2,793 research outputs found

    Curvature blow up in Bianchi VIII and IX vacuum spacetimes

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    The maximal globally hyperbolic development of non-Taub-NUT Bianchi IX vacuum initial data and of non-NUT Bianchi VIII vacuum initial data is C2 inextendible. Furthermore, a curvature invariant is unbounded in the incomplete directions of inextendible causal geodesics.Comment: 20 pages, no figures. Submitted to Classical and Quantum Gravit

    Asymptotic silence-breaking singularities

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    We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and non-generic singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure

    The future asymptotics of Bianchi VIII vacuum solutions

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    Bianchi VIII vacuum solutions to Einstein's equations are causally geodesically complete to the future, given an appropriate time orientation, and the objective of this article is to analyze the asymptotic behaviour of solutions in this time direction. For the Bianchi class A spacetimes, there is a formulation of the field equations that was presented in an article by Wainwright and Hsu, and we analyze the asymptotic behaviour of solutions in these variables. We also try to give the analytic results a geometric interpretation by analyzing how a normalized version of the Riemannian metric on the spatial hypersurfaces of homogeneity evolves.Comment: 34 pages, no figure

    Neuroanatomical shifts mirror patterns of ecological divergence in three diverse clades of mimetic butterflies

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    Microhabitat partitioning in heterogenous environments can support more diverse communities but may expose partitioned species to distinct perceptual challenges. Divergence across microhabitats could therefore lead to local adaptation to contrasting sensory conditions across small spatial scales, but this aspect of community structuring is rarely explored. Diverse communities of ithomiine butterflies provide an example where closely related species partition tropical forests, where shifts in mimetic coloration are tightly associated with shifts in habitat preference. We test the hypothesis that these mimetic and ecological shifts are associated with distinct patterns of sensory neural investment by comparing brain structure across 164 individuals of 16 species from three ithomiine clades. We find distinct brain morphologies between Oleriina and Hypothyris, which are mimetically homogenous and occupy a single microhabitat. Oleriina, which occurs in low‐light microhabitats, invests less in visual brain regions than Hypothyris, with one notable exception, Hyposcada anchiala, the only Oleriina sampled to have converged on mimicry rings found in Hypothyris. We also find that Napeogenes, which has diversified into a range of mimicry rings, shows intermediate patterns of sensory investment. We identify flight height as a critical factor shaping neuroanatomical diversity, with species that fly higher in the canopy investing more in visual structures. Our work suggests that the sensory ecology of species may be impacted by, and interact with, the ways in which communities of closely related organisms are adaptively assembled

    Rehabilitation strategies for optimisation of functional recovery after major joint replacement

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    Exercise-based interventions applied before and after total hip and knee arthroplasty (THA and TKA, respectively) have been investigated for a number of years, based on the assumption that they will enhance post-operative recovery. Although recent studies suggest that high-volume, pre-operative exercise may enhance post-operative recovery after TKA, studies of post-operative exercise-based interventions, have not found superiority of one exercise regime over another. It seems, however, that post-operative, exercise-based, rehabilitation is superior to no or minimal rehabilitation after THA and TKA. The goal of this commentary is to summarize recent evidence for the efficacy of different peri-operative exercise-based interventions to enhance recovery after THA and TKA, and to propose new strategies to further enhance post-operative recovery. There is a major need to improve functional recovery after THA and TKA. We propose a strategy of “enriched” trials where specific rehabilitation interventions are applied to different patients based on, for example, their expectations for post-operative recovery, willingness to undertake exercise and physical activity, and pre-operative functional performance

    Cosmic No Hair for Collapsing Universes

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    It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the isotropic attractor solution for a collapsing Bianchi type IX universe is supersymmetric when interpreted in an eleven-dimensional context.Comment: Extended discussion to include Kantowski-Sachs universe. In press, Classical and Quantum Gravit

    A new proof of the Bianchi type IX attractor theorem

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    We consider the dynamics towards the initial singularity of Bianchi type IX vacuum and orthogonal perfect fluid models with a linear equation of state. The `Bianchi type IX attractor theorem' states that the past asymptotic behavior of generic type IX solutions is governed by Bianchi type I and II vacuum states (Mixmaster attractor). We give a comparatively short and self-contained new proof of this theorem. The proof we give is interesting in itself, but more importantly it illustrates and emphasizes that type IX is special, and to some extent misleading when one considers the broader context of generic models without symmetries.Comment: 26 pages, 5 figure

    Self-similar Bianchi models: I. Class A models

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    We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII0_0 models and irrotational Bianchi VI0_0 models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit
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