diff --git a/ass3-12-a-weak-junction.py b/ass3-12-a-weak-junction.py old mode 100644 new mode 100755 index bc59f47..347fd70 --- a/ass3-12-a-weak-junction.py +++ b/ass3-12-a-weak-junction.py @@ -5,15 +5,16 @@ from scipy.integrate import odeint from matplotlib import pyplot as plt import pandas as pd -#phi_dot = lambda phi, t, I_DC, I_RF, I_J, omega_RF, hbar, e, R: 2*e*R/hbar*( I_DC + I_RF*np.cos(omega_RF*t) - I_J(np.sin(phi)) ) def phi_dot(phi, t, I_DC, I_RF): R = 10.e-3 #Ohm I_J = 1.e-3 #A omega_RF = 2*np.pi*.96e9 #rad/s hbar = 1.0545718e-34 #m^2kg/s e = 1.60217662e-19 #C - + return 2*e*R/hbar*( I_DC + I_RF*np.cos(omega_RF*t) - I_J*(np.sin(phi)) ) + # I attempted to solve it without the constants, as I suspected overflows + # were occurring. The next line did not improve the result. #return R*( I_DC + I_RF*np.sin(omega_RF*t) - I_J*(np.sin(phi)) ) # We need an initial value to phi @@ -28,15 +29,20 @@ e = 1.60217662e-19 #C df = pd.DataFrame(columns=['I_DC','I_RF','V_DC_bar']) +# For testing: #phi = odeint(phi_dot, phi_0, t, (.5e-3, .5e-3))[:, 0] #for I_DC in [1e-4, .5e-3, 1.e-3, 1.5e-3, 2.e-3, 2.5e-3]: + for I_DC in np.arange(0, 1e-3, 1e-5): for I_RF in [0., .5e-3, 2.e-3]: + # The individual solutions for phi do seem sane, at least, the ones + # I inspected. phi = odeint(phi_dot, phi_0, t, (I_DC, I_RF)) + # I initially thought to average over the tail to look at the asymptotic behaviour. #N_asymp = N_points//2 - I_DC_bar = np.mean(phi[N_asymp:]/t[N_asymp:]) + #V_DC_bar = hbar/(2*e)*np.mean(phi[N_asymp:]/t[N_asymp:]) + # Then I choose to just take the last point to see if that gave better results. V_DC_bar = hbar/(2*e)*phi[-1]/t[-1] - #V_DC_bar = I_DC_bar print("For I_DC =", I_DC, "\t I_RF = ", I_RF, "\twe find V_DC_bar =", V_DC_bar) df = df.append({'I_DC': I_DC, 'I_RF': I_RF, 'V_DC_bar': V_DC_bar}, ignore_index = True) diff --git a/superconductivity_assignment3_kvkempen.pdf b/superconductivity_assignment3_kvkempen.pdf index d0c43a0..1e7980c 100644 Binary files a/superconductivity_assignment3_kvkempen.pdf and b/superconductivity_assignment3_kvkempen.pdf differ diff --git a/superconductivity_assignment3_kvkempen.tex b/superconductivity_assignment3_kvkempen.tex index 0dee10f..3125474 100755 --- a/superconductivity_assignment3_kvkempen.tex +++ b/superconductivity_assignment3_kvkempen.tex @@ -114,7 +114,6 @@ Equating these expressions and rewriting yields v_L = \frac{U}{B\ell} = \SI{3.75e5}{\meter\per\second}. % https://www.wolframalpha.com/input?i=1.5*10%5E-5+%2F+%285*+.08%29 \] -\todo{Direction?} \textbf{(b)} The vortices are aranged in a lattice with separation $r_{sep} = \sqrt{\frac{\Phi_0}{B}}$. @@ -156,9 +155,16 @@ Solving for $J_{max}$, this yields the beautiful expression J_{max} = \frac{6B_c\lambda R}{\mu \left[ 4\lambda^3 - 9\lambda^2R + 3\lambda R^2- 3\lambda R + 3R^3 -3R^2 \right]}. % https://www.wolframalpha.com/input?i=R*B+%3D+m*x%2Fl*%28%28R%5E3-%28R-l%29%5E3%29%2F3+-+%28R%2Bl%29*%28R+-+%28R-l%29%5E2%29%2F2%29 \] + +\textbf{(b)} + + \section{A weak junction} See the code in appendix \ref{appendix:program-task-12}. +It unfortunately does not seem to produce any useful results. +In the code, I left many comments as it is mostly in a debugging state. + \bibliographystyle{vancouver} \bibliography{references.bib}