Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 30, Issue 5, Pages 1889-1971Publisher
SPRINGER
DOI: 10.1007/s00332-017-9397-y
Keywords
Lagrangian coherent structure; Dynamic Laplace operator; Weighted Riemannian manifold; Transfer operator; Finite-time coherent set; Dynamic isoperimetric problem
Categories
Ask authors/readers for more resources
Transport and mixing in dynamical systems are important properties for many physical, chemical, biological, and engineering processes. The detection of transport barriers for dynamics with general time dependence is a difficult, but important problem, because such barriers control how rapidly different parts of phase space (which might correspond to different chemical or biological agents) interact. The key factor is the growth of interfaces that partition phase space into separate regions. The paper Froyland (Nonlinearity 28(10):3587-3622,2015) introduced the notion ofdynamic isoperimetry: the study of sets with persistently small boundary size (the interface) relative to enclosed volume, when evolved by the dynamics. Sets with this minimal boundary size to volume ratio were identified as level sets of dominant eigenfunctions of adynamic Laplace operator. In this present work we extend the results of Froyland (Nonlinearity 28(10):3587-3622,2015) to the situation where the dynamics (1) is not necessarily volume preserving, (2) acts on initial agent concentrations different from uniform concentrations, and (3) occurs on a possibly curved phase space. Our main results include generalised versions of the dynamic isoperimetric problem, the dynamic Laplacian, Cheeger's inequality, and the Federer-Fleming theorem. We illustrate the computational approach with some simple numerical examples.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available