Topology of chaotic mixing patterns.
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.
Thiffeault
Jean-Luc
JL
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706, USA. jeanluc@mailaps.org
Finn
Matthew D
MD
Gouillart
Emmanuelle
E
Hall
Toby
T
D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D009991:Oscillometry / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D012212:Rheology / Q000379:methods*