6,334 research outputs found

    Topological Chaos in a Three-Dimensional Spherical Fluid Vortex

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    In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are techniques which exploit the topology of dynamically invariant structures. However, the path to extending many such topological techniques to three dimensions is filled with roadblocks that prevent their application to a wider variety of physical systems. Here, we overcome these roadblocks and successfully analyze a realistic model of 3D fluid advection, by extending the homotopic lobe dynamics (HLD) technique, previously developed for 2D area-preserving dynamics, to 3D volume-preserving dynamics. We start with numerically-generated finite-time chaotic-scattering data for particles entrained in a spherical fluid vortex, and use this data to build a symbolic representation of the dynamics. We then use this symbolic representation to explain and predict the self-similar fractal structure of the scattering data, to compute bounds on the topological entropy, a fundamental measure of mixing, and to discover two different mixing mechanisms, which stretch 2D material surfaces and 1D material curves in distinct ways.Comment: 14 pages, 11 figure

    Environmental Factors and Limbic Vulnerability in Childhood Autism

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    The rise in prevalence of autism spectrum disorders (ASD) is suggestive of a new etiology. Diagnostic substitution alone is unlikely to account for the increase, while genetic association with detoxification gene alleles points to an environmental contribution. Subtle structural anomalies in the ASD brain are widespread but limbic damage seems important for the development of behaviors diagnostic of ASD. The limbic brain is especially susceptible to environmental challenge: internal sensing, physiological feedback and neuroinflammatory processes may underlie this sensitivity to insult. Primary damage leading to ASD in later life is likely to take place in utero and/or in the immediate postnatal period. Despite evidence of heavy metal involvement, a causal connection may not yet be concluded because subjects exposed to metals tend to be exposed to other environmental agents. Because maternal minerals and lipids are supplied to the unborn child, historic toxic exposure of the mother may be pivotal. A two-hit combination of genetic susceptibility and environmental challenge is argued to underlie the rise in ASD

    A Robust Numerical Method for Integration of Point-Vortex Trajectories in Two Dimensions

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    The venerable 2D point-vortex model plays an important role as a simplified version of many disparate physical systems, including superfluids, Bose-Einstein condensates, certain plasma configurations, and inviscid turbulence. This system is also a veritable mathematical playground, touching upon many different disciplines from topology to dynamic systems theory. Point-vortex dynamics are described by a relatively simple system of nonlinear ODEs which can easily be integrated numerically using an appropriate adaptive time stepping method. As the separation between a pair of vortices relative to all other inter-vortex length scales decreases, however, the computational time required diverges. Accuracy is usually the most discouraging casualty when trying to account for such vortex motion, though the varying energy of this ostensibly Hamiltonian system is a potentially more serious problem. We solve these problems by a series of coordinate transformations: We first transform to action-angle coordinates, which, to lowest order, treat the close pair as a single vortex amongst all others with an internal degree of freedom. We next, and most importantly, apply Lie transform perturbation theory to remove the higher-order correction terms in succession. The overall transformation drastically increases the numerical efficiency and ensures that the total energy remains constant to high accuracy.Comment: 21 pages, 4 figure

    Towards conformationally-locked difluorosugar analogues : an unexpected sense of dihydroxylation

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    Difluorinated cyclooctenones, synthesised using RCM, can be used as templates for stereoselective oxidative transformations to products that undergo transannular reactions to afford conformationally-locked analogues of 2-deoxy-2,2-difluorosugars with different stereochemical relationships between the C-2 and C-3 hydroxyl groups

    Rapid assembly of highly-functionalised difluorinated cyclooctenones via ring-closing metathesis

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    Building block methodology from trifluoroethanol and ringclosing metathesis using a Fürstner modification of Grubbs’ conditions allows the rapid synthesis of novel difluorinated cyclooctenones
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