2,942 research outputs found

    Quantum astrometric observables II: time delay in linearized quantum gravity

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    A clock synchronization thought experiment is modeled by a diffeomorphism invariant "time delay" observable. In a sense, this observable probes the causal structure of the ambient Lorentzian spacetime. Thus, upon quantization, it is sensitive to the long expected smearing of the light cone by vacuum fluctuations in quantum gravity. After perturbative linearization, its mean and variance are computed in the Minkowski Fock vacuum of linearized gravity. The na\"ive divergence of the variance is meaningfully regularized by a length scale μ\mu, the physical detector resolution. This is the first time vacuum fluctuations have been fully taken into account in a similar calculation. Despite some drawbacks this calculation provides a useful template for the study of a large class of similar observables in quantum gravity. Due to their large volume, intermediate calculations were performed using computer algebra software. The resulting variance scales like (sp/μ)2(s \ell_p/\mu)^2, where p\ell_p is the Planck length and ss is the distance scale separating the ("lab" and "probe") clocks. Additionally, the variance depends on the relative velocity of the lab and the probe, diverging for low velocities. This puzzling behavior may be due to an oversimplified detector resolution model or a neglected second order term in the time delay.Comment: 30 pages, 8 figures, revtex4-1; v3: minor updates and corrections, close to published versio

    Coupled structural, thermal, phase-change and electromagnetic analysis for superconductors, volume 1

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    This research program has dealt with the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements; (2) finite element modeling of the electromagnetic problem; (3) coupling of thermal and mechanical effects; and (4) computer implementation and solution of the superconductivity transition problem. The research was carried out over the period September 1988 through March 1993. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles; (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements; and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects; and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The grant has fully supported the thesis work of one doctoral student (James Schuler, who started on January 1989 and completed on January 1993), and partly supported another thesis (Carmelo Militello, who started graduate work on January 1988 completing on August 1991). Twenty-three publications have acknowledged full or part support from this grant, with 16 having appeared in archival journals and 3 in edited books or proceedings

    Families of L-functions and their Symmetry

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    In [90] the first-named author gave a working definition of a family of automorphic L-functions. Since then there have been a number of works [33], [107], [67] [47], [66] and especially [98] by the second and third-named authors which make it possible to give a conjectural answer for the symmetry type of a family and in particular the universality class predicted in [64] for the distribution of the zeros near s=1/2. In this note we carry this out after introducing some basic invariants associated to a family

    Spectral functions of charmonium with 2+1 flavours of dynamical quarks

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    Finite temperature charmonium spectral functions in the pseudoscalar(PS) and vector(V) channels are studied in lattice QCD with 2+1 flavours of dynamical Wilson quarks, on fine isotropic lattices (with a lattice spacing of 0.057fm), with a non-physical pion mass of 545MeV. The highest temperature studied is approximately 1.4Tc. Up to this temperature no significant variation of the spectral function is seen in the PS channel. The V channel shows some temperature dependence, which seems to be consistent with a temperature dependent low frequency peak related to heavy quark transport, plus a temperature independent term at omega > 0. These results are in accord with previous calculations using the quenched approximation.Comment: Conference proceedings: The 32nd International Symposium on Lattice Field Theory - Lattice 2014 June 23-28, 2014 Columbia University, New York, New York This conference contribution draws heavily from the paper: arXiv:1401.5940 [hep-lat

    Reduction of dynamical biochemical reaction networks in computational biology

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    Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques
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