We define objective Eulerian Coherent Structures (OECSs) in two-dimensional, non-autonomous dynamical systems as instantaneously most influential material curves. Specifically, OECSs are stationary curves of the averaged instantaneous material stretching-rate or material shearingrate functionals. From these objective (frame-invariant) variational principles, we obtain explicit differential equations for hyperbolic, elliptic and parabolic OECSs. As illustration, we compute OECSs in an unsteady ocean velocity data set. In comparison to structures suggested by other common Eulerian diagnostic tools, we find OECSs to be the correct short-term cores of observed trajectory deformation patterns.

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.

Elucidating the developmental process of an organism will require the complete cartography of cellular lineages in the spatial, temporal, and molecular domains. We present Zebrahub, a comprehensive dynamic atlas of zebrafish embryonic development that combines single-cell sequencing time course data with light-sheet microscopy-based lineage reconstructions. Zebrahub is a foundational resource to study developmental processes at both transcriptional and spatiotemporal levels. It is publicly accessible as a web-based resource, providing an open-access collection of datasets and tools. Using this resource we shed new light on the pluripotency of Neuro-Mesodermal Progenitors (NMPs). We find that NMPs are pluripotent only during early axis elongation before becoming exclusively mesodermal progenitors. We attribute this restriction in NMP cell fate to emerging morphodynamic features that compartmentalize tissue motion.

Every year, hundreds of people die at sea because of vessel and airplane accidents. A key challenge in reducing the number of these fatalities is to make Search and Rescue (SAR) algorithms more efficient. Here, we address this challenge by uncovering hidden TRansient Attracting Profiles (TRAPs) in ocean-surface velocity data. Computable from a single velocity-field snapshot, TRAPs act as short-term attractors for all floating objects. In three different ocean field experiments, we show that TRAPs computed from measured as well as modeled velocities attract deployed drifters and manikins emulating people fallen in the water. TRAPs, which remain hidden to prior flow diagnostics, thus provide critical information for hazard responses, such as SAR and oil spill containment, and hence have the potential to save lives and limit environmental disasters.

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