2008/04/30 by Jean‐Luc Thiffeault, Jean-Luc Thiffeault, Matthew D. Finn +2
Mathematics · Physics and Astronomy · #Artificial intelligence #Chaotic #Chaotic mixing #Classical mechanics #Combinatorics #Computer science #Discrete mathematics #Domain (mathematical analysis) #Geometric and Algebraic Topology #Geometry #Homeomorphism (graph theory) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Mixing (physics) #Motion (physics) #Physics #Pure mathematics #Quantum chaos and dynamical systems #Rod #Surface (topology) #Topological conjugacy #Topology (electrical circuits) #nlin.CD
paper · pdf · doi:10.1063/1.2973815
published as Chaos 18, 033123 (2008) · 15 pages, 13 figures, RevTeX4 macros. Final version
arxiv created 2008/08/26 · openalex publication_date 2008/08/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically complex motion guarantees at least a minimal amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.