Infinities of stable periodic orbits in systems of coupled oscillators

We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting example the existence of an infinite family of stable periodic orbits that accumulate on the cycling, whereas for a free-running example loss of stability of the cycling gives rise to a single quasiperiodic or chaotic attractor

Nearest pattern interaction and global pattern formation

We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general, we found that this study is relevant in particular to the pattern formation on a periodically vibrated granular layer, as it gives a unified perspective of the experimentally observed pattern dynamics such as oscillon and stripe formations, skew-varicose and crossroll instabilities, and also a kink formation and decoration

Coarse-grained reconfigurable array architectures

Coarse-Grained Reconfigurable Array (CGRA) architectures accelerate the same inner loops that benefit from the high ILP support in VLIW architectures. By executing non-loop code on other cores, however, CGRAs can focus on such loops to execute them more efficiently. This chapter discusses the basic principles of CGRAs, and the wide range of design options available to a CGRA designer, covering a large number of existing CGRA designs. The impact of different options on flexibility, performance, and power-efficiency is discussed, as well as the need for compiler support. The ADRES CGRA design template is studied in more detail as a use case to illustrate the need for design space exploration, for compiler support and for the manual fine-tuning of source code

Fundamental scaling laws of on-off intermittency in a stochastically driven dissipative pattern forming system

Noise driven electroconvection in sandwich cells of nematic liquid crystals exhibits on-off intermittent behaviour at the onset of the instability. We study laser scattering of convection rolls to characterize the wavelengths and the trajectories of the stochastic amplitudes of the intermittent structures. The pattern wavelengths and the statistics of these trajectories are in quantitative agreement with simulations of the linearized electrohydrodynamic equations. The fundamental $\tau^{-3/2}$ distribution law for the durations $\tau$ of laminar phases as well as the power law of the amplitude distribution of intermittent bursts are confirmed in the experiments. Power spectral densities of the experimental and numerically simulated trajectories are discussed.Comment: 20 pages and 17 figure

Controlled Dynamics of Interfaces in a Vibrated Granular Layer

We present experimental study of a topological excitation, {\it interface}, in a vertically vibrated layer of granular material. We show that these interfaces, separating regions of granular material oscillation with opposite phases, can be shifted and controlled by a very small amount of an additional subharmonic signal, mixed with the harmonic driving signal. The speed and the direction of interface motion depends sensitively on the phase and the amplitude of the subharmonic driving.Comment: 4 pages, 6 figures, RevTe

A Continuum Description of Vibrated Sand

The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent impact of the grains on the plate. A linear stability theory reveals that the waves are excited non-resonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continuum scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with experiments. For strong hysteresis we find localized oscillon solutions.Comment: paper has been considerably extended (11 instead of 6 pages; 6 instead of 4 figures) much better agreement with experiment. obtain now oscillons in 1 dimensio

Mass coupling and Q−1ofimpurity−limitednormalQ^{-1} of impurity-limited normal ^3$He in a torsion pendulum

We present results of the $Q^{-1}$ and period shift, $\Delta P$, for $^3$He confined in a 98% nominal open aerogel on a torsion pendulum. The aerogel is compressed uniaxially by 10% along a direction aligned to the torsion pendulum axis and was grown within a 400 $\mu$m tall pancake (after compression) similar to an Andronikashvili geometry. The result is a high $Q$ pendulum able to resolve $Q^{-1}$ and mass coupling of the impurity-limited $^3$He over the whole temperature range. After measuring the empty cell background, we filled the cell above the critical point and observe a temperature dependent period shift, $\Delta P$, between 100 mK and 3 mK that is 2.9$$ of the period shift (after filling) at 100 mK. The $Q^{-1}$ due to the $^3$He decreases by an order of magnitude between 100 mK and 3 mK at a pressure of $0.14\pm0.03$ bar. We compare the observable quantities to the corresponding calculated $Q^{-1}$ and period shift for bulk $^3$He.Comment: 8 pages, 3 figure

Dimension reduction for systems with slow relaxation

We develop reduced, stochastic models for high dimensional, dissipative dynamical systems that relax very slowly to equilibrium and can encode long term memory. We present a variety of empirical and first principles approaches for model reduction, and build a mathematical framework for analyzing the reduced models. We introduce the notions of universal and asymptotic filters to characterize `optimal' model reductions for sloppy linear models. We illustrate our methods by applying them to the practically important problem of modeling evaporation in oil spills.Comment: 48 Pages, 13 figures. Paper dedicated to the memory of Leo Kadanof

Continuum-type stability balloon in oscillated granular layers

The stability of convection rolls in a fluid heated from below is limited by secondary instabilities, including the skew-varicose and crossroll instabilities. We observe a stability boundary defined by the same instabilities in stripe patterns in a vertically oscillated granular layer. Molecular dynamics simulations show that the mechanism of the skew-varicose instability in granular patterns is similar to that in convection. These results suggest that pattern formation in granular media can be described by continuum models analogous to those used in fluid systems.Comment: 4 pages, 6 ps figs, submitted to PR

Volatility clustering and scaling for financial time series due to attractor bubbling

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or