2,368 research outputs found
Shear Effects in Non-Homogeneous Turbulence
Motivated by recent experimental and numerical results, a simple unifying
picture of intermittency in turbulent shear flows is suggested. Integral
Structure Functions (ISF), taking into account explicitly the shear intensity,
are introduced on phenomenological grounds. ISF can exhibit a universal scaling
behavior, independent of the shear intensity. This picture is in satisfactory
agreement with both experimental and numerical data. Possible extension to
convective turbulence and implication on closure conditions for Large-Eddy
Simulation of non-homogeneous flows are briefly discussed.Comment: 4 pages, 5 figure
Self-organization in turbulence as a route to order in plasma and fluids
Transitions from turbulence to order are studied experimentally in thin fluid
layers and magnetically confined toroidal plasma. It is shown that turbulence
self-organizes through the mechanism of spectral condensation. The spectral
redistribution of the turbulent energy leads to the reduction in the turbulence
level, generation of coherent flow, reduction in the particle diffusion and
increase in the system's energy. The higher order state is sustained via the
nonlocal spectral coupling of the linearly unstable spectral range to the
large-scale mean flow. The similarity of self-organization in two-dimensional
fluids and low-to-high confinement transitions in plasma suggests the
universality of the mechanism.Comment: 5 pages, 4 figure
Scaling Analysis and Evolution Equation of the North Atlantic Oscillation Index Fluctuations
The North Atlantic Oscillation (NAO) monthly index is studied from 1825 till
2002 in order to identify the scaling ranges of its fluctuations upon different
delay times and to find out whether or not it can be regarded as a Markov
process. A Hurst rescaled range analysis and a detrended fluctuation analysis
both indicate the existence of weakly persistent long range time correlations
for the whole scaling range and time span hereby studied. Such correlations are
similar to Brownian fluctuations. The Fokker-Planck equation is derived and
Kramers-Moyal coefficients estimated from the data. They are interpreted in
terms of a drift and a diffusion coefficient as in fluid mechanics. All partial
distribution functions of the NAO monthly index fluctuations have a form close
to a Gaussian, for all time lags, in agreement with the findings of the scaling
analyses. This indicates the lack of predictive power of the present NAO
monthly index. Yet there are some deviations for large (and thus rare) events.
Whence suggestions for other measurements are made if some improved
predictability of the weather/climate in the North Atlantic is of interest. The
subsequent Langevin equation of the NAO signal fluctuations is explicitly
written in terms of the diffusion and drift parameters, and a characteristic
time scale for these is given in appendix.Comment: 6 figures, 54 refs., 16 pages; submitted to Int. J. Mod. Phys. C:
Comput. Phy
Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D
We present an extension of the Karman-Howarth theorem to the Lagrangian
averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws
resulting as a corollary of this theorem are studied in numerical simulations,
as well as the scaling of the longitudinal structure function exponents
indicative of intermittency. Numerical simulations for a magnetic Prandtl
number equal to unity are presented both for freely decaying and for forced two
dimensional MHD turbulence, solving directly the MHD equations, and employing
the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the
third-order structure function with length is observed. The LAMHD-alpha
equations also capture the anomalous scaling of the longitudinal structure
function exponents up to order 8.Comment: 34 pages, 7 figures author institution addresses added magnetic
Prandtl number stated clearl
Hybrid method for simulating front propagation in reaction-diffusion systems
We study the propagation of pulled fronts in the
microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In
the mean field approximation the process is described by the deterministic
Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation. In particular we
concentrate on the corrections to the deterministic behavior due to the number
of particles per site . By means of a new hybrid simulation scheme, we
manage to reach large macroscopic values of which allows us to show
the importance in the dynamics of microscopic pulled fronts of the interplay of
microscopic fluctuations and their macroscopic relaxation.Comment: 5 pages, 4 figure
On the universality of small scale turbulence
The proposed universality of small scale turbulence is investigated for a set
of measurements in a cryogenic free jet with a variation of the Reynolds number
(Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity
increments by means of structure functions or probability density functions is
replaced by a new method which is based on the theory of stochastic Markovian
processes. It gives access to a more complete characterization by means of
joint probabilities of finding velocity increments at several scales. Based on
this more precise method our results call in question the concept of
universality.Comment: 4 pages, 4 figure
Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics
A theoretical formula for the probability density function (PDF) of velocity
derivatives in a fully developed turbulent flow is derived with the
multifractal aspect based on the generalized measures of entropy, i.e., the
extensive Renyi entropy or the non-extensive Tsallis entropy, and is used,
successfully, to analyze the PDF's observed in the direct numerical simulation
(DNS) conducted by Gotoh et al.. The minimum length scale r_d/eta in the
longitudinal (transverse) inertial range of the DNS is estimated to be
r_d^L/eta = 1.716 (r_d^T/eta = 2.180) in the unit of the Kolmogorov scale eta.Comment: 6 pages, 1 figur
Superconvergent Perturbation Method in Quantum Mechanics
An analogue of Kolmogorov's superconvergent perturbation theory in classical
mechanics is constructed for self adjoint operators. It is different from the
usual Rayleigh--Schr\"odinger perturbation theory and yields expansions for
eigenvalues and eigenvectors in terms of functions of the perturbation
parameter.Comment: 11 pages, LaTe
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
We provide Lyapunov-like characterizations of boundedness and convergence of
non-trivial solutions for a class of systems with unstable invariant sets.
Examples of systems to which the results may apply include interconnections of
stable subsystems with one-dimensional unstable dynamics or critically stable
dynamics. Systems of this type arise in problems of nonlinear output
regulation, parameter estimation and adaptive control.
In addition to providing boundedness and convergence criteria the results
allow to derive domains of initial conditions corresponding to solutions
leaving a given neighborhood of the origin at least once. In contrast to other
works addressing convergence issues in unstable systems, our results require
neither input-output characterizations for the stable part nor estimates of
convergence rates. The results are illustrated with examples, including the
analysis of phase synchronization of neural oscillators with heterogenous
coupling
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