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  • 1
    Electronic Resource
    Electronic Resource
    Anomalous scaling from controlled closure in a shell model of turbulence (2000)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 12 (2000), S. 803-821 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: We present a model of hydrodynamic turbulence for which the program of computing the scaling exponents from first principles can be developed in a controlled fashion. The model consists of N suitably coupled copies of the "Sabra" shell model of turbulence. The couplings are chosen to include two components: random and deterministic, with a relative importance that is characterized by a parameter called ε. It is demonstrated, using numerical simulations of up to 25 copies and 28 shells that in the N→∞ limit but for 0〈ε≤1 this model exhibits correlation functions whose scaling exponents are anomalous. The theoretical calculation of the scaling exponents follows verbatim the closure procedure suggested recently for the Navier–Stokes problem, with the additional advantage that in the N→∞ limit the parameter ε can be used to regularize the closure procedure. The main result of this paper is a finite and closed set of scale-invariant equations for the 2nd and 3rd order statistical objects of the theory. This set of equations takes into account terms up to order ε4 and neglects terms of order ε6. Preliminary analysis of this set of equations indicates a K41 normal scaling at ε=0, with a birth of anomalous exponents at larger values of ε, in agreement with the numerical simulations. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.870337
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  • 2
    Electronic Resource
    Electronic Resource
    The size and dynamics of magnetic flux structures in magnetohydrodynamic turbulence (1995)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 2 (1995), S. 1148-1156 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The structures in magnetohydrodynamic (MHD) flow, flux tubes in particular, are investigated with respect to coherence in the direction of the magnetic field. A length scale, which is interpreted as the diameter of the tubes, is derived from the MHD equations. This scale implies that the tendency towards alignment of flux lines in tubes is a diffusion driven phenomenon. The dynamics of the tubes is also investigated; the major conclusion is that stronger tubes are expected to be straighter. These ideas are tested out on data from numerical simulations of turbulent MHD convection. It is also seen that alignment of flux lines increases with the strength of the tube. Possible reasons for this effect are discussed. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871393
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  • 3
    Electronic Resource
    Electronic Resource
    The universal scaling exponents of anisotropy in turbulence and their measurement (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 8 (1996), S. 2565-2567 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Correlation functions of non-scalar fields in isotropic hydrodynamic turbulence are characterized by a set of universal exponents. These exponents also characterize the rate of decay of the effects of anisotropic forcing in developed turbulence. These exponents are important for the general theory of turbulence, and for modeling anisotropic flows. We propose methods for measuring these exponents by designing new laboratory experiments. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.869065
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  • 4
    Electronic Resource
    Electronic Resource
    Turbulence Go with the flow (2001)
    [s.l.] : Nature Publishing Group
    Nature 409 (2001), S. 993-995 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Turbulence is the chaotic and unpredictable motion of fluids flowing at high rates. It plays a major role in many processes from the environmental, for example cloud formation, to the technological, such as in industrial chemical reactors. Clearly, a deeper understanding of this phenomenon would be ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/35059196
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  • 5
    Electronic Resource
    Electronic Resource
    A note on the bimodal stationary distributions in hard chemical instabilities (1978)
    Springer
    Journal of statistical physics 18 (1978), S. 633-635 
    Details
    ISSN: 1572-9613
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014482
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  • 6
    Electronic Resource
    Electronic Resource
    Universal properties of dynamically complex systems: the organization of chaos (1988)
    [s.l.] : Nature Publishing Group
    Nature 333 (1988), S. 618-623 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Natural systems far from equilibrium often show complex dynamic behaviour. There is fundamental progress in understanding universal aspects of the paths to such behaviour, of the trajectories just at the borderline of chaos and of the nature of the complexity in the chaotic region. A grammar of ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/333618a0
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  • 7
    Electronic Resource
    Electronic Resource
    Complex or just complicated? (1988)
    [s.l.] : Nature Publishing Group
    Nature 333 (1988), S. 498-499 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] THE dynamical behaviour of the wind in the atmosphere is much simpler than any-thing that could be anticipated, according to Tsonis and Elsner on page 545 of this issue1. They conclude that one can accu-rately model the wind dynamics using just eight coupled ordinary differential equations. Such a ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/333498a0
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  • 8
    Electronic Resource
    Electronic Resource
    Analytic results for asymmetric Random Walk with exponential transition probabilities (1978)
    Springer
    Journal of statistical physics 19 (1978), S. 525-541 
    Details
    ISSN: 1572-9613
    Keywords: Random walks ; stochastic processes ; exponential models ; mean first passage time ; branching ratio
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present here exact analytic results for a random walk on a one-dimensional lattice with asymmetric, exponentially distributed jump probabilities. We derive the generating functions of such a walk for a perfect lattice and for a lattice with absorbing boundaries. We obtain solutions for some interesting moment properties, such as mean first passage time, drift velocity, dispersion, and branching ratio for absorption. The symmetric exponential walk is solved as a special case. The scaling of the mean first passage time with the size of the system for the exponentially distributed walk is determined by the symmetry and is independent of the range.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01011697
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  • 9
    Electronic Resource
    Electronic Resource
    Computing the Scaling Exponents in Fluid Turbulence from First Principles: Demonstration of Multiscaling (1998)
    Springer
    Journal of statistical physics 93 (1998), S. 797-832 
    Details
    ISSN: 1572-9613
    Keywords: Turbulence ; universal statistics ; anomalous scaling ; multi-fractals
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We develop a consistent closure procedure for the calculation of the scaling exponents ζ n of the nth-order correlation functions in fully developed hydro-dynamic turbulence, starting from first principles. The closure procedure is constructed to respect the fundamental rescaling symmetry of the Euler equation. The starting point of the procedure is an infinite hierarchy of coupled equations that are obeyed identically with respect to scaling for any set of scaling exponents ζ n . This hierarchy was discussed in detail in a recent publication by V. S. L'vov and I. Procaccia. The scaling exponents in this set of equations cannot be found from power counting. In this paper we present in detail the lowest non-trivial closure of this infinite set of equations, and prove that this closure leads to the determination of the scaling exponents from solvability conditions. The equations under consideration after this closure are nonlinear integro-differential equations, reflecting the nonlinearity of the original Navier–Stokes equations. Nevertheless they have a very special structure such that the determination of the scaling exponents requires a procedure that is very similar to the solution of linear homogeneous equations, in which amplitudes are determined by fitting to the boundary conditions in the space of scales. The renormalization scale that is necessary for any anomalous scaling appears at this point. The Hölder inequalities on the scaling exponents select the renormalization scale as the outer scale of turbulence L. We demonstrate that the solvability condition of our equations leads to non-Kolmogorov values of the scaling exponents ζ n . Finally, we show that this solutions is a first approximation in a systematic series of improving approximations for the calculation of the anomalous exponents in turbulence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/B:JOSS.0000033164.35116.35
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  • 10
    Electronic Resource
    Electronic Resource
    Fractal structures in turbulence (1984)
    Springer
    Journal of statistical physics 36 (1984), S. 649-663 
    Details
    ISSN: 1572-9613
    Keywords: Fractals ; turbulence ; passive scalars ; clouds ; wave propagation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a qualitative overview of our work on the issue of fractal structures in turbulence. We explain why fully developed turbulence is not space filling and describe how its fractal dimension can be estimated theoretically. The implications of the fractal nature of turbulence on transport processes like turbulent diffusion and on fluctuations in passive scalars are discussed. The latter affect wave propagation in turbulent media and these effects are examined. In addition we consider clouds in the atmosphere which are claimed to have fractal perimeters (or surfaces) and outline the physical reasons for this phenomenon. The fractal dimension of clouds is tied to the theory of turbulent diffusion and is computed theoretically. Indications of the road ahead are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01012929
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