Internal Temperature Decline Rate in Beef Primals is Reduced in Heavier Carcasses

The objective of this study was to determine the influence of increasing beef hot carcass weights on internal temperature decline during chilling

Winding number instability in the phase-turbulence regime of the Complex Ginzburg-Landau Equation

We give a statistical characterization of states with nonzero winding number in the Phase Turbulence (PT) regime of the one-dimensional Complex Ginzburg-Landau equation. We find that states with winding number larger than a critical one are unstable, in the sense that they decay to states with smaller winding number. The transition from Phase to Defect Turbulence is interpreted as an ergodicity breaking transition which occurs when the range of stable winding numbers vanishes. Asymptotically stable states which are not spatio-temporally chaotic are described within the PT regime of nonzero winding number.Comment: 4 pages,REVTeX, including 4 Figures. Latex (or postscript) version with figures available at http://formentor.uib.es/~montagne/textos/nupt

Dynamics and Selection of Giant Spirals in Rayleigh-Benard Convection

For Rayleigh-Benard convection of a fluid with Prandtl number \sigma \approx 1, we report experimental and theoretical results on a pattern selection mechanism for cell-filling, giant, rotating spirals. We show that the pattern selection in a certain limit can be explained quantitatively by a phase-diffusion mechanism. This mechanism for pattern selection is very different from that for spirals in excitable media

Stochastic to deterministic crossover of fractal dimension for a Langevin equation

Using algorithms of Higuchi and of Grassberger and Procaccia, we study numerically how fractal dimensions cross over from finite-dimensional Brownian noise at short time scales to finite values of deterministic chaos at longer time scales for data generated from a Langevin equation that has a strange attractor in the limit of zero noise. Our results suggest that the crossover occurs at such short time scales that there is little chance of finite-dimensional Brownian noise being incorrectly identified as deterministic chaos.Comment: 12 pages including 3 figures, RevTex and epsf. To appear Phys. Rev. E, April, 199

Studies of Phase Turbulence in the One Dimensional Complex Ginzburg-Landau Equation

The phase-turbulent (PT) regime for the one dimensional complex Ginzburg-Landau equation (CGLE) is carefully studied, in the limit of large systems and long integration times, using an efficient new integration scheme. Particular attention is paid to solutions with a non-zero phase gradient. For fixed control parameters, solutions with conserved average phase gradient $\nu$ exist only for $|\nu|$ less than some upper limit. The transition from phase to defect-turbulence happens when this limit becomes zero. A Lyapunov analysis shows that the system becomes less and less chaotic for increasing values of the phase gradient. For high values of the phase gradient a family of non-chaotic solutions of the CGLE is found. These solutions consist of spatially periodic or aperiodic waves travelling with constant velocity. They typically have incommensurate velocities for phase and amplitude propagation, showing thereby a novel type of quasiperiodic behavior. The main features of these travelling wave solutions can be explained through a modified Kuramoto-Sivashinsky equation that rules the phase dynamics of the CGLE in the PT phase. The latter explains also the behavior of the maximal Lyapunov exponents of chaotic solutions.Comment: 16 pages, LaTeX (Version 2.09), 10 Postscript-figures included, submitted to Phys. Rev.

The dynamics of thin vibrated granular layers

We describe a series of experiments and computer simulations on vibrated granular media in a geometry chosen to eliminate gravitationally induced settling. The system consists of a collection of identical spherical particles on a horizontal plate vibrating vertically, with or without a confining lid. Previously reported results are reviewed, including the observation of homogeneous, disordered liquid-like states, an instability to a `collapse' of motionless spheres on a perfect hexagonal lattice, and a fluctuating, hexagonally ordered state. In the presence of a confining lid we see a variety of solid phases at high densities and relatively high vibration amplitudes, several of which are reported for the first time in this article. The phase behavior of the system is closely related to that observed in confined hard-sphere colloidal suspensions in equilibrium, but with modifications due to the effects of the forcing and dissipation. We also review measurements of velocity distributions, which range from Maxwellian to strongly non-Maxwellian depending on the experimental parameter values. We describe measurements of spatial velocity correlations that show a clear dependence on the mechanism of energy injection. We also report new measurements of the velocity autocorrelation function in the granular layer and show that increased inelasticity leads to enhanced particle self-diffusion.Comment: 11 pages, 7 figure

A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics

In a Ginzburg-Landau model for parametrically driven waves a transition between a state of ordered and one of disordered spatio-temporal defect chaos is found. To characterize the two different chaotic states and to get insight into the break-down of the order, the trajectories of the defects are tracked in detail. Since the defects are always created and annihilated in pairs the trajectories form loops in space time. The probability distribution functions for the size of the loops and the number of defects involved in them undergo a transition from exponential decay in the ordered regime to a power-law decay in the disordered regime. These power laws are also found in a simple lattice model of randomly created defect pairs that diffuse and annihilate upon collision.Comment: 4 pages 5 figure

Mean flow and spiral defect chaos in Rayleigh-Benard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. Firstly, we show that, in the absence of mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wavenumbers that approach those uniquely selected by focus-type singularities, which, in the absence of mean flow, lie at the zig-zag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with Rayleigh number.Comment: 14 pages, 19 figure

Scarred Patterns in Surface Waves

Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.Comment: 9 pages, 10 figures (low resolution gif files). Updated and added references and text. For high resolution images: http://physics.clarku.edu/~akudrolli/stadium.htm

Extensive Chaos in the Nikolaevskii Model

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $\epsilon$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.Comment: 4 pages (including 5 figures) LaTeX file. Submitted to Phys. Rev. Let