Curvature Fields, Topology, and the Dynamics of Spatiotemporal Chaos

The curvature field is measured from tracer particle trajectories in a two-dimensional fluid flow that exhibits spatiotemporal chaos, and is used to extract the hyperbolic and elliptic points of the flow. These special points are pinned to the forcing when the driving is weak, but wander over the domain and interact in pairs at stronger driving, changing the local topology of the flow. Their behavior reveals a two-stage transition to spatiotemporal chaos: a gradual loss of spatial and temporal order followed by an abrupt onset of topological changes.Comment: 5 pages, 5 figure

Correlation of gravimetric and satellite geodetic data Interim progress report, 11 Sep. 1967 - 29 Feb. 1968

Gravimetric and geodetic data correlation for satellite position prediction accuracy with error analysi

Dynamic Topology in Spatiotemporal Chaos

By measuring the tracks of tracer particles in a quasi-two-dimensional spatiotemporally chaotic laboratory flow, we determine the instantaneous curvature along each trajectory and use it to construct the instantaneous curvature field. We show that this field can be used to extract the time-dependent hyperbolic and elliptic points of the flow. These important topological features are created and annihilated in pairs only above a critical Reynolds number that is largest for highly symmetric flows. We also study the statistics of curvature for different driving patterns and show that the curvature probability distribution is insensitive to the details of the flow

Correlation of gravimetric and satellite geodetic data, part 2 Interim scientific report, 11 Sep. 1967 - 29 Feb. 1968

Graphical output from computer correlated gravimetric and satellite geodetic dat

Interaction of Supernova Ejecta with Nearby Protoplanetary Disks

The early Solar System contained short-lived radionuclides such as 60Fe (t1/2 = 1.5 Myr) whose most likely source was a nearby supernova. Previous models of Solar System formation considered a supernova shock that triggered the collapse of the Sun's nascent molecular cloud. We advocate an alternative hypothesis, that the Solar System's protoplanetary disk had already formed when a very close (< 1 pc) supernova injected radioactive material directly into the disk. We conduct the first numerical simulations designed to answer two questions related to this hypothesis: will the disk be destroyed by such a close supernova; and will any of the ejecta be mixed into the disk? Our simulations demonstrate that the disk does not absorb enough momentum from the shock to escape the protostar to which it is bound. Only low amounts (< 1%) of mass loss occur, due to stripping by Kelvin-Helmholtz instabilities across the top of the disk, which also mix into the disk about 1% of the intercepted ejecta. These low efficiencies of destruction and injectation are due to the fact that the high disk pressures prevent the ejecta from penetrating far into the disk before stalling. Injection of gas-phase ejecta is too inefficient to be consistent with the abundances of radionuclides inferred from meteorites. On the other hand, the radionuclides found in meteorites would have condensed into dust grains in the supernova ejecta, and we argue that such grains will be injected directly into the disk with nearly 100% efficiency. The meteoritic abundances of the short-lived radionuclides such as 60Fe therefore are consistent with injection of grains condensed from the ejecta of a nearby (< 1 pc) supernova, into an already-formed protoplanetary disk.Comment: 57 pages, 16 figure

Accurate Determination of the Mass Distribution in Spiral Galaxies: II. Testing the Shape of Dark Halos

New high resolution CFHT Fabry-Perot data, combined with published VLA 21 cm observations are used to determine the mass distribution of NGC 3109 and IC 2574. The multi-wavelength rotation curves allow to test with confidence different dark halo functional forms from the pseudo-isothermal sphere to some popular halo distributions motivated by N-body simulations. It appears that density distribution with an inner logarithmic slope <= -1 are very hard to reconcile with rotation curves of late type spirals. Modified Newtonian Dynamics (MOND) is also considered as a potential solution to missing mass and tested the same way. The new higher resolution data show that MOND can reproduce in details the rotation curve of IC 2574 but confirm its difficulty to fit the kinematics of NGC 3109.Comment: 28 pages, accepted by AJ. New HI profile increases the compatibility of NGC 3109 rotation curve with MON