Condensed Matter Physics, 2014, vol. 17, No. 4, 43002
DOI:10.5488/CMP.17.43002           arXiv:1501.03468

Title: Exact solutions for chemical concentration waves of self-propelling camphor particles racing on a ring: a novel potential dynamics perspective
  T.D. Frank (CESPA, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, CT 06269, USA )

A potential dynamics approach is developed to determine the periodic standing and traveling wave patterns associated with self-propelling camphor objects floating on ring-shaped water channels. Exact solutions of the wave patterns are derived. The bifurcation diagram describing the transition between the immobile and self-propelling modes of camphor objects is derived semi-analytically. The bifurcation is of a pitchfork type which is consistent with earlier theoretical work in which natural boundary conditions have been considered.

Key words: chemical concentration waves, self-motion, pitchfork bifurcation
PACS: 05.45.-a, 82.40.Ck

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