Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular,...Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular, within the studies of finite-time nonautonomous dynamical systems. Here we recall “shape coherent sets” which is proven to correspond to slowly evolving curvature, for which tangency of finite time stable foliations (related to a “forward time” perspective) and finite time unstable foliations (related to a “backwards time” perspective) serve a central role. We compare and contrast this perspective to both the variational method of geodesics [17], as well as the coherent pairs perspective [12] from transfer operators.展开更多
Classical optical flow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smooth- ness of the flow field. If these assumptions ...Classical optical flow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smooth- ness of the flow field. If these assumptions are dropped, such techniques can be adapted to compute apparent fows between time snapshots of data that do not come from images, even if these flows are turbulent and divergent, as in the case of flows representing complex spatiotemporal dynamics. While imaging methods have been used to analyze dynamics in experimental applications, they are only beginning to be applied to dynamics computa- tions in settings outside the laboratory, for example in the analysis of species population dynamics from satellite data. In this work we present a variational optical flow approach based on the continuity equation and total variation regularization for computing the flow fields between population densities generated from a two-species predator-prey model for phyto- and zooplankton interactions. Given the time-varying vector fields produced from the optical flow~ computational methods from dynamical systems can be employed to study pseudo-barriers present in the species interaction. This method allows to measure the mix- ing of the species, as well as the transport of the populations throughout the domain.展开更多
文摘Mixing and coherence are fundamental issues at the heart of understanding fluid dynamics and other non-autonomous dynamical systems. Recently the notion of coherence has come to a more rigorous footing, in particular, within the studies of finite-time nonautonomous dynamical systems. Here we recall “shape coherent sets” which is proven to correspond to slowly evolving curvature, for which tangency of finite time stable foliations (related to a “forward time” perspective) and finite time unstable foliations (related to a “backwards time” perspective) serve a central role. We compare and contrast this perspective to both the variational method of geodesics [17], as well as the coherent pairs perspective [12] from transfer operators.
文摘Classical optical flow techniques were developed for computing virtual motion fields between two images of the same scene, assuming conservation of intensity and a smooth- ness of the flow field. If these assumptions are dropped, such techniques can be adapted to compute apparent fows between time snapshots of data that do not come from images, even if these flows are turbulent and divergent, as in the case of flows representing complex spatiotemporal dynamics. While imaging methods have been used to analyze dynamics in experimental applications, they are only beginning to be applied to dynamics computa- tions in settings outside the laboratory, for example in the analysis of species population dynamics from satellite data. In this work we present a variational optical flow approach based on the continuity equation and total variation regularization for computing the flow fields between population densities generated from a two-species predator-prey model for phyto- and zooplankton interactions. Given the time-varying vector fields produced from the optical flow~ computational methods from dynamical systems can be employed to study pseudo-barriers present in the species interaction. This method allows to measure the mix- ing of the species, as well as the transport of the populations throughout the domain.
