28,263 research outputs found

    Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics

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    In this paper we study Lagrangian transport in the near wake of the flow around an obstacle, which we take to be a cylinder. In this case, for the range of Reynolds numbers investigated, the flow is two-dimensional and time periodic. We use ideas and methods from transport theory in dynamical systems to describe and quantify transport in the near wake. We numerically solve the Navier-Stokes equations for the velocity field and apply these methods to the resulting numerical representation of the velocity field. We show that the method of lobe dynamics can be used in conjunction with computational fluid dynamics methods to give very detailed and quantitative information about Lagrangian transport. In particular, we show how the stable and unstable manifolds of certain saddle-type stagnation points on the cylinder, and one in the wake, can be used to divide the flow into three distinct regions, an upper wake, a lower wake, and a wake cavity. The significance of the division using stable and unstable manifolds lies in the fact that these invariant manifolds form a template on which the transport occurs. Using this, we compute fluxes from the upper and lower wakes into the wake cavity using the associated turnstile lobes. We also compute escape time distributions as well as compare transport properties for two different Reynolds numbers

    Topological current of point defects and its bifurcation

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    From the topological properties of a three dimensional vector order parameter, the topological current of point defects is obtained. One shows that the charge of point defects is determined by Hopf indices and Brouwer degrees. The evolution of point defects is also studied. One concludes that there exist crucial cases of branch processes in the evolution of point defects when the Jacobian D(Ï•x)=0D(\frac \phi x)=0.Comment: revtex,14 pages,no figur

    Evolution of the Chern-Simons Vortices

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    Based on the gauge potential decomposition theory and the Ï•\phi -mapping theory, the topological inner structure of the Chern-Simons-Higgs vortex has been showed in detail. The evolution of CSH vortices is studied from the topological properties of the Higgs scalar field. The vortices are found generating or annihilating at the limit points and encountering, splitting or merging at the bifurcation points of the scalar field Ï•.\phi .Comment: 10 pages, 10 figure

    Comment on "Quantum Phase Slips and Transport in Ultrathin Superconducting Wires"

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    In a recent Letter (Phys. Rev. Lett.78, 1552 (1997) ), Zaikin, Golubev, van Otterlo, and Zimanyi criticized the phenomenological time-dependent Ginzburg-Laudau model which I used to study the quantum phase-slippage rate for superconducting wires. They claimed that they developed a "microscopic" model, made qualitative improvement on my overestimate of the tunnelling barrier due to electromagnetic field. In this comment, I want to point out that, i), ZGVZ's result on EM barrier is expected in my paper; ii), their work is also phenomenological; iii), their renormalization scheme is fundamentally flawed; iv), they underestimated the barrier for ultrathin wires; v), their comparison with experiments is incorrect.Comment: Substantial changes made. Zaikin et al's main result was expected from my work. They underestimated tunneling barrier for ultrathin wires by one order of magnitude in the exponen

    Topology of Knotted Optical Vortices

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    Optical vortices as topological objects exist ubiquitously in nature. In this paper, by making use of the Ï•\phi-mapping topological current theory, we investigate the topology in the closed and knotted optical vortices. The topological inner structure of the optical vortices are obtained, and the linking of the knotted optical vortices is also given.Comment: 11 pages, no figures, accepted by Commun. Theor. Phys. (Beijing, P. R. China
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