Examples/Python-examples.md

@@ -81,4 +81,55 @@ fig.savefig("rho_a.png")
 plt.show()
 ```
 The result of this example:
-![rho_a](uploads/af555a49c8279e60d1ca1186af98ff9b/rho_a.png)
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+![rho_a](uploads/af555a49c8279e60d1ca1186af98ff9b/rho_a.png)
+
+# Cross section of velocity field for quantum vortex
+```python
+#!/usr/bin/python3
+
+import numpy as np
+import matplotlib.pyplot as plt
+import matplotlib.cm as cm
+from scipy.interpolate import interp1d
+from wdata.io import WData, Var
+
+# This data set contains vortex solution of SLADE functional. 
+# It is provided as supplementary material of publication: 
+#   todo
+fwtxt="/home/gabrielw/Desktop/st-vortex/sv-ddcc05p00-T0p05.wtxt"
+data = WData.load(fwtxt)
+
+j_a = data.j_a[-1] # last frame
+rho_a = data.rho_a[-1] # last frame
+
+x = data.xyz[0]
+sec=int(data.Nxyz[0]/2)
+j_a = j_a[0,sec,:]      # extract x component of j_a along y axis for x=Nx/2 (center of box)
+rho_a = rho_a[sec,:]    # extract rho_a along y axis for x=Nx/2 (center of box)
+vs = np.abs(j_a/rho_a)  # computer velocity (absolute value)
+
+# interpolate data
+vs_int = interp1d(x[:,0], vs, kind='quadratic')
+newx=np.linspace(-20,20,200)
+
+# flow for ideal vortex
+r = np.linspace(3,40,100)    # take range [3-40]
+vs_ideal = 0.5 / r           # vs=1/2r (m=hbar=1, and factor 2 accounts for Cooper pairs)
+
+# plot 
+fig, ax = plt.subplots()
+ax.plot(x, vs, 'bo', markersize=3, label='data') 
+ax.plot(newx, vs_int(newx), 'b', linestyle="-") 
+ax.plot(r, vs_ideal, color="k", linestyle="--", label=r'$\sim 1/r$') 
+ax.plot(r*(-1.0), vs_ideal, color="k", linestyle="--") 
+
+ax.set(xlabel='y', ylabel=r'$v(0,y)$')
+ax.set_xlim([-20,20])
+ax.grid()
+plt.legend(loc='upper right')
+
+fig.savefig("velocity.png")
+plt.show()
+```
+Output
+![velocity](uploads/a7f74f745d9abda5630bac010ca1b666/velocity.png)
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