22,342 research outputs found

    Cuntz-Pimsner C*-algebras associated with subshifts

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    By using C*-correspondences and Cuntz-Pimsner algebras, we associate to every subshift (also called a shift space) XX a C*-algebra OXO_X, which is a generalization of the Cuntz-Krieger algebras. We show that OXO_X is the universal C*-algebra generated by partial isometries satisfying relations given by XX. We also show that OXO_X is a one-sided conjugacy invariant of XX.Comment: 28 pages. This is a slightly updated version of a preprint from 2004. Submitted for publication. In version 2 the Introduction has been changed, two remarks (Remark 7.6 and 7.7) have been added and the list of references has been update

    Complex-space singularities of 2D Euler flow in Lagrangian coordinates

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    We show that, for two-dimensional space-periodic incompressible flow, the solution can be evaluated numerically in Lagrangian coordinates with the same accuracy achieved in standard Eulerian spectral methods. This allows the determination of complex-space Lagrangian singularities. Lagrangian singularities are found to be closer to the real domain than Eulerian singularities and seem to correspond to fluid particles which escape to (complex) infinity by the current time. Various mathematical conjectures regarding Eulerian/Lagrangian singularities are presented.Comment: 5 pages, 2 figures, submitted to Physica

    Singularities of Euler flow? Not out of the blue!

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    Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.(A version of the paper with higher-quality figures is available at http://www.obs-nice.fr/etc7/complex.pdf)Comment: RevTeX4, 10 pages, 9 figures. J.Stat.Phys. in press (updated version

    Description of Four-Body Breakup Reaction with the Method of Continuum-Discretized Coupled-Channels

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    We present a method for smoothing discrete breakup SS-matrix elements calculated by the method of continuum-discretized coupled-channels (CDCC). This smoothing method makes it possible to apply CDCC to four-body breakup reactions. The reliability of the smoothing method is confirmed for two cases, 58^{58}Ni(dd, pnp n) at 80 MeV and the E1E1 transition of 6^6He. We apply CDCC with the smoothing method to 6^6He breakup reaction at 22.5 MeV. Multi-step breakup processes are found to be important.Comment: 19 pages, 7 figures, published in Progress of Theoretical Physic
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