Emergence of the stochastic resonance in glow discharge plasma

stochastic resonance, glow discharge plasma, excitable medium, absolute mean differenceComment: St

Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Intermittency and the Slow Approach to Kolmogorov Scaling

From a simple path integral involving a variable volatility in the velocity differences, we obtain velocity probability density functions with exponential tails, resembling those observed in fully developed turbulence. The model yields realistic scaling exponents and structure functions satisfying extended self-similarity. But there is an additional small scale dependence for quantities in the inertial range, which is linked to a slow approach to Kolmogorov (1941) scaling occurring in the large distance limit.Comment: 10 pages, 5 figures, minor changes to mirror version to appear in PR

Double scaling and intermittency in shear dominated flows

The Refined Kolmogorov Similarity Hypothesis is a valuable tool for the description of intermittency in isotropic conditions. For flows in presence of a substantial mean shear, the nature of intermittency changes since the process of energy transfer is affected by the turbulent kinetic energy production associated with the Reynolds stresses. In these conditions a new form of refined similarity law has been found able to describe the increased level of intermittency which characterizes shear dominated flows. Ideally a length scale associated with the mean shear separates the two ranges, i.e. the classical Kolmogorov-like inertial range, below, and the shear dominated range, above. However, the data analyzed in previous papers correspond to conditions where the two scaling regimes can only be observed individually. In the present letter we give evidence of the coexistence of the two regimes and support the conjecture that the statistical properties of the dissipation field are practically insensible to the mean shear. This allows for a theoretical prediction of the scaling exponents of structure functions in the shear dominated range based on the known intermittency corrections for isotropic flows. The prediction is found to closely match the available numerical and experimental data.Comment: 7 pages, 3 figures, submitted to PR

Pulses in the Zero-Spacing Limit of the GOY Model

We study the propagation of localised disturbances in a turbulent, but momentarily quiescent and unforced shell model (an approximation of the Navier-Stokes equations on a set of exponentially spaced momentum shells). These disturbances represent bursts of turbulence travelling down the inertial range, which is thought to be responsible for the intermittency observed in turbulence. Starting from the GOY shell model, we go to the limit where the distance between succeeding shells approaches zero (``the zero spacing limit'') and helicity conservation is retained. We obtain a discrete field theory which is numerically shown to have pulse solutions travelling with constant speed and with unchanged form. We give numerical evidence that the model might even be exactly integrable, although the continuum limit seems to be singular and the pulses show an unusual super exponential decay to zero as $\exp(- \mathrm{const} \sigma^n)$ when $n \to \infty$, where $\sigma$ is the {\em golden mean}. For finite momentum shell spacing, we argue that the pulses should accelerate, moving to infinity in a finite time. Finally we show that the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio

Direct evidence of plastic events and dynamic heterogeneities in soft-glasses

By using fluid-kinetic simulations of confined and concentrated emulsion droplets, we investigate the nature of space non-homogeneity in soft-glassy dynamics and provide quantitative measurements of the statistical features of plastic events in the proximity of the yield-stress threshold. Above the yield stress, our results show the existence of a finite stress correlation scale, which can be mapped directly onto the {\it cooperativity scale}, recently introduced in the literature to capture non-local effects in the soft-glassy dynamics. In this regime, the emergence of a separate boundary (wall) rheology with higher fluidity than the bulk, is highlighted in terms of near-wall spontaneous segregation of plastic events. Near the yield stress, where the cooperative scale cannot be estimated with sufficient accuracy, the system shows a clear increase of the stress correlation scale, whereas plastic events exhibit intermittent clustering in time, with no preferential spatial location. A quantitative measurement of the space-time correlation associated with the motion of the interface of the droplets is key to spot the long-range amorphous order at the yield stress threshold

Internal dynamics and activated processes in Soft-Glassy materials

Plastic rearrangements play a crucial role in the characterization of soft-glassy materials, such as emulsions and foams. Based on numerical simulations of soft-glassy systems, we study the dynamics of plastic rearrangements at the hydrodynamic scales where thermal fluctuations can be neglected. Plastic rearrangements require an energy input, which can be either provided by external sources, or made available through time evolution in the coarsening dynamics, in which the total interfacial area decreases as a consequence of the slow evolution of the dispersed phase from smaller to large droplets/bubbles. We first demonstrate that our hydrodynamic model can quantitatively reproduce such coarsening dynamics. Then, considering periodically oscillating strains, we characterize the number of plastic rearrangements as a function of the external energy-supply, and show that they can be regarded as activated processes induced by a suitable "noise" effect. Here we use the word noise in a broad sense, referring to the internal non-equilibrium dynamics triggered by spatial random heterogeneities and coarsening. Finally, by exploring the interplay between the internal characteristic time-scale of the coarsening dynamics and the external time-scale associated with the imposed oscillating strain, we show that the system exhibits the phenomenon of stochastic resonance, thereby providing further credit to the mechanical activation scenario.Comment: 21 Pages, 9 figure

Preconditioning techniques for the coupled Stokes–Darcy problem: spectral and field-of-values analysis

We study the performance of some preconditioning techniques for a class of block three-by-three linear systems of equations arising from finite element discretizations of the coupled Stokes–Darcy flow problem. In particular, we investigate preconditioning techniques including block preconditioners, constraint preconditioners, and augmented Lagrangian-based ones. Spectral and field-of-value analyses are established for the exact versions of these preconditioners. The result of numerical experiments are reported to illustrate the performance of inexact variants of the various preconditioners used with flexible GMRES in the solution of a 3D test problem with large jumps in the permeability

Evidences of Bolgiano scaling in 3D Rayleigh-Benard convection

We present new results from high-resolution high-statistics direct numerical simulations of a tri-dimensional convective cell. We test the fundamental physical picture of the presence of both a Bolgiano-like and a Kolmogorov-like regime. We find that the dimensional predictions for these two distinct regimes (characterized respectively by an active and passive role of the temperature field) are consistent with our measurements.Comment: 4 pages, 3 figure