Experimental insights into deformation dynamics and intermittency in rapid granular shear flows

This work concerns the experimental study of rapid granular shear flows in annular Couette geometry. The flow is induced by continuous driving of the horizontal plate at the top of the granular bed in an annulus. The compressive pressure, driving torque, instantaneous bed height and rotational speed of the shearing plate are measured. Moreover, local stress fluctuations are measured in a medium made of steel spheres 2 and 3 mm in diameter. Both monodisperse packing and bidisperse packing are investigated to reveal the influence of size diversity in intermittent features of granular materials. Experiments are conducted in an annulus that can contain up to 15 kg of spherical steel balls. The shearing granular medium takes place via the rotation of the upper plate which compresses the material loaded inside the annulus. Fluctuations of compressive force are locally measured at the bottom of the annulus using a piezoelectric sensor. Rapid shear flow experiments are pursued at different compressive forces and shear rates and the sensitivity of fluctuations are then investigated by different means through monodisperse and bidisperse packings. Another important feature of rapid granular shear flows is the formation of ordered structures upon shearing. It requires a certain range for the amount of granular material (uniform size distribution) loaded in the system in order to obtain stable flows. This is studied more deeply in this thesis. The results of the current work bring some new insights into deformation dynamics and intermittency in rapid granular shear flows. The experimental apparatus is modified in comparison to earlier investigations. The measurements produce data for various quantities continuously sampled from the start of shearing to the end. Static failure and dynamic shearing ofa granular medium is investigated. The results of this work revealed some important features of failure dynamics and structure formation in the system. Furthermore, some computer simulations are performed in a 2D annulus to examine the nature of kinetic energy dissipation. It is found that turbulent flow models can statistically represent rapid granular flows with high accuracy. In addition to academic outcomes and scientific publications our results have a number of technological applications associated with grinding, mining and massive grain storages.

Periodic compression of an adiabatic gas: Intermittency-enhanced Fermi acceleration

A gas of non-interacting particles diffuses in a lattice of pulsating scatterers. In the finite-horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described by a master equation, leading to an asymptotic universal non-Maxwellian velocity distribution scaling as v∼t. The infinite-horizon case has intermittent dynamics which enhances the acceleration, leading to v∼t ln t and a non-universal distribution. © Copyright EPLA, 2013.

Intermittency reinjection probability density function with and without noise effects.

Intermittency phenomenon is a continuous route from regular to chaotic behaviour. Intermittency is an occurrence of a signal that alternates chaotic bursts between quasi-regular periods called laminar phases, driven by the so called reinjection probability density function (RPD). In this paper is introduced a new technique to obtain the RPD for type-II and III intermittency. The new RPD is more general than the classical one and includes the classical RPD as a particular case. The probabilities of the laminar length, the average laminar lengths and the characteristic relations are determined with and without lower bound of the reinjection in agreement with numerical simulations. Finally, it is analyzed the noise effect in intermittency. A method to obtain the noisy RPD is developed extending the procedure used in the noiseless case. The analytical results show a good agreement with numerical simulations.

Wind intermittency and CO2 reductions: the case of the spanish power system

Renewable energy sources are believed to reduce drastically greenhouse gas emissions that would otherwise be generated from fossil fuels used to generate electricity. This implies that a unit of renewable energy will replace a unit of fossil-fuel, with its CO2 emissions, on an equivalent basis (with no other effects on the grid). But, the fuel economy and emissions in the existing power systems are not proportional with the electricity production of intermittent sources due to cycling of the fossil fuel plants that make up the balance of the grid (i.e. changing the power output makes thermal units to operate less efficiently). This study focuses in the interactions between wind generation and thermal plants cycling, by establishing the levels of extra fuel use caused by decreased efficiencies of fossil back-up for wind electricity in Spain. We analyze the production of all thermal plants in 2011, studying different scenarios where wind penetration causes major deviations in programming, while we define a procedure for quantifying the carbon reductions by using emission factors and efficiency curves from the existing installations. The objectives are to discuss the real contributions of renewable energies to the environmental targets as well as suggest alternatives that would improve the reliability of future power systems.

Horizontal visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associatedHVgraphs.We showhowthe alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics.We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

Theory of intermittency applied to classical pathological cases

The classical theory of intermittency developed for return maps assumes uniform density of points reinjected from the chaotic to laminar region. Though it works fine in some model systems, there exist a number of so-called pathological cases characterized by a significant deviation of main characteristics from the values predicted on the basis of the uniform distribution. Recently, we reported on how the reinjection probability density (RPD) can be generalized. Here, we extend this methodology and apply it to different dynamical systems exhibiting anomalous type-II and type-III intermittencies. Estimation of the universal RPD is based on fitting a linear function to experimental data and requires no a priori knowledge on the dynamical model behind. We provide special fitting procedure that enables robust estimation of the RPD from relatively short data sets (dozens of points). Thus, the method is applicable for a wide variety of data sets including numerical simulations and real-life experiments. Estimated RPD enables analytic evaluation of the length of the laminar phase of intermittent behaviors. We show that the method copes well with dynamical systems exhibiting significantly different statistics reported in the literature. We also derive and classify characteristic relations between the mean laminar length and main controlling parameter in perfect agreement with data provided by numerical simulations

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Origin of scale-free intermittency in structural first-order phase transitions

16 pages, 22 figures

Multistable behavior above synchronization in a locally coupled Kuramoto model

A system of nearest neighbors Kuramoto-like coupled oscillators placed in a ring is studied above the critical synchronization transition. We find a richness of solutions when the coupling increases, which exists only within a solvability region (SR). We also find that the solutions possess different characteristics, depending on the section of the boundary of the SR where they appear. We study the birth of these solutions and how they evolve when the coupling strength increases, and determine the diagram of solutions in phase space.

Multifractality in plasma edge electrostatic turbulence

Plasma edge turbulence in Tokamak Chauffage Alfven Bresilien (TCABR) [R. M. O. Galvao et al., Plasma Phys. Contr. Fusion 43, 1181 (2001)] is investigated for multifractal properties of the fluctuating floating electrostatic potential measured by Langmuir probes. The multifractality in this signal is characterized by the full multifractal spectra determined by applying the wavelet transform modulus maxima. In this work, the dependence of the multifractal spectrum with the radial position is presented. The multifractality degree inside the plasma increases with the radial position reaching a maximum near the plasma edge and becoming almost constant in the scrape-off layer. Comparisons between these results with those obtained for random test time series with the same Hurst exponents and data length statistically confirm the reported multifractal behavior. Moreover, the persistence of these signals, characterized by their Hurst exponent, present radial profile similar to the deterministic component estimated from analysis based on dynamical recurrences. (C) 2008 American Institute of Physics.

Low dimensional behavior in three-dimensional coupled map lattices

The analysis of one-, two-, and three-dimensional coupled map lattices is here developed under a statistical and dynamical perspective. We show that the three-dimensional CML exhibits low dimensional behavior with long range correlation and the power spectrum follows 1/f noise. This approach leads to an integrated understanding of the most important properties of these universal models of spatiotemporal chaos. We perform a complete time series analysis of the model and investigate the dependence of the signal properties by change of dimension. (c) 2008 Elsevier Ltd. All rights reserved.

Observation of generalized synchronization of chaos in a driven chaotic system

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the driving signal.

Turbulent spots in boundary layers in a free-piston shock-tunnel flow

In this paper, experiments to detect turbulent spots in the transitional boundary layers, formed on a flat plate in a free-piston shock tunnel how, are reported. Experiments indicate that thin-film heat-transfer gauges are suitable for identifying turbulent-spot activity and can be used to identify parameters such as the convection rate of spots and the intermittency of turbulence.

Transforming chaos to periodic oscillations

We demonstrate that the dynamics of an autonomous chaotic class C laser can be controlled to a periodic state via external modulation of the pump. In the absence of modulation, above the chaos threshold, the laser exhibits Lorenz-like chaotic pulsations. The average amplitude and frequency of these pulsations depend on the pump power. We find that there exist parameter windows where modulation of the pump power extinguishes the chaos in favor of simpler periodic behavior. Moreover we find a number of locking ratios between the pump and laser output follow the Farey sequence.

Modelagem da dispersão de odores em ambientes urbanos

O presente trabalho investigou o problema da modelagem da dispersão de compostos odorantes em presença de obstáculos (cúbicos e com forma complexa) sob condição de estabilidade atmosférica neutra. Foi empregada modelagem numérica baseada nas equações de transporte (CFD1) bem como em modelos algébricos baseados na pluma Gausseana (AERMOD2, CALPUFF3 e FPM4). Para a validação dos resultados dos modelos e a avaliação do seu desempenho foram empregados dados de experimentos em túnel de vento e em campo. A fim de incluir os efeitos da turbulência atmosférica na dispersão, dois diferentes modelos de sub-malha associados à Simulação das Grandes Escalas (LES5) foram investigados (Smagorinsky dinâmico e WALE6) e, para a inclusão dos efeitos de obstáculos na dispersão nos modelos Gausseanos, foi empregado o modelo PRIME7. O uso do PRIME também foi proposto para o FPM como uma inovação. De forma geral, os resultados indicam que o uso de CFD/LES é uma ferramenta útil para a investigação da dispersão e o impacto de compostos odorantes em presença de obstáculos e também para desenvolvimento dos modelos Gausseanos. Os resultados também indicam que o modelo FPM proposto, com a inclusão dos efeitos do obstáculo baseado no PRIME também é uma ferramenta muito útil em modelagem da dispersão de odores devido à sua simplicidade e fácil configuração quando comparado a modelos mais complexos como CFD e mesmo os modelos regulatórios AERMOD e CALPUFF. A grande vantagem do FPM é a possibilidade de estimar-se o fator de intermitência e a relação pico-média (P/M), parâmetros úteis para a avaliação do impacto de odores. Os resultados obtidos no presente trabalho indicam que a determinação dos parâmetros de dispersão para os segmentos de pluma, bem como os parâmetros de tempo longo nas proximidades da fonte e do obstáculo no modelo FPM pode ser melhorada e simulações CFD podem ser usadas como uma ferramenta de desenvolvimento para este propósito. Palavras chave: controle de odor, dispersão, fluidodinâmica computacional, modelagem matemática, modelagem gaussiana de pluma flutuante, simulação de grandes vórtices (LES).