On Wed, Sep 25, 2013 at 1:41 PM, David Goldsmith wrote:

Thanks, guys. Yeah, I realized the problem w/ the uniform-increment-variable-direction approach this morning: physically, it ignores the fact that the particles hitting the particle being tracked are going to have a distribution of momentum, not all the same, just varying in direction. But I don't quite understand Warren's observation: "the 'angles' that describe the position undergo a random walk [actually, it would seem that they don't, since they too fail the varying-as-white-noise test], so the particle tends to move in the same direction over short intervals"--is this just another way of saying that, since I was varying the angles by -1, 0, or 1 unit each time, the simulation is susceptible to "unnaturally" long strings of -1, 0, or 1 increments? Thanks again,

Note: I was interpreting your code as the discretization of a stochastic process, and I was experimenting with values of `incr` that were small, e.g. `incr = 0.01`. This code t = 2*np.pi*incr*(R.randint(3, size=(N,))-1) t[0] = 0 t = t.cumsum() makes `t` a (discrete) random walk. At each time step, t either remains the same, or changes by +/- 2*np.pi*incr. If `incr` is small, then `t[1]` is a small step from `t[0]`. Similarly, `p[1]` will be close to `p[0]`. So the particle "remembers" its direction. A particle undergoing Brownian motion does not have this memory. Warren

DG

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