Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUniversal Scaling Laws for Large Events in Driven Nonequilibrium Systems
89
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
For many driven-nonequilibrium systems, the probability distribution functions of magnitude and recurrence-time of large events follow a powerlaw indicating a strong temporal correlation. In this paper we argue why these probability distribution functions are ubiquitous in driven nonequilibrium systems, and we derive universal scaling laws connecting the magnitudes, recurrence-time, and spatial intervals of large events. The relationships between the scaling exponents have also been studied. We show that the ion-channel current in Voltage-dependent Anion Channels obeys the universal scaling law.
rate research
Read More
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parametrizations of weakly coupled dynamical systems. Such parametrizations yield a set of stochastic integro-differential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integro-differential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equations-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings support, on the one hand, the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations.
We present a comprehensive investigation of $epsilon$-entropy, $h(epsilon)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the $epsilon$-entropy based on the exit-time statistics. The advantages of this method are demonstrated in examples of deterministic diffusive maps, intermittent maps, stochastic self-affine and multi-affine signals and experimental turbulent data. Concerning turbulence, the multifractal formalism applied to the exit time statistics allows us to predict that $h(epsilon)sim epsilon^{-3}$ for velocity time measurement. This power law is independent of the presence of intermittency and has been confirmed by the experimental data analysis. Moreover, we show that the $epsilon$-entropy density of a 3-dimensional velocity field is affected by the correlations induced by the sweeping of large scales.
In this paper we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of vortical structures induced by the shear. By using direct numerical simulations, we show that the refined Kolmogorov similarity is broken and a new form of similarity is observed, in agreement to previous results obtained in turbulent boundary layers. As a consequence, the intermittency of velocity fluctuations increases with respect to homogeneous and isotropic turbulence. We find here that the statistical properties of the energy dissipation are practically unchanged with respect to homogeneous isotropic conditions, while the increased intermittency is entirely captured in terms of the new similarity law.
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades: period and chaotic- band doubling of attractors. Approximate Pascal triangles are exhibited by the sets of lengths of supercycle diameters and by the sets of widths of opening bands. Additionally, power-law scaling manifests along periodic attractor supercycle positions and chaotic band splitting points. Consequently, the attractor at the mutual accumulation point of the doubling cascades, the onset of chaos, displays both Gaussian and power-law distributions. Their combined existence implies both ordinary and exceptional statistical-mechanical descriptions of dynamical properties.
The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears. Recently such behavior was observed and some of the earlier predicted exponents were found in experiments on several types of systems described by a model of a modulated oscillator. Here we establish the range where different scaling behavior is displayed and show how the crossover between different types of scaling occurs. The analysis is done for a nonlinear oscillator with two coexisting stable states of forced vibrations. Our numerical calculations, based on the the instanton method allow the mapping of the entire parameter range of bi-stability. We find the regions where the scaling exponents are 1 or 3/2, depending on the damping. The exponent 3/2 is found to extend much further from the bifurcation then were it would be expected to hold as a result of an over-damped soft mode. We also uncover a new scaling behavior with exponent of $approx$ 1.3 which extends, numerically, beyond the close vicinity of the bifurcation point.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
