… a metric (geodesic deviation) … transport barrier theory to non-Euclidean flow domains, such
as a sphere, follows directly. We illustrate our main results by computing key transport barriers …

… To this end, we use here the recent theory of geodesic transport barriers to uncover finite-time
mixing barriers in the wind field extracted from a video captured by NASA’s Cassini space …

… , and hyperbolic barriers. Different diagnostics in detecting transport barriers and the analysis
of … from dynamical systems theory, for detecting transport barriers in simple kinematic and …

… theory of transport barriers for three-dimensional unsteady flows with arbitrary time-dependence.
The barriers … Such a general approach, the geodesic theory of transport barriers, has …

… of barriers are special null-geodesics … theory of shearless transport barriers for unsteady
flows has been established. The need for such a general theory of unsteady shearless barriers …

… in theoretical computer science, machine learning, quantum information theory and statistics.
… role for speeding up multimarginal transport as matrix scaling for optimal transport, and yet …

… KAM tori or jet core barriers). LCS in each type follow as null geodesics of a Lorentzian
metric … We reported on several applications of the geodesic LCS theory to oceanic flows: 1) …

… Throughout this book, we will adopt the geometric view of nonlinear dynamical systems
theory on transport. That is, rather than focusing on individual fluid particle positions or pointwise …

… , we analyze the geodesic walk for the logarithmic barrier. The … showing that the geodesic,
parallel transport and Jacobi field … standard logarithmic barrier, one step of the geodesic walk …

… LCSs) are special material surfaces that act as transport barriers, guiding the formation of
these … Here, we extend a recent theory of elliptic LCSs from two- to three-dimensional flows and …