Edge of Chaos and Genesis of Turbulence

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable travelling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space

Existence, uniqueness and analyticity of space-periodic solutions to the regularised long-wave equation

We consider space-periodic evolutionary and travelling-wave solutions to the regularised long-wave equation (RLWE) with damping and forcing. We establish existence, uniqueness and smoothness of the evolutionary solutions for smooth initial conditions, and global in time spatial analyticity of such solutions for analytical initial conditions. The width of the analyticity strip decays at most polynomially. We prove existence of travelling-wave solutions and uniqueness of travelling waves of a sufficiently small norm. The importance of damping is demonstrated by showing that the problem of finding travelling-wave solutions to the undamped RLWE is not well-posed. Finally, we demonstrate the asymptotic convergence of the power series expansion of travelling waves for a weak forcing.Comment: 29 pp., 4 figures, 44 reference

A novel type of intermittency in a nonlinear dynamo in a compressible flow

The transition to intermittent mean--field dynamos is studied using numerical simulations of isotropic magnetohydrodynamic turbulence driven by a helical flow. The low-Prandtl number regime is investigated by keeping the kinematic viscosity fixed while the magnetic diffusivity is varied. Just below the critical parameter value for the onset of dynamo action, a transient mean--field with low magnetic energy is observed. After the transition to a sustained dynamo, the system is shown to evolve through different types of intermittency until a large--scale coherent field with small--scale turbulent fluctuations is formed. Prior to this coherent field stage, a new type of intermittency is detected, where the magnetic field randomly alternates between phases of coherent and incoherent large--scale spatial structures. The relevance of these findings to the understanding of the physics of mean--field dynamo and the physical mechanisms behind intermittent behavior observed in stellar magnetic field variability are discussed.Comment: 19 pages, 13 figure

Nonintegrable Interaction of Ion-Acoustic and Electromagnetic Waves in a Plasma

In this paper we re-examine the one-dimensional interaction of electromagnetic and ion acoustic waves in a plasma. Our model is similar to one solved by Rao et al. (Phys. Fluids, vol. 26, 2488 (1983)) under a number of analytical approximations. Here we perform a numerical investigation to examine the stability of the model. We find that for slightly over dense plasmas, the propagation of stable solitary modes can occur in an adiabatic regime where the ion acoustic electric field potential is enslaved to the electromagnetic field of a laser. But if the laser intensity or plasma density increases or the laser frequency decreases, the adiabatic regime loses stability via a transition to chaos. New asymptotic states are attained when the adiabatic regime no longer exists. In these new states, the plasma becomes rarefied, and the laser field tends to behave like a vacuum field.Comment: 19 pages, REVTeX, 6 ps figures, accepted for publication in Phys. Rev.

Chaotic saddles in nonlinear modulational interactions in a plasma

A nonlinear model of modulational processes in the subsonic regime involving a linearly unstable wave and two linearly damped waves with different damping rates in a plasma is studied numerically. We compute the maximum Lyapunov exponent as a function of the damping rates in a two-parameter space, and identify shrimp-shaped self-similar structures in the parameter space. By varying the damping rate of the low-frequency wave, we construct bifurcation diagrams and focus on a saddle-node bifurcation and an interior crisis associated with a periodic window. We detect chaotic saddles and their stable and unstable manifolds, and demonstrate how the connection between two chaotic saddles via coupling unstable periodic orbits can result in a crisis-induced intermittency. The relevance of this work for the understanding of modulational processes observed in plasmas and fluids is discussed.Comment: Physics of Plasmas, in pres

Detection of Current Sheets and Magnetic Reconnections a the Turbulent Leading Edge of an Interplanetary Coronal Mass Ejection

The relation between current sheets, turbulence, and magnetic reconnections at the leading edge of an interplanetary coronal mass ejection detected by four Cluster spacecraft on 2005 January 21 is studied. We report the observational evidence of two magnetically reconnected current sheets in the vicinity of a front magnetic cloud boundary layer with the following characteristics: (1) a Kolmogorov power spectrum in the inertial subrange of the magnetic turbulence, (2) the scaling exponent of structure functions of magnetic fluctuations exhibiting multi-fractal scaling predicted by the She-Leveque magnetohydrodynamic model, and (3) bifurcated current sheets with the current density computed by both single-spacecraft and multi-spacecraft techniques

Reversible changes in protein phosphorylation during germinal vesicle breakdown and pronuclear formation in bovine oocytes in vitro

This study examined the event of protein phosphorylation in bovine oocytes during germinal vesicle breakdown (GVBD) and formation of pronuclei following fertilisation in vitro. Immature oocytes were obtained from abattoir materials and cultured in vitro. The oocytes were labelled with [32P]orthophosphate at 3 h intervals from 0 to 12 h following maturation in culture or from 3 to 18 h following insemination. One-dimensional gel electrophoresis indicated that levels of protein phosphorylation are low prior to GVBD. However, the levels of protein phosphorylation at approximately 40 kDa, 27 kDa, 23 kDa and 18 kDa increased substantially following GVBD and then decreased gradually as maturation in culture progressed. In contrast, the levels of protein phosphorylation increased gradually in the oocytes following pronucleus formation. Further, two-dimensional gel electrophoresis indicated that the protein at approximately 18 kDa reversibly changed in the oocytes during maturation and fertilisation. These results indicate that the reversible changes of this phosphoprotein may be related to either cell cycle transition or pronucleus formation during maturation and fertilisation in bovine oocytes.</p

Seismic velocities within the sedimentary succession of the Canada Basin and southern Alpha-Mendeleev Ridge, Arctic Ocean : evidence for accelerated porosity reduction?

Author Posting. © Crown Copyright, 2015. This article is posted here by permission of Oxford University Press for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 204 (2016): 1-20, doi:10.1093/gji/ggv416.The Canada Basin and the southern Alpha-Mendeleev ridge complex underlie a significant proportion of the Arctic Ocean, but the geology of this undrilled and mostly ice-covered frontier is poorly known. New information is encoded in seismic wide-angle reflections and refractions recorded with expendable sonobuoys between 2007 and 2011. Velocity–depth samples within the sedimentary succession are extracted from published analyses for 142 of these records obtained at irregularly spaced stations across an area of 1.9E + 06 km2. The samples are modelled at regional, subregional and station-specific scales using an exponential function of inverse velocity versus depth with regionally representative parameters determined through numerical regression. With this approach, smooth, non-oscillatory velocity–depth profiles can be generated for any desired location in the study area, even where the measurement density is low. Practical application is demonstrated with a map of sedimentary thickness, derived from seismic reflection horizons interpreted in the time domain and depth converted using the velocity–depth profiles for each seismic trace. A thickness of 12–13 km is present beneath both the upper Mackenzie fan and the middle slope off of Alaska, but the sedimentary prism thins more gradually outboard of the latter region. Mapping of the observed-to-predicted velocities reveals coherent geospatial trends associated with five subregions: the Mackenzie fan; the continental slopes beyond the Mackenzie fan; the abyssal plain; the southwestern Canada Basin; and, the Alpha-Mendeleev magnetic domain. Comparison of the subregional velocity–depth models with published borehole data, and interpretation of the station-specific best-fitting model parameters, suggests that sandstone is not a predominant lithology in any of the five subregions. However, the bulk sand-to-shale ratio likely increases towards the Mackenzie fan, and the model for this subregion compares favourably with borehole data for Miocene turbidites in the eastern Gulf of Mexico. The station-specific results also indicate that Quaternary sediments coarsen towards the Beaufort-Mackenzie and Banks Island margins in a manner that is consistent with the variable history of Laurentide Ice Sheet advance documented for these margins. Lithological factors do not fully account for the elevated velocity–depth trends that are associated with the southwestern Canada Basin and the Alpha-Mendeleev magnetic domain. Accelerated porosity reduction due to elevated palaeo-heat flow is inferred for these regions, which may be related to the underlying crustal types or possibly volcanic intrusion of the sedimentary succession. Beyond exploring the variation of an important physical property in the Arctic Ocean basin, this study provides comparative reference for global studies of seismic velocity, burial history, sedimentary compaction, seismic inversion and overpressure prediction, particularly in mudrock-dominated successions

Nonlinear stability of solitons against strong external perturbations

We study soliton stability under the action of strong external perturbations. Limits on the weak perturbation approach are established with the help of average Lagrangian methods and full simulations. We found that for the same relative perturbation, larger amplitude solitons develop instability earlier than weaker amplitude solitons.F. B. Rizzato, G. I. de Oliveira, and A. C.-L. Chia