Kees van Kempen
dc5d73a9d2
Hoi Roos, In de bijlage vind je de pdf van mijn uitwerkingen en de code voor taak 12 (die ook in de appendix staat). Door tijdgebrek ben ik niet overal aan toegekomen. Het was erg veel werk. Met vriendelijke groet, Kees van Kempen
60 lines
2.0 KiB
Python
Executable File
60 lines
2.0 KiB
Python
Executable File
#!/bin/env python3
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import numpy as np
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from scipy.integrate import odeint
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from matplotlib import pyplot as plt
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import pandas as pd
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def phi_dot(phi, t, I_DC, I_RF):
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R = 10.e-3 #Ohm
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I_J = 1.e-3 #A
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omega_RF = 2*np.pi*.96e9 #rad/s
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hbar = 1.0545718e-34 #m^2kg/s
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e = 1.60217662e-19 #C
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return 2*e*R/hbar*( I_DC + I_RF*np.cos(omega_RF*t) - I_J*(np.sin(phi)) )
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# I attempted to solve it without the constants, as I suspected overflows
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# were occurring. The next line did not improve the result.
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#return R*( I_DC + I_RF*np.sin(omega_RF*t) - I_J*(np.sin(phi)) )
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# We need an initial value to phi
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phi_0 = 0
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# Let's try it for a lot of periods
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N_points = 10000
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t = np.linspace(0, 100, N_points)
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hbar = 1.0545718e-34 #m^2kg/s
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e = 1.60217662e-19 #C
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df = pd.DataFrame(columns=['I_DC','I_RF','V_DC_bar'])
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# For testing:
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#phi = odeint(phi_dot, phi_0, t, (.5e-3, .5e-3))[:, 0]
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#for I_DC in [1e-4, .5e-3, 1.e-3, 1.5e-3, 2.e-3, 2.5e-3]:
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for I_DC in np.arange(0, 1e-3, 1e-5):
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for I_RF in [0., .5e-3, 2.e-3]:
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# The individual solutions for phi do seem sane, at least, the ones
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# I inspected.
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phi = odeint(phi_dot, phi_0, t, (I_DC, I_RF))
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# I initially thought to average over the tail to look at the asymptotic behaviour.
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#N_asymp = N_points//2
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#V_DC_bar = hbar/(2*e)*np.mean(phi[N_asymp:]/t[N_asymp:])
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# Then I choose to just take the last point to see if that gave better results.
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V_DC_bar = hbar/(2*e)*phi[-1]/t[-1]
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print("For I_DC =", I_DC, "\t I_RF = ", I_RF, "\twe find V_DC_bar =", V_DC_bar)
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df = df.append({'I_DC': I_DC, 'I_RF': I_RF, 'V_DC_bar': V_DC_bar}, ignore_index = True)
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## Plotting the thing
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plt.figure()
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plt.xlabel("$\\overline{V_{DC}}$")
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plt.ylabel("$I_{DC}$")
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for I_RF in df.I_RF.unique():
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x, y = df[df.I_RF == I_RF][["V_DC_bar", "I_DC"]].to_numpy().T
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plt.plot(x, y, label="$I_{RF} = " + str(I_RF) + "$")
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plt.legend()
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plt.show() |