Changes

Expressing in terms of ${{:omega1}}, {{:omegaeff}} <br><math> \sin^2\theta \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + \omega_\textrm{e}^2} \right) = \frac{w_\textrm{1}^2}{w_\textrm{weff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}, ^2 + \Omega^2} \right) =\frac{w_\textrm{1}^2}{w_\textrm{1}^2 + \Omega^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{wk}_\textrm{effex}^2 + w_\textrm{1}^2 + \Omega^2} \right)</math>  == Ramp code ==<source lang="python">import matplotlib.pyplot as pltimport numpy as npfrom math import atan2 phi = 2.0kex = 3.0 def calc(w1_arr, Omega_arr, p, k): val_arr = [] for w1 in w1_arr: for Omega in Omega_arr: theta = atan2(w1 , Omega) val = w1**2/(w1**2+Omega**2) * (p*k/(k**2 + w1**2 + Omega**2)) #val = (p*k/(k**2 + w1**2 + Omega**2)) val_arr.append([w1, Omega, theta, val]) return np.array(val_arr) w1 = np.arange(0., 20, 1)Omega = np.array([5])data = calc(w1, Omega, phi, kex) plt.figure(1)plt.plot(data[:,2], data[:,3], '.')plt.ylabel(r'Imaginary Rex, ramping spin-lock field strength, nu1')plt.xlabel(r'Rotating frame tilt angle') Omega = np.arange(0., 20, 1)w1 = np.array([5])data = calc(w1, Omega, phi, kex) plt.figure(2)plt.plot(data[:,2], data[:,3], '.')plt.ylabel(r'Imaginary Rex, ramping spin-lock offset')plt.xlabel(r'Rotating frame tilt angle') plt.show()</source> === Ramping ===[[File:ramp_w1_ramping_spin-lock_field_strength.png|thumb|center|upright=2|Ramping spin-lock field strength : w1]][[File:ramp_Omega_spin-lock_offset.png|thumb|center|upright=2|Ramping spin-lock offset : Omega]] == Figure ==See Figure 1 and 10 in the reference: * {{#lst:Citations|PalmerMassi06}}$ [[File:Fig1 Palmer Massi 2006.png|thumb|center|upright=3|Try to reproduce Figure 1.]]Figure produced with script [[Relax_disp.spin_lock_offset%2Bfield_figure | found here. ]] == See also ==[[Category:Relaxation_dispersion analysis]]