59 research outputs found
Yakhot's model of strong turbulence: A generalization of scaling models of turbulence
We report on some implications of the theory of turbulence developed by V.
Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on
the expression for the scaling exponents . We show that Yakhot's
result contains three well known scaling models as special cases, namely K41,
K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys.
Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical
justification for the method of extended self--similarity (ESS).Comment: 8 page
Two-Loop Calculation of the Anomalous Exponents in the Kazantsev--Kraichnan Model of Magnetic Hydrodynamics
The problem of anomalous scaling in magnetohydrodynamics turbulence is
considered within the framework of the kinematic approximation, in the presence
of a large-scale background magnetic field. Field theoretic renormalization
group methods are applied to the Kazantsev-Kraichnan model of a passive vector
advected by the Gaussian velocity field with zero mean and correlation function
. Inertial-range anomalous scaling for the
tensor pair correlators is established as a consequence of the existence in the
corresponding operator product expansions of certain "dangerous" composite
operators, whose negative critical dimensions determine the anomalous
exponents. The main technical result is the calculation of the anomalous
exponents in the order of the expansion (two-loop
approximation).Comment: Presented in the Conference "Mathematical Modeling and Computational
Physics" (Stara Lesna, Slovakia, July 2011
Turbulent luminance in impassioned van Gogh paintings
We show that the patterns of luminance in some impassioned van Gogh paintings display the mathematical structure of fluid turbulence. Specifically, we show that the probability distribution function (PDF) of luminance fluctuations of points (pixels) separated by a distance R compares notably well with the PDF of the velocity differences in a turbulent flow, as predicted by the statistical theory of A.N. Kolmogorov. We observe that turbulent paintings of van Gogh belong to his last period, during which episodes of prolonged psychotic agitation of this artist were frequent. Our approach suggests new tools that open the possibility of quantitative objective research for art representation
Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence
Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and
R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different
approaches that have the Navier-Stokes equations as the common starting point,
a set of steady-state dynamic equations for structure functions of arbitrary
order in hydrodynamic turbulence. These equations are not closed. Yakhot
proposed a "mean field theory" to close the equations for locally isotropic
turbulence, and obtained scaling exponents of structure functions and an
expression for the tails of the probability density function of transverse
velocity increments. At high Reynolds numbers, we present some relevant
experimental data on pressure and dissipation terms that are needed to provide
closure, as well as on aspects predicted by the theory. Comparison between the
theory and the data shows varying levels of agreement, and reveals gaps
inherent to the implementation of the theory.Comment: 16 pages, 23 figure
Hydrodynamic turbulence and intermittent random fields
In this article, we construct two families of nonsymmetrical multifractal
fields. One of these families is used for the modelization of the velocity
field of turbulent flows.Comment: 25 Pages; to appear in Communications in Mathematical Physic
Diffusion in supersonic, turbulent, compressible flows
We investigate diffusion in supersonic, turbulent, compressible flows.
Supersonic turbulence can be characterized as network of interacting shocks. We
consider flows with different rms Mach numbers and where energy necessary to
maintain dynamical equilibrium is inserted at different spatial scales. We find
that turbulent transport exhibits super-diffusive behavior due to induced bulk
motions. In a comoving reference frame, however, diffusion behaves normal and
can be described by mixing length theory extended into the supersonic regime.Comment: 11 pages, incl. 5 figures, accepted for publication in Physical
Review E (a high-resolution version is available at
http://www.aip.de./~ralf/Publications/p21.abstract.html
How does the electromagnetic field couple to gravity, in particular to metric, nonmetricity, torsion, and curvature?
The coupling of the electromagnetic field to gravity is an age-old problem.
Presently, there is a resurgence of interest in it, mainly for two reasons: (i)
Experimental investigations are under way with ever increasing precision, be it
in the laboratory or by observing outer space. (ii) One desires to test out
alternatives to Einstein's gravitational theory, in particular those of a
gauge-theoretical nature, like Einstein-Cartan theory or metric-affine gravity.
A clean discussion requires a reflection on the foundations of electrodynamics.
If one bases electrodynamics on the conservation laws of electric charge and
magnetic flux, one finds Maxwell's equations expressed in terms of the
excitation H=(D,H) and the field strength F=(E,B) without any intervention of
the metric or the linear connection of spacetime. In other words, there is
still no coupling to gravity. Only the constitutive law H= functional(F)
mediates such a coupling. We discuss the different ways of how metric,
nonmetricity, torsion, and curvature can come into play here. Along the way, we
touch on non-local laws (Mashhoon), non-linear ones (Born-Infeld,
Heisenberg-Euler, Plebanski), linear ones, including the Abelian axion (Ni),
and find a method for deriving the metric from linear electrodynamics (Toupin,
Schoenberg). Finally, we discuss possible non-minimal coupling schemes.Comment: Latex2e, 26 pages. Contribution to "Testing Relativistic Gravity in
Space: Gyroscopes, Clocks, Interferometers ...", Proceedings of the 220th
Heraeus-Seminar, 22 - 27 August 1999 in Bad Honnef, C. Laemmerzahl et al.
(eds.). Springer, Berlin (2000) to be published (Revised version uses
Springer Latex macros; Sec. 6 substantially rewritten; appendices removed;
the list of references updated
Kolmogorov turbulence, Anderson localization and KAM integrability
The conditions for emergence of Kolmogorov turbulence, and related weak wave
turbulence, in finite size systems are analyzed by analytical methods and
numerical simulations of simple models. The analogy between Kolmogorov energy
flow from large to small spacial scales and conductivity in disordered solid
state systems is proposed. It is argued that the Anderson localization can stop
such an energy flow. The effects of nonlinear wave interactions on such a
localization are analyzed. The results obtained for finite size system models
show the existence of an effective chaos border between the
Kolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energy
does not flow to small scales, and developed chaos regime emerging above this
border with the Kolmogorov turbulent energy flow from large to small scales.Comment: 8 pages, 6 figs, EPJB style
Comparison of some Reduced Representation Approximations
In the field of numerical approximation, specialists considering highly
complex problems have recently proposed various ways to simplify their
underlying problems. In this field, depending on the problem they were tackling
and the community that are at work, different approaches have been developed
with some success and have even gained some maturity, the applications can now
be applied to information analysis or for numerical simulation of PDE's. At
this point, a crossed analysis and effort for understanding the similarities
and the differences between these approaches that found their starting points
in different backgrounds is of interest. It is the purpose of this paper to
contribute to this effort by comparing some constructive reduced
representations of complex functions. We present here in full details the
Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM)
together with other approaches that enter in the same category
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