Adiabatically switched-on electrical bias in continuous systems, and the Landauer-Buttiker formula

Consider a three dimensional system which looks like a cross-connected pipe system, i.e. a small sample coupled to a finite number of leads. We investigate the current running through this system, in the linear response regime, when we adiabatically turn on an electrical bias between leads. The main technical tool is the use of a finite volume regularization, which allows us to define the current coming out of a lead as the time derivative of its charge. We finally prove that in virtually all physically interesting situations, the conductivity tensor is given by a Landauer-B{\"u}ttiker type formula.Comment: 20 pages, submitte

Scale model testing of the jet noise characteristics of the JT8D refan engine nozzle system

The results are presented of static scale model acoustic tests of the nozzle system for the JT8D-9 baseline engine and candidate nozzle systems for JT8D-109, JT8D-115, and JT8D-117 refan engines. The objective of these tests was to determine the jet noise benefit of the three refan engine cycles relative to the baseline JT8D-9, and to provide acoustic information toward selection of the optimum primary-secondary area match and centerbody contour for the refan engine cycles. One of the nozzle configurations was tested with and without simulated turbine exit swirl to determine what effect, if any, swirl has no jet noise. The JT8D-109 cycle was found to afford approximately 9 db (0ASPL) jet noise reduction relative to the JT8D-9 when compared on an equal static thrust basis. The JT8D-115 and JT8D-117 afford an 8 db and 6 db reduction, respectively, relative to the JT8D-9, at equal static thrust. Turbine exit swirl was found to have no significant effect on the jet noise of the JT8D-109 nozzle system

On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations

We discuss the relationship between kinetic equations of the Fokker-Planck type (two linear and one non-linear) and the Kolmogorov (a.k.a. master) equations of certain N-body diffusion processes, in the context of Kac's "propagation of chaos" limit. The linear Fokker-Planck equations are well-known, but here they are derived as a limit N->infty of a simple linear diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N) (with C=1 or 4 depending on whether the system conserves energy only or energy and momentum). In this case, a spectral gap separating the zero eigenvalue from the positive spectrum of the Laplacian remains as N->infty,so that the exponential approach to equilibrium of the master evolution is passed on to the limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation is known as Landau's equation in the plasma physics literature. Its N-particle master equation, originally introduced (in the 1950s) by Balescu and Prigogine (BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown that the BP master equation represents a superposition of diffusion processes on certain two-dimensional sub-manifolds of R^{3N} determined by the conservation laws for two-particle collisions. The initial value problem for the BP master equation is proved to be well-posed and its solutions are shown to decay exponentially fast to equilibrium. However, the first non-zero eigenvalue of the BP operator is shown to vanish in the limit N->infty. This indicates that the exponentially fast approach to equilibrium may not be passed from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a few minor technical fixes. Modified title slightl

Skylab/EREP application to ecological, geological, and oceanographic investigations of Delaware Bay

Skylab/EREP S190A and S190B film products were optically enhanced and visually interpreted to extract data suitable for; (1) mapping coastal land use; (2) inventorying wetlands vegetation; (3) monitoring tidal conditions; (4) observing suspended sediment patterns; (5) charting surface currents; (6) locating coastal fronts and water mass boundaries; (7) monitoring industrial and municipal waste dumps in the ocean; (8) determining the size and flow direction of river, bay and man-made discharge plumes; and (9) observing ship traffic. Film products were visually analyzed to identify and map ten land-use and vegetation categories at a scale of 1:125,000. Digital tapes from the multispectral scanner were used to prepare thematic maps of land use. Classification accuracies obtained by comparison of derived thematic maps of land-use with USGS-CARETS land-use maps in southern Delaware ranged from 44 percent to 100 percent

Endomorphisms and automorphisms of locally covariant quantum field theories

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of *-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covariant theories that obey standard assumptions in Minkowski space, including energy compactness, have no proper endomorphisms (i.e., all endomorphisms are automorphisms) and have a compact automorphism group. Further, it is shown how the endomorphisms and automorphisms of a locally covariant theory may, in principle, be classified in any single spacetime. As an example, the endomorphisms and automorphisms of a system of finitely many free scalar fields are completely classified.Comment: v2 45pp, expanded to include additional results; presentation improved and an error corrected. To appear in Rev Math Phy

Time-Dependent Models for Dark Matter at the Galactic Center

The prospects of indirect detection of dark matter at the galactic center depend sensitively on the mass profile within the inner parsec. We calculate the distribution of dark matter on sub-parsec scales by integrating the time-dependent Fokker-Planck equation, including the effects of self-annihilations, scattering of dark matter particles by stars, and capture in the supermassive black hole. We consider a variety of initial dark matter distributions, including models with very high densities ("spikes") near the black hole, and models with "adiabatic compression" of the baryons. The annihilation signal after 10 Gyr is found to be substantially reduced from its initial value, but in dark matter models with an initial spike, order-of-magnitude enhancements can persist compared with the rate in spike-free models, with important implications for indirect dark matter searches with GLAST and Air Cherenkov Telescopes like HESS and CANGAROO.Comment: Four page

Skylab/EREP application to ecological, geological, and oceanographic investigations of Delaware Bay

The author has identified the following significant results. Skylab/EREP S190A and S190B film products were optically enhanced and visually interpreted to extract data suitable for mapping coastal land use; inventorying wetlands vegetation; monitoring tidal conditions; observing suspended sediment patterns; charting surface currents; locating coastal fronts and water mass boundaries; monitoring industrial and municipal waste dumps in the ocean; and determining the size and flow direction of river, bay, and man-made discharge plumes. Film products were visually analyzed to identify and map ten land use and vegetation categories at a scale of 1:125,000. Thematic maps were compared with CARETS land use maps, resulting in classification accuracies of 50 to 98%. Digital tapes from S192 were used to prepare thematic land use maps. The resolutions of the S190A, S190B, and S192 systems were 20-40m, 10-20m, and 70-100m, respectively