5,418 research outputs found

    Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology

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    All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly and the geometrical significance of continuous and discrete labels is elucidated. As a corollary we gain insight into the (in general non-trivial) topology of the reduced phase space. The classification covers basically all 2D metrics of Lorentzian signature with a (local) Killing symmetry.Comment: 39 pages, 22 figures, uses AMSTeX, extended version of former chapter 7 (Gravitational Kinks) now available as gr-qc/9707053, problem with figure 6 fixe

    Aspherical gravitational monopoles

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    We show how to construct non-spherically-symmetric extended bodies of uniform density behaving exactly as pointlike masses. These ``gravitational monopoles'' have the following equivalent properties: (i) they generate, outside them, a spherically-symmetric gravitational potential M/xxOM/|x - x_O|; (ii) their interaction energy with an external gravitational potential U(x)U(x) is MU(xO)- M U(x_O); and (iii) all their multipole moments (of order l1l \geq 1) with respect to their center of mass OO vanish identically. The method applies for any number of space dimensions. The free parameters entering the construction are: (1) an arbitrary surface Σ\Sigma bounding a connected open subset Ω\Omega of R3R^3; (2) the arbitrary choice of the center of mass OO within Ω\Omega; and (3) the total volume of the body. An extension of the method allows one to construct homogeneous bodies which are gravitationally equivalent (in the sense of having exactly the same multipole moments) to any given body.Comment: 55 pages, Latex , submitted to Nucl.Phys.

    Recovery of 3-D objects with multiple curved surfaces from 2-D contours

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    Cataloged from PDF version of article.Inference of 3-D shape from 2-D contours in a single image is an important problem in machine vision. Often, techniques to solve this problem examine each surface in the scene separately whereas our perception of their shapes clearly depends on the interplay between them as well. In this paper, we describe a technique that attempts to recover the shapes of all the surfaces of an object simultaneously, though it is limited to objects made of zero-Gaussian curvature surfaces. Our technique is based on an analysis of three kinds of symmetries defined in the paper and the constraints that derive from them, and from other boundaries. This technique uses some of the constraints developed in an earlier paper that was limited to examining a zero-Gaussian curvature surface cut by parallel planes. This restriction has been removed here and the constraints have been reformulated to allow integration of constraints from all the neighboring surfaces. Results on some complex examples are shown

    Shape-induced force fields in optical trapping

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    Advances in optical tweezers, coupled with the proliferation of two-photon polymerization systems, mean that it is now becoming routine to fabricate and trap non-spherical particles. The shaping of both light beams and particles allows fine control over the flow of momentum from the optical to mechanical regimes. However, understanding and predicting the behaviour of such systems is highly complex in comparison with the traditional optically trapped microsphere. In this Article, we present a conceptually new and simple approach based on the nature of the optical force density. We illustrate the method through the design and fabrication of a shaped particle capable of acting as a passive force clamp, and we demonstrate its use as an optically trapped probe for imaging surface topography. Further applications of the design rules highlighted here may lead to new sensors for probing biomolecule mechanics, as well as to the development of optically actuated micromachines

    Maximizing Minimum Pressure in Fluid Dynamic Bearings of Hard Disk Drives

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    We focus on the central spindle which supports the rotating magnetic platters which hold all of the data. The spindle must operate with great precision and stability at high rotational speeds. Design practice has converged on oil-lubricated hydrodynamic journal bearings as the most common choice for spindles. That is, a layer of viscous oil separates a rotating shaft (the bearing) from the fixed outer sleeve (the journal). In hard drives, it is very important for the shaft to be centered within the sleeve. Plain journal bearings (i.e. both surfaces are circular cylinders) are unstable to perturbations that push the shaft off-center. It was found that this stability problem can be overcome by cutting diagonal grooves into the journal in a pattern called a herring-bone. Another consequence of this design is that very high pressures are generated by the grooves as they drive the oil to the middle of the bearing, away from the top/bottom ends of the spindle. This pumping action generally works to oppose leakage out of the bearing. We examine how choices for the groove pattern can influence the key properties of the bearing. The focus is to understand the effect of the groove geometry on the pumping action. In particular the undesirable behavior caused by the low pressures created near the top/bottom ends of the bearing which, under many conditions, may result in the pressure becoming negative, relative to atmospheric pressure. Negative pressure can result in cavitation or, when it occurs near an air-oil interface, can cause air to be ingested and hence create bubbles. Any bubbles in the oil can corrupt the lubricating layer in the bearing and, as they are created and collapse, can cause significant undesirable vibrations. The negative pressures have therefore been identified as one of the key problems in design of hard disk drive bearings. We will use numerical computations and some analysis to show that by modifying the groove geometry we can reduce the negative pressure while retaining good stability characteristics

    Mapping haptic exploratory procedures to multiple shape representations

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    Research in human haptics has revealed a number of exploratory procedures (EPs) that are used in determining attributes on an object, particularly shape. This research has been used as a paradigm for building an intelligent robotic system that can perform shape recognition from touch sensing. In particular, a number of mappings between EPs and shape modeling primitives have been found. The choice of shape primitive for each EP is discussed, and results from experiments with a Utah-MIT dextrous hand system are presented. A vision algorithm to complement active touch sensing for the task of autonomous shape recovery is also presented

    Constant mean curvature surfaces

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    In this article we survey recent developments in the theory of constant mean curvature surfaces in homogeneous 3-manifolds, as well as some related aspects on existence and descriptive results for HH-laminations and CMC foliations of Riemannian nn-manifolds.Comment: 102 pages, 17 figure
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