2005/10/31 by Emmanuelle Gouillart, Jean‐Luc Thiffeault, Jean-Luc Thiffeault +3 · 5 citations
Mathematics · Medicine · Physics and Astronomy · #Braid #Classical mechanics #Combinatorics #Flow (mathematics) #Materials science #Mathematical Dynamics and Fractals #Mathematics #Mechanics #Medicine #Mixing (physics) #Motion (physics) #Order (exchange) #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Rod #Stochastic processes and statistical mechanics #Topology (electrical circuits) #Work (physics) #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.73.036311
published as Phys. Rev. E 73, 036311 (2006) (8 pages) · 13 pages, 11 figures. RevTeX4 format. (Final version)
arxiv created 2006/05/10 · arxiv updated 2009/12/01 · openalex publication_date 2013/01/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/24
Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call "ghost rods", because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.