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→Figure: Switched to labelled section transclusions for the citation.
__TOC__
== Equation ==
<math>
</math>
Expressing in terms of $\textrm{w{:omega1}_\textrm{1}, \textrm{w{:omegaeff}_\textrm{eff}$ <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{eff}^2} \cdot \left( \frac{\Phi_\textrm{ex} \textrm{k}_\textrm{ex}}{\textrm{k}_\textrm{ex}^2 + w_\textrm{1}^2 + \Omega_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{k}_\textrm{effex}^2 + w_\textrm{1}^2 + \Omega^2} \right)
</math>
== Ramp code ==
<source lang="python">
import matplotlib.pyplot as plt
import numpy as np
from math import atan2
phi = 2.0
kex = 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]]
