918 research outputs found
Anomalous scaling in two and three dimensions for a passive vector field advected by a turbulent flow
A model of the passive vector field advected by the uncorrelated in time
Gaussian velocity with power-like covariance is studied by means of the
renormalization group and the operator product expansion. The structure
functions of the admixture demonstrate essential power-like dependence on the
external scale in the inertial range (the case of an anomalous scaling). The
method of finding of independent tensor invariants in the cases of two and
three dimensions is proposed to eliminate linear dependencies between the
operators entering into the operator product expansions of the structure
functions. The constructed operator bases, which include the powers of the
dissipation operator and the enstrophy operator, provide the possibility to
calculate the exponents of the anomalous scaling.Comment: 9 pages, LaTeX2e(iopart.sty), submitted to J. Phys. A: Math. Ge
Walking near a Conformal Fixed Point: the 2-d O(3) Model at theta near pi as a Test Case
Slowly walking technicolor models provide a mechanism for electroweak
symmetry breaking whose nonperturbative lattice investigation is rather
challenging. Here we demonstrate walking near a conformal fixed point
considering the 2-d lattice O(3) model at vacuum angle .
The essential features of walking technicolor models are shared by this toy
model and can be accurately investigated by numerical simulations. We show
results for the running coupling and the beta-function and we perform a finite
size scaling analysis of the massgap close to the conformal point.Comment: 5 pages, 4 figure
Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix
Analysis of the singularities of the polarization field of CMB, where
polarization is equal to zero, is presented. It is found that the
classification of the singular points differs from the usual three types known
in the ordinary differential equations. The new statistical properties of
polarization field are discussed, and new methods to detect the presence of
primordial tensor perturbations are indicated.Comment: 7 pages, 1 figure
Theory for the single-point velocity statistics of fully developed turbulence
We investigate the single-point velocity probability density function (PDF)
in three-dimensional fully developed homogeneous isotropic turbulence within
the framework of PDF equations focussing on deviations from Gaussianity. A
joint analytical and numerical analysis shows that these deviations may be
quantified studying correlations of dynamical quantities like pressure
gradient, external forcing and energy dissipation with the velocity. A
stationary solution for the PDF equation in terms of these quantities is
presented, and the theory is validated with the help of direct numerical
simulations indicating sub-Gaussian tails of the PDF.Comment: 6 pages, 4 figures, corrected typo in eq. (4
Stochastic Perturbations in Vortex Tube Dynamics
A dual lattice vortex formulation of homogeneous turbulence is developed,
within the Martin-Siggia-Rose field theoretical approach. It consists of a
generalization of the usual dipole version of the Navier-Stokes equations,
known to hold in the limit of vanishing external forcing. We investigate, as a
straightforward application of our formalism, the dynamics of closed vortex
tubes, randomly stirred at large length scales by gaussian stochastic forces.
We find that besides the usual self-induced propagation, the vortex tube
evolution may be effectively modeled through the introduction of an additional
white-noise correlated velocity field background. The resulting
phenomenological picture is closely related to observations previously reported
from a wavelet decomposition analysis of turbulent flow configurations.Comment: 16 pages + 2 eps figures, REVTeX
Exact Equal Time Statistics of Orszag-McLaughlin Dynamics By The Hopf Characteristic Functional Approach
By employing Hopf's functional method, we find the exact characteristic
functional for a simple nonlinear dynamical system introduced by Orszag.
Steady-state equal-time statistics thus obtained are compared to direct
numerical simulation. The solution is both non-trivial and strongly
non-Gaussian.Comment: 6 pages and 2 figure
Exact Statistics of Chaotic Dynamical Systems
We present an inverse method to construct large classes of chaotic invariant
sets together with their exact statistics. The associated dynamical systems are
characterized by a probability distribution and a two-form. While our emphasis
is on classical systems, we briefly speculate about possible applications to
quantum field theory, in the context of generalizations of stochastic
quantization.Comment: 18 pages, 5 figure
Large-scale dynamics of magnetic helicity
In this paper we investigate the dynamics of magnetic helicity in
magnetohydrodynamic (MHD) turbulent flows focusing at scales larger than the
forcing scale. Our results show a nonlocal inverse cascade of magnetic
helicity, which occurs directly from the forcing scale into the largest scales
of the magnetic field. We also observe that no magnetic helicity and no energy
is transferred to an intermediate range of scales sufficiently smaller than the
container size and larger than the forcing scale. Thus, the statistical
properties of this range of scales, which increases with scale separation, is
shown to be described to a large extent by the zero flux solutions of the
absolute statistical equilibrium theory exhibited by the truncated ideal MHD
equations.Comment: 6 pages, 5 figures, postprint versio
Superstatistics as the statistics of quasi-equilibrium states: Application to fully developed turbulence
In non-equilibrium states, currents are produced by irreversible processes
that take a system toward the equilibrium state, where the current vanishes. We
demonstrate, in a general setting, that a superstatistics arises when the
system relaxes to a (stationary) quasi-equilibrium state instead, where only
the \textit{mean} current vanishes because of fluctuations. In particular, we
show that a current with Gaussian white noise takes the system to a unique
class of quasi-equilibrium states, where the superstatistics coincides with
Tsallis escort -distributions. Considering the fully developed turbulence as
an example of such quasi-equilibrium states, we analytically deduce the
power-law spectrum of the velocity structure functions, yielding a correction
to the log-normal model which removes its shortcomings with regard to the
decreasing higher order moments and the Novikov inequality, and obtain
exponents that agree well with the experimental data.Comment: To appear in Phys. Rev. E (2011
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