3,106 research outputs found

    Scaling Laws and Intermittency in Highly Compressible Turbulence

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    We use large-scale three-dimensional simulations of supersonic Euler turbulence to study the physics of a highly compressible cascade. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We find that the inertial range velocity scaling deviates strongly from the incompressible Kolmogorov laws. We propose an extension of Kolmogorov's K41 phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that low-order statistics of 'v' are invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69 and the third-order structure function of 'v' scales linearly with separation. We directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m=2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 7 pages, 3 figures; in press, AIP Conference Proceedings: "Turbulence and Nonlinear Processes in Astrophysical Plasmas", Waikiki Beach, Hawaii, March 21, 200

    Information flow in one-dimensional non-unitary quantum cellular automata

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    The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e. for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.Comment: 21 pages, 23 figure

    Finite element approximation of multi-scale elliptic problems using patches of elements

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    In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations are not necessarily conforming. This paper provides proofs of the results published earlier (see C. R. Acad. Sci. Paris, Ser. I 337 (2003) 679-684), gives a generalization of the latter to more than two domains and contains extensive numerical illustrations. New results including the spectral analysis of the iteration operator and a numerical method to evaluate the constant of the strengthened Cauchy-Buniakowski-Schwarz inequality are presente
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