956 research outputs found

    Collisions of particles in locally AdS spacetimes II Moduli of globally hyperbolic spaces

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    We investigate 3-dimensional globally hyperbolic AdS manifolds containing "particles", i.e., cone singularities of angles less than 2π2\pi along a time-like graph Γ\Gamma. To each such space we associate a graph and a finite family of pairs of hyperbolic surfaces with cone singularities. We show that this data is sufficient to recover the space locally (i.e., in the neighborhood of a fixed metric). This is a partial extension of a result of Mess for non-singular globally hyperbolic AdS manifolds.Comment: 29 pages, 3 figures. v2: 41 pages, improved exposition. To appear, Comm. Math. Phys. arXiv admin note: text overlap with arXiv:0905.182

    Microwave Electronics

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    Contains reports on three research projects.Office of Naval Research (Contract Nonr 1841(05)Purchase Order DDL-B15

    Microwave Electronics

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    Contains research objectives and reports on three research projects.Department of the ArmyDepartment of the NavyDepartment of the Air Force under Contract AF19(122)-458U. S. Navy (Office of Naval Research) under Contract Nonr-1841(49)Lincoln Laboratory, Purchase Order DDL-B22

    Microwave Electronics

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    Contains reports on five research projects

    Harmonic fields on the extended projective disc and a problem in optics

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    The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for weakly harmonic 1-fields, changing type on the unit circle, is derived under Dirichlet conditions imposed on the non-characteristic portion of the boundary. A similar system arises in the analysis of wave motion near a caustic. A class of elliptic-hyperbolic boundary-value problems is formulated for those equations as well. For both classes of boundary-value problems, an arbitrarily small lower-order perturbation of the equations is shown to yield solutions which are strong in the sense of Friedrichs.Comment: 30 pages; Section 3.3 has been revise

    Perpendicular momentum injection by lower hybrid wave in a tokamak

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    The injection of lower hybrid waves for current drive into a tokamak affects the profile of intrinsic rotation. In this article, the momentum deposition by the lower hybrid wave on the electrons is studied. Due to the increase in the poloidal momentum of the wave as it propagates into the tokamak, the parallel momentum of the wave increases considerably. The change of the perpendicular momentum of the wave is such that the toroidal angular momentum of the wave is conserved. If the perpendicular momentum transfer via electron Landau damping is ignored, the transfer of the toroidal angular momentum to the plasma will be larger than the injected toroidal angular momentum. A proper quasilinear treatment proves that both perpendicular and parallel momentum are transferred to the electrons. The toroidal angular momentum of the electrons is then transferred to the ions via different mechanisms for the parallel and perpendicular momentum. The perpendicular momentum is transferred to ions through an outward radial electron pinch, while the parallel momentum is transferred through collisions.Comment: 22 pages, 4 figure

    Plasma Physics

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    Contains reports on seven research projects.United States Atomic Energy Commission under Contract AT(30-1)-1842Joint Services Electronics Programs (U.S. Army, U.S. Navy, and U.S. Air Force) under Contract DA 28-043-AMC-02536(E

    Microwave Electronics

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    Contains reports on two research projects

    On the injectivity of the circular Radon transform arising in thermoacoustic tomography

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    The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.Comment: To appear in Inverse Problem
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