From dc5d73a9d24f21168c1cc4bcfef30025ec1f1ec5 Mon Sep 17 00:00:00 2001 From: Kees van Kempen Date: Fri, 18 Mar 2022 10:00:49 +0100 Subject: [PATCH] ass3: Wrap up the set and hand it in 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 --- ass3-12-a-weak-junction.py | 14 ++++++++++---- superconductivity_assignment3_kvkempen.pdf | Bin 45818 -> 252769 bytes superconductivity_assignment3_kvkempen.tex | 8 +++++++- 3 files changed, 17 insertions(+), 5 deletions(-) mode change 100644 => 100755 ass3-12-a-weak-junction.py 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 d0c43a0330f20567bdc34370cf9c7486733541df..1e7980cdf9bcc40e729d858954c591fe0e87c7d2 100644 GIT binary patch literal 252769 zcmce7WpE?ilBJp1ZZosnATu*FbDP~}W@cu)&D>^YW@ct)W@cJ{v$GK!I}tnc=e-I^ zA=S;gb+b+?m3dByOkP-&mVu51hHQF%U>Sy)ke<-Sz#N8~8wQ~4W@|(UP?s|>H!^gD z0Vp{cIR3{TQ5$WR95ab8&HH?w<@BbY6e)rGP*}fV`u92UPZIpsIKlew zbK;-K{g*hw`hSPhf2MCnj&FSaWBc#ZcLnyC{eI(3Wz{yVvPi%-{IpS#LDBjA>WylK z$|z(N;yfHnZnDs*=ehgc!-;4B?w?)L15ylRu(T-eE>Ug{a_*P41+^wMpI6Z`VcVn| zY0{>ru=p^HG&cmBko}_j?3bNOcM7jnxRA3<#h)K)+MR&a%JVAyCz8vPd#9JN5_a^5 z2U(~Ql~-fez!)vf`nN(}xVKKvnCs|mmDePk&(|TfwxuoDoo$iz=}*Md7{24PY@4o* 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zcmyF(K^{JHOMVOUcmI2b5kSkv8-mRvzz6tX!1LE^UZelv()^DIFs?}nwQm~FdQW`x zv$)iUB3r_O0upl6pW`Iz>tl1FYpYMpvg1TjaiUGe255bYCft;vrVOW(!jug35AKs= z*_1=bP*X%%x3YZso&5AFGc9e$D~cyEqPqb^x63@IL=rVlk<@vT+3P!tR#^h;;37E6h3Cbvh(v`-HBkYb=4xQwPU%xZeZqfn|p+Oj*wlP$g}ll9KL$LKSe z%Vx8C!~-6~vek~I;TZ-)TJdXQCPvGs&jV(PC={iWUlZQ$o6+;n$RN=Ez>Z875vYFm6gUd&EU7d*B5sn3}3W8)%^nEWuqNKLR1*$$vMqZ8a!VE(WB<>G1vbM=HlpxFEZ PJi@}*%*^s?3fTV-ar~6L 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}