The Vortex Filament Equation as a Pseudorandom Generator
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$\mathbf{X}_t = \mathbf{X}_s\wedge\mathbf{X}_{ss}, $$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel point of view: that of an evolution equation which yields a very good generator of pseudorandom numbers in a completely natural way. This essential randomness of VFE is in agreement with the randomness of the physical phenomena upon which it is based.
vortex filament equation schrdinger map on the sphere generalized quadratic gausums explicit inversive congruential generators 11k45 11lxx 35q35 35q41