2017/02/28 by Simon Candelaresi, S. Candelaresi, D. I. Pontin +3
Computer Science · Physics and Astronomy · #Computation #Entropy (arrow of time) #Limit (mathematics) #Measure (data warehouse) #Micro and Nano Robotics #Quantum chaos and dynamical systems #Topological and Geometric Data Analysis #Topological data analysis #Topological entropy #Topology (electrical circuits) #nlin.CD #physics.flu-dyn #physics.plasm-ph
paper · pdf · doi:10.1063/1.5000812
published as Chaos 27, 093102 (2017); doi: http://dx.doi.org/10.1063/1.5000812 · 11 pages, 9 figures
openalex created_date 2017/02/17 · openalex publication_date 2017/09/01 · arxiv created 2017/10/18 · arxiv updated 2017/10/19 · openalex updated_date 2026/08/05
We present a simple method to efficiently compute a lower limit of the topological entropy and its spatial distribution for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional magnetic fields, which are periodic in one direction. This method is based on measuring the length of a material line in the flow. Depending on the nature of the flow, the fluid can be mixed very efficiently which causes the line to stretch. Here, we study a method that adaptively increases the resolution at locations along the line where folds lead to a high curvature. This reduces the computational cost greatly which allows us to study unprecedented parameter regimes. We demonstrate how this efficient implementation allows the computation of the variation of the finite-time topological entropy in the mapping. This measure quantifies spatial variations of the braiding efficiency, important in many practical applications.