1,207 research outputs found

    Hackney, Sheldon: Humanities Chairman Nomination Hearing (1993): News Article 20

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    On the Universality of the Entropy-Area Relation

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    We present an argument that, for a large class of possible dynamics, a canonical quantization of gravity will satisfy the Bekenstein-Hawking entropy-area relation. This result holds for temperatures low compared to the Planck temperature and for boundaries with areas large compared to Planck area. We also relate our description, in terms of a grand canonical ensemble, to previous geometric entropy calculations using area ensembles.Comment: 6 page

    Rotordynamic Computation of a Permanent-Magnetic excited Synchronous Machine due to Electromagnetic Force Excitation

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    For the acoustical computation of electromagnetic noise, it is very important to consider both, the rotor and stator vibrations of the electrical machine. Rotor vibrations can be transmitted as structure-borne sound to connected systems which might be excited at their resonances and radiate airborne sound. In order to predict the dynamical behaviour of complex electrical machine rotors (such like rotors of permanent-magnetic excited synchronous machines) in frequency domain, finite element (FE) computations can be efficiently applied using rotating coordinates. Hereby, it has to be taken into account that rotor vibrations are mainly influenced by stiffness and damping of the built-in laminated stacks and mechanical joints. Therefore, a FE model of the rotor is required which takes these parameters into account. In order to obtain the material properties, two experimental set-ups are considered. On the one hand, a generic lap joint is considered to determine the stiffness and damping of mechanical joints. On the other hand, a test rig for laminated stacks is presented which allows for the determination of direction-dependent stiffness and damping of laminated stacks by a shear and dilatation test. All identified parameters are included into the FE model. Thereby, local stiffness and damping of mechanical joints are modelled by so-called thin-layer elements. In order to prove the quality of the rotor FE model, a numerical modal analysis without considering rotor spin speed is carried out and compared to experimental results. Electromagnetic force densities are computed in the air gap of the electrical machine using an electromagnetic FE model. To cover different FE meshes of the mechanical and electromagnetic model, a method is presented which allows for converting force densities into equivalent nodal forces on the rotor surface. These excitation forces are used to compute electromagnetically caused rotor vibrations dependent on rotor spin speed by a frequency domain rotor dynamic analysis

    Spin foam model from canonical quantization

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    We suggest a modification of the Barrett-Crane spin foam model of 4-dimensional Lorentzian general relativity motivated by the canonical quantization. The starting point is Lorentz covariant loop quantum gravity. Its kinematical Hilbert space is found as a space of the so-called projected spin networks. These spin networks are identified with the boundary states of a spin foam model and provide a generalization of the unique Barrette-Crane intertwiner. We propose a way to modify the Barrett-Crane quantization procedure to arrive at this generalization: the B field (bi-vectors) should be promoted not to generators of the gauge algebra, but to their certain projection. The modification is also justified by the canonical analysis of Plebanski formulation. Finally, we compare our construction with other proposals to modify the Barret-Crane model.Comment: 26 pages; presentation improved, important changes concerning the closure constraint and the vertex amplitude; minor correctio

    A generalized Hamiltonian Constraint Operator in Loop Quantum Gravity and its simplest Euclidean Matrix Elements

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    We study a generalized version of the Hamiltonian constraint operator in nonperturbative loop quantum gravity. The generalization is based on admitting arbitrary irreducible SU(2) representations in the regularization of the operator, in contrast to the original definition where only the fundamental representation is taken. This leads to a quantization ambiguity and to a family of operators with the same classical limit. We calculate the action of the Euclidean part of the generalized Hamiltonian constraint on trivalent states, using the graphical notation of Temperley-Lieb recoupling theory. We discuss the relation between this generalization of the Hamiltonian constraint and crossing symmetry.Comment: 35 pp, 20 eps figures; minor corrections, references added; version to appear in Class. Quant. Gra
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