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- George Haller
- 2001

We prove analytic criteria for the existence of finite-time attracting and repelling material surfaces and lines in threedimensional 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)

We introduce a Lagrangian definition for the boundaries of coherent structures in two-dimensional turbulence. The boundaries are defined as material lines that are linearly stable or unstable for longer times than any of their neighbors. Such material lines are responsible for stretching and folding in the mixing of passive tracers. We derive an analytic… (More)

- William B Atwood, Ammar A Abdo, +109 authors Jonathan F. Ormes
- 2009

The Large Area Telescope (Fermi/LAT, hereafter LAT), the primary instrument on the Fermi Gamma-ray Space Telescope (Fermi) mission, is an imaging, wide field-of-view, high-energy γ-ray telescope, covering the energy range from below 20 MeV to more than 300 GeV. The LAT was built by an international collaboration with contributions from space agencies,… (More)

The most widely used definitions of a vortex are not objective: they identify different structures as vortices in frames that rotate relative to each other. Yet a frame-independent vortex definition is essential for rotating flows and for flows with interacting vortices. Here we define a vortex as a set of fluid trajectories along which the strain… (More)

- Manikandan Mathur, George Haller, Thomas Bevill Peacock, Jori Elan Ruppert-Felsot, Harry L. Swinney
- Physical review letters
- 2007

We present a technique that uncovers the Lagrangian building blocks of turbulence, and apply this technique to a quasi-two-dimensional turbulent flow experiment. Our analysis identifies an intricate network of attracting and repelling material lines. This chaotic tangle, the Lagrangian skeleton of turbulence, shows a level of complexity found previously… (More)

- Greg A. Voth, George Haller, Jerry P. Gollub
- Physical review letters
- 2002

Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching field. This quantity, previously available only numerically, attains local maxima along lines that coincide with the stable and unstable manifolds of hyperbolic fixed points of Poincaré… (More)

We introduce a simple variational principle for coherent material vortices in twodimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit… (More)

- Wenbo Tang, Pak Wai Chan, George Haller
- Chaos
- 2010

Locating Lagrangian coherent structures (LCS) for dynamical systems defined on a spatially limited domain present a challenge because trajectory integration must be stopped at the boundary for lack of further velocity data. This effectively turns the domain boundary into an attractor, introduces edge effects resulting in spurious ridges in the associated… (More)

- Amr Abdo, Marit Ackermann, +249 authors Magda Ziegler
- Science
- 2009

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)

- David A. Hungerford, William J. Mellman, Gloria Balaban, Gérard Labadie, L R Messatzzia, George Haller
- Proceedings of the National Academy of Sciences…
- 1970

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)