4,709 research outputs found

    An exact quantification of backreaction in relativistic cosmology

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    An important open question in cosmology is the degree to which the Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations are able to model the large-scale behaviour of the locally inhomogeneous observable universe. We investigate this problem by considering a range of exact n-body solutions of Einstein's constraint equations. These solutions contain discrete masses, and so allow arbitrarily large density contrasts to be modelled. We restrict our study to regularly arranged distributions of masses in topological 3-spheres. This has the benefit of allowing straightforward comparisons to be made with FLRW solutions, as both spacetimes admit a discrete group of symmetries. It also provides a time-symmetric hypersurface at the moment of maximum expansion that allows the constraint equations to be solved exactly. We find that when all the mass in the universe is condensed into a small number of objects (<10) then the amount of backreaction in dust models can be large, with O(1) deviations from the predictions of the corresponding FLRW solutions. When the number of masses is large (>100), however, then our measures of backreaction become small (<1%). This result does not rely on any averaging procedures, which are notoriously hard to define uniquely in general relativity, and so provides (to the best of our knowledge) the first exact and unambiguous demonstration of backreaction in general relativistic cosmological modelling. Discrete models such as these can therefore be used as laboratories to test ideas about backreaction that could be applied in more complicated and realistic settings.Comment: 13 pages, 9 figures. Corrections made to Tables IV and

    Quantum matchgate computations and linear threshold gates

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    The theory of matchgates is of interest in various areas in physics and computer science. Matchgates occur in e.g. the study of fermions and spin chains, in the theory of holographic algorithms and in several recent works in quantum computation. In this paper we completely characterize the class of boolean functions computable by unitary two-qubit matchgate circuits with some probability of success. We show that this class precisely coincides with that of the linear threshold gates. The latter is a fundamental family which appears in several fields, such as the study of neural networks. Using the above characterization, we further show that the power of matchgate circuits is surprisingly trivial in those cases where the computation is to succeed with high probability. In particular, the only functions that are matchgate-computable with success probability greater than 3/4 are functions depending on only a single bit of the input

    Distributed Drug Discovery, Part 2: Global Rehearsal of Alkylating Agents for the Synthesis of Resin-Bound Unnatural Amino Acids and Virtual D3 Catalog Construction

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    Thermodynamic metrics and optimal paths

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    A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page

    Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

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    We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset SS of volume at most kk and bipartiteness ratio θ\theta, then for any 0<ϵ<1/20<\epsilon<1/2, it finds a set SS' of volume at most 2k1+ϵ2k^{1+\epsilon} and bipartiteness ratio at most 4θ/ϵ4\sqrt{\theta/\epsilon}. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time O(ϵ2θ2k1+ϵln3k)O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k), independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the kkth \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

    Optical energies of AllnN epilayers

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    Optical energy gaps are measured for high-quality Al1−xInxN-on-GaN epilayers with a range of compositions around the lattice match point using photoluminescence and photoluminescence excitation spectroscopy. These data are combined with structural data to determine the compositional dependence of emission and absorption energies. The trend indicates a very large bowing parameter of 6 eV and differences with earlier reports are discussed. Very large Stokes' shifts of 0.4-0.8 eV are observed in the composition range 0.13<x<0.24, increasing approximately linearly with InN fraction despite the change of sign of the piezoelectric fiel
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