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 $A \leftrightarrow A+A$ 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 $\Omega$. By means of a new hybrid simulation scheme, we manage to reach large macroscopic values of $\Omega$ 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

Mathematical modeling of genome replication

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