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We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in three-dimensional unsteady flows. The longest lived such structures define coherent structures in a Lagrangian sense. Our existence criteria involve the invariants of the velocity gradient tensor along fluid trajectories. An alternative(More)
Recently developed pachytene maps of the two small acrocentric autosomes (numbers 21 and 22) of man have been applied to a case of Down's syndrome mosaic for normal and trisomic cells (46,XY/47,XY,21+). Trivalents in trisomic spermatocytes, and thus the supernumerary chromosome, were recognized as compatible in length and chromomere pattern with the shorter(More)
The motion of inertial (i.e., finite-size) particles is analyzed in a three-dimensional unsteady simulation of Hurricane Isabel. As established recently, the long-term dynamics of inertial particles in a fluid is governed by a reduced-order inertial equation, obtained as a small perturbation of passive fluid advection on a globally attracting slow manifold(More)
Gamma-ray bursts (GRBs) are highly energetic explosions signaling the death of massive stars in distant galaxies. The Gamma-ray Burst Monitor and Large Area Telescope onboard the Fermi Observatory together record GRBs over a broad energy range spanning about 7 decades of gammaray energy. In September 2008, Fermi observed the exceptionally luminous GRB(More)
[1] Application of recent geometric tools for Lagrangian coherent structures (LCS) shows that material attraction in geostrophic velocities derived from altimetry data imposed an important constraint to the motion of drifters from the Grand Lagrangian Deployment (GLAD) in the Gulf of Mexico. This material attraction is largely transparent to traditional(More)
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space(More)
Recent developments in identifying Lagrangian coherent structures from finite time velocity data have provided a theoretical basis for understanding chaotic transport in general flows with aperiodic dependence on time. As these theoretical developments are extended and applied to more complex flows, an accurate and general numerical method for computing(More)