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

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

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

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

Contrasting non-dynamic and dynamic models of the water-energy nexus in small, off-grid Mediterranean islands

Water and energy supply in small Mediterranean islands are strictly interrelated and face a large number of challenging issues, mainly caused by the distance from the mainland, the lack of accessible and safe potable water sources, and the high seasonal variability of the water and energy demands driven by touristic fluxes. The energy system generally relies on carbon intensive, expensive stand-alone diesel generators, while potable water supply is provided by tank vessels. Although this combination provides essential services for local communities, it is often economically and environmentally unsustainable due to high operational costs and greenhouse gas (GHG) emissions. A traditional approach to improve the sustainability and the efficiency of the water and energy systems is to couple renewable energy sources (RES) with water supply technologies (e.g., desalination), in order to obtain efficient planning solutions (i.e. RES capacity, desalination plant capacity) in a least-cost fashion. However, this approach is generally non-dynamic and optimizes the power allocation using fixed electricity loads as a surrogate of the actual water demand supplied by the desalination plant through the water distribution network. Although this load reflects the actual water demand on the long-term (i.e. monthly or annual time scale), it could strongly deviate from the real water demand if we consider shorter time scales (i.e. daily or hourly), over which the water distribution network is able to store and move water in space and time. In this work, we comparatively analyse this traditional non-dynamic model of the water-energy nexus with a novel dynamic modelling approach, where the operation of both the nexus components (i.e. power allocation and operations of the water distribution network) is conjunctively optimized with respect to multiple economic and sustainability indicators (e.g., net present costs, GHG emissions, water supply deficit, RES penetration). This comparative analysis is performed over the real case study of the Italian Ustica island in the Mediterranean Sea. Preliminary results show the effectiveness of the dynamic approach in improving the static solution with respect to almost all the system performance metrics considered