176 research outputs found
Passive Scalar: Scaling Exponents and Realizability
An isotropic passive scalar field advected by a rapidly-varying velocity
field is studied. The tail of the probability distribution for
the difference in across an inertial-range distance is found
to be Gaussian. Scaling exponents of moments of increase as
or faster at large order , if a mean dissipation conditioned on is
a nondecreasing function of . The computed numerically
under the so-called linear ansatz is found to be realizable. Some classes of
gentle modifications of the linear ansatz are not realizable.Comment: Substantially revised to conform with published version. Revtex (4
pages) with 2 postscript figures. Send email to [email protected]
The Lyapunov Spectrum of a Continuous Product of Random Matrices
We expose a functional integration method for the averaging of continuous
products of random matrices. As an application, we
compute exactly the statistics of the Lyapunov spectrum of . This
problem is relevant to the study of the statistical properties of various
disordered physical systems, and specifically to the computation of the
multipoint correlators of a passive scalar advected by a random velocity field.
Apart from these applications, our method provides a general setting for
computing statistical properties of linear evolutionary systems subjected to a
white noise force field.Comment: Latex, 9 page
Hardware design of transformer remote monitoring system based on Internet of things
The architecture for intelligent monitoring systems in the power industry is considered. The equipment for remote monitoring is described. Based on the research and analysis of dry-type transformers, this paper designs a remote monitoring system for transformers based on the Internet of Things technology and draws the following conclusions: the design scheme with GPRS as the communication means and Arduino as the system carrier is determined
The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions
It is shown that the idea that scaling behavior in turbulence is limited by
one outer length and one inner length is untenable. Every n'th order
correlation function of velocity differences \bbox{\cal
F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length to
dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . One result of this Letter
is that when all these separations are of the same order this length scales
like with
, with being
the scaling exponent of the 'th order structure function. We derive a class
of scaling relations including the ``bridge relation" for the scaling exponent
of dissipation fluctuations .Comment: PRL, Submitted. REVTeX, 4 pages, I fig. (not included) PS Source of
the paper with figure avalable at http://lvov.weizmann.ac.il/onlinelist.htm
Anomalous Scaling in a Model of Passive Scalar Advection: Exact Results
Kraichnan's model of passive scalar advection in which the driving velocity
field has fast temporal decorrelation is studied as a case model for
understanding the appearance of anomalous scaling in turbulent systems. We
demonstrate how the techniques of renormalized perturbation theory lead (after
exact resummations) to equations for the statistical quantities that reveal
also non perturbative effects. It is shown that ultraviolet divergences in the
diagrammatic expansion translate into anomalous scaling with the inner length
acting as the renormalization scale. In this paper we compute analytically the
infinite set of anomalous exponents that stem from the ultraviolet divergences.
Notwithstanding, non-perturbative effects furnish a possibility of anomalous
scaling based on the outer renormalization scale. The mechanism for this
intricate behavior is examined and explained in detail. We show that in the
language of L'vov, Procaccia and Fairhall [Phys. Rev. E {\bf 50}, 4684 (1994)]
the problem is ``critical" i.e. the anomalous exponent of the scalar primary
field . This is precisely the condition that allows for
anomalous scaling in the structure functions as well, and we prove that this
anomaly must be based on the outer renormalization scale. Finally, we derive
the scaling laws that were proposed by Kraichnan for this problem, and show
that his scaling exponents are consistent with our theory.Comment: 43 pages, revtex
Magnetic field correlations in a random flow with strong steady shear
We analyze magnetic kinematic dynamo in a conducting fluid where the
stationary shear flow is accompanied by relatively weak random velocity
fluctuations. The diffusionless and diffusion regimes are described. The growth
rates of the magnetic field moments are related to the statistical
characteristics of the flow describing divergence of the Lagrangian
trajectories. The magnetic field correlation functions are examined, we
establish their growth rates and scaling behavior. General assertions are
illustrated by explicit solution of the model where the velocity field is
short-correlated in time
Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar
For a delta-correlated velocity field, simultaneous correlation functions of
a passive scalar satisfy closed equations. We analyze the equation for the
four-point function. To describe a solution completely, one has to solve the
matching problems at the scale of the source and at the diffusion scale. We
solve both the matching problems and thus find the dependence of the four-point
correlation function on the diffusion and pumping scale for large space
dimensionality . It is shown that anomalous scaling appears in the first
order of perturbation theory. Anomalous dimensions are found analytically
both for the scalar field and for it's derivatives, in particular, for the
dissipation field.Comment: 19 pages, RevTex 3.0, Submitted to Phys.Rev. E, revised versio
Anomalous exponents in the rapid-change model of the passive scalar advection in the order
Field theoretic renormalization group is applied to the Kraichnan model of a
passive scalar advected by the Gaussian velocity field with the covariance
. Inertial-range
anomalous exponents, related to the scaling dimensions of tensor composite
operators built of the scalar gradients, are calculated to the order
of the expansion. The nature and the convergence of
the expansion in the models of turbulence is are briefly discussed.Comment: 4 pages; REVTeX source with 3 postscript figure
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