Merge branch 'animation-drude-model' into 'master'

animate random walkers

See merge request !69

src/3_drude_model.md

@@ -26,17 +26,20 @@ Ohm's law states that $V=IR=I\rho\frac{l}{A}$. In this lecture we will investiga
 - In-between scattering events electrons respond to the Lorentz force ${\bf F}_{\rm L}=-e\left({\bf E}+{\bf v}\times{\bf B}\right)$.
 
 ```python
-import numpy as np
+%matplotlib inline
 import matplotlib.pyplot as plt
+import numpy as np
+import matplotlib.animation as animation
+from IPython.display import HTML
 
-walker_number = 20 # number of particles
+walkers = 20 # number of particles
 tau = 1 # relaxation time
 gamma = .3 # dissipation strength
 a = 1 # acceleration
 dt = .1 # infinitesimal
 T = 20 # simulation time 
 
-v = np.zeros((2, int(T // dt), walker_number), dtype=float) 
+v = np.zeros((2, int(T // dt), walkers), dtype=float) # 
 
 scattering_events = np.random.binomial(1, dt/tau, size=v.shape[1:])
 angles = np.random.uniform(high=2*np.pi, size=scattering_events.shape) * scattering_events
@@ -59,9 +62,36 @@ r = np.cumsum(v * dt, axis=1)
 scattering_positions = np.copy(r)
 scattering_positions[:, ~scattering_events.astype(bool)] = np.nan
 
-plt.plot(*r[:, :100], alpha=.5, c='#1f77b4');
-plt.scatter(*scattering_positions[:, :100], s=10);
+fig = plt.figure()
+
+scatter_pts = scattering_positions[:, :100]
+trace = r[:, :100]
+
+nz_scatters = tuple((np.hstack(scatter_pts[0])[~np.isnan(np.hstack(scatter_pts[0]))],
+                    np.hstack(scatter_pts[1])[~np.isnan(np.hstack(scatter_pts[1]))]))
+
+plt.axis([min(nz_scatters[0])-1, 
+          max(nz_scatters[0])+1,
+          min(nz_scatters[1])-1, 
+          max(nz_scatters[1])+1])
+
+lines = []
+scatterers = []
+for index in range(walkers):
+    lobj = plt.plot([],[], lw=1, color='b', alpha=0.5)[0]
+    lines.append(lobj)
+    scatterers.append(plt.scatter([], [], s=10, c='r'))
+
+def animate(i):
+    for lnum, line in enumerate(lines):
+        line.set_data(trace[0][:i, lnum], trace[1][:i, lnum])
+        data = np.stack((scatter_pts[0][:i,lnum], scatter_pts[1][:i, lnum])).T
+        scatterers[lnum].set_offsets(data)
+#         
+anim = animation.FuncAnimation(fig, animate, interval=100)
 plt.axis('off');
+
+HTML(anim.to_html5_video())
 ```
 
 We start by considering only an electric field (_i.e._ ${\bf B}=0$). What velocity do electrons acquire in-between collisions?