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dTfdT.append((fictiveTemp[i+1]-fictiveTemp[i]) / (temperatures[i+1]-temperatures[i]))
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temperaturesCut.append(temperatures[i+1])
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"""
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fig, (ax1) = P.subplots(1)
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print(fictiveTemp[:30])
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fig, ax1 = plt.subplots(1)
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ax1.set_xlabel('Temperature / K')
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ax1.set_ylabel('Fictive Temperature / K')
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#ax1.set_xlim(left=coordsGl[0][0])
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#ax1.set_xlim(right=coordsLq[1][0])
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#ax1.set_ylim(bottom=coordsGl[0][1]-0.1)
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#ax1.set_ylim(top=coordsLq[1][1]+0.1)
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ax1.plot(temperatures,fictiveTemp, 'ro')
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#ax1.plot(temperatures,(T_f_0+temperatures*0), 'b-')
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ax1.axhline(y=T_f_0[0], color='b', linestyle='-')
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#ax1.plot(temperatures[:-1],dTfdT, 'ro')
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P.show()
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"""
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# ax1.plot(temperatures, fictiveTemp, 'ro')
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ax1.plot(temperaturesCut, dTfdT)
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# ax1.axhline(y=T_f_0[0], color='b', linestyle='-')
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plt.show()
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# Second step: Calcualte and Fit TNMH-model
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try:
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@ -207,6 +201,7 @@ T_f_ns = []
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markovs = [coordsLq[1][0]]
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R = 8.31
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# TNMH Code (adapted from Badrinarayanan's PhD Thesis):
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def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
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delhR = deltaE/8.314
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@ -250,7 +245,6 @@ def tnmfunc2(xdata, tau_0, xx, beta, deltaE):
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T_f_ns.append(Tfinit)
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Tfinit = Tf[1]
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print(T_f_ns[:10])
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return T_f_ns
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@ -297,25 +291,15 @@ tau_0, xx, beta, deltaE = p0
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fitResult = fitTNMH(p0, temperaturesInterpol)
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"""
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fig, (ax1) = P.subplots(1)
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fig, ax1 = plt.subplots()
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ax1.set_xlabel('Temperature / K')
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ax1.set_ylabel('Fictive Temperature / K')
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#ax1.set_xlim(left=coordsGl[0][0])
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#ax1.set_xlim(right=coordsLq[1][0])
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#ax1.set_ylim(bottom=coordsGl[0][1]-0.1)
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#ax1.set_ylim(top=coordsLq[1][1]+0.1)
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#ax1.plot(temperatures,fictiveTemp, 'bo')
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#ax1.plot(temperatures,T_f_ns, 'r-')
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ax1.plot(temperaturesCut, dTfdT, 'bo')
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#ax1.plot(temperatures[0:5454],dTNMHdT[0:5454], 'bo')
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#ax1.plot(temperatures[5456:],dTNMHdT[5455:], 'ro')
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#ax1.plot(temperaturesModel[0:99],dTNMHdT[0:99], 'b-')
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#ax1.plot(temperaturesModel[100:199],dTNMHdT[100:199], 'r-')
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ax1.plot(temperaturesInterpol, dTfdTInterpol, 'yo')
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ax1.plot(temperaturesInterpol, fitResult, 'r-')
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P.show()
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"""
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plt.show()
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dataOutName = os.path.splitext(str(dataName))[0] + "_dTfdT_tau.fit"
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dataOut = np.column_stack((temperaturesInterpol, dTfdTInterpol, fitResult))
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