A partial solution of the isoperimetric problem for the Heisenberg group

We provide a partial solution to the isoperimetric problem in the Heisenberg group.Comment: 32 pages, 1 figur

Misconceptions About General Relativity in Theoretical Black Hole Astrophysics

The fundamental role played by black holes in our study of microquasars, gamma ray bursts, and the outflows from active galactic nuclei requires an appreciation for, and at times some in-depth analysis of, curved spacetime. We highlight misconceptions surrounding the notion of coordinate transformation in general relativity as applied to metrics for rotating black holes that are beginning to increasingly appear in the literature. We emphasize that there is no coordinate transformation that can turn the metric of a rotating spacetime into that for a Schwarzschild spacetime, or more generally, that no coordinate transformation exists that can diagonalize the metric for a rotating spacetime. We caution against the notion of "local" coordinate transformation, which is often incorrectly associated with a global analysis of the spacetime.Comment: MNRAS accepte

Application of ERTS-1 data to the protection and management of New Jersey's coastal environment

ERTS-1 imagery is being used by the New Jersey Department of Environmental Protection (NJDEP) to develop information products that will assist the state in optimally managing its coastal resources and in allocating funds. Interviews with NJDEP personnel have identified significant problem areas in the coastal zone, and the types of remote sensor derived information products that can be used in real-time decision making. Initial analyses of imagery from several successive ERTS-1 orbits have shown the extent, predominant drift, and dispersion characteristics of waste disposal in coastal New Jersey waters. Imagery (MSS Bands 4 and 5) for several orbits, shows that New-York Harbor tidal discharge extending as far south as Long Branch, New Jersey

Handle-hand compatibility effects for the right and left hand using reach-to-touch movements

In stimulus-response compatibility tasks, performance is better when the handle of an object is oriented on the same side of the response than when the handle is oriented on the opposite side. Two major alternative accounts, the motor affordance and spatial accounts, have been proposed to explain this handle-hand compatibility effect. In two experiments, we tested between these two accounts by administering a go/no-go task to right-handed participants. Handled objects presented on a touchscreen were used as stimuli. Half of the participants had to reach-to-touch the stimuli by using their dominant hand, the other half by using their nondominant hand. Liftoff times (LTs), movement times (MTs) and spatial coordinates of the movement endpoints were recorded. Results from the LTs and MTs analyses showed no evidence of handle-hand compatibility effects. In contrast, the analyses of the spatial coordinates revealed that participants' touches were shifted more laterally towards the handle when the handles were oriented on the same side of the responding hand (Experiments 1 and 2). Furthermore, the right-hand touches landed higher (towards the handle) than the left-hand touches, especially when the vertical object dimension was particularly salient (Experiment 1). Overall, these results are in line with the activation of hand motor programs to reach and grasp the object as predicted by the motor account, at least for the right/dominant hand

Trapping of magnetic flux by the plunge region of a black hole accretion disk

The existence of the radius of marginal stability means that accretion flows around black holes invariably undergo a transition from a MHD turbulent disk-like flow to an inward plunging flow. We argue that the plunging inflow can greatly enhance the trapping of large scale magnetic field on the black hole, and therefore may increase the importance of the Blandford-Znajek (BZ) effect relative to previous estimates that ignore the plunge region. We support this hypothesis by constructing and analyzing a toy-model of the dragging and trapping of a large scale field by a black hole disk, revealing a strong dependence of this effect on the effective magnetic Prandtl number of the MHD turbulent disk. Furthermore, we show that the enhancement of the BZ effect depends on the geometric thickness of the accretion disk. This may be, at least in part, the physical underpinnings of the empirical relation between the inferred geometric thickness of a black hole disk and the presence of a radio jet.Comment: 18 pages, 3 figures, accepted for publication in the Astrophysical Journal. See http://www.astro.umd.edu/~chris/publications/movies/flux_trapping.html for animation