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Acta Applicandae Mathematicae

, Volume 138, Issue 1, pp 135–151 | Cite as

The Vortex Filament Equation as a Pseudorandom Generator

  • Francisco de la HozEmail author
  • Luis Vega
Article

Abstract

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.

Keywords

Vortex filament equation Schrödinger map on the sphere Generalized quadratic Gauß sums Explicit inversive congruential generators 

Mathematics Subject Classification (2010)

11K45 11Lxx 35Q35 35Q41 

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Applied Mathematics, Statistics and Operations Research, Faculty of Science and TechnologyUniversity of the Basque Country UPV-EHULeioaSpain
  2. 2.Department of Mathematics, Faculty of Science and TechnologyUniversity of the Basque Country UPV-EHULeioaSpain
  3. 3.BCAM—Basque Center for Applied MathematicsBilbaoSpain

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