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Filamentation

​
time
keep x fixed at
keep v fixed at
∂
t
f + v
∂
x
f = 0, f(t = 0, x, v) = (1 + sin(x))
-
v
2
/2
e
This Demonstration shows the phenomenon of filamentation (i.e. the appearance of smaller and smaller structures in the phase space direction associated with velocity) for a simple advection equation that can be solved analytically.
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