A perturbative approach to Lagrangian flow networks
arXiv:1611.06021 · doi:10.1063/1.4978549
Abstract
Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway or airline infrastructure over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals or volcanic aerosols.
9 pages, 3 figures
References in corpus (12)
- Understanding individual human mobility patterns
- The backbone of the climate network
- The spatial structure of networks
- A review of linear response theory for general differentiable dynamical systems
- Hydrodynamic provinces and oceanic connectivity from a transport network help designing marine reserves
- Time lagged ordinal partition networks for capturing dynamics of continuous dynamical systems
- Flow networks: A characterization of geophysical fluid transport
- An early warning indicator for atmospheric blocking events using transfer operators
- A climate network-based index to discriminate different types of El Niño and La Niña
- BioLogistics and the Struggle for Efficiency: Concepts and Perspectives
- Response Operators for Markov Processes in a Finite State Space: Radius of Convergence and Link to the Response Theory for Axiom A Systems
- Clustering coefficient and periodic orbits in flow networks