Coupled complex Ginzburg-Landau systems with saturable nonlinearity and asymmetric cross-phase modulation

We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg-Landau systems under the added assumption of saturable media. When the saturation parameter is set to zero, we recover a general complex cubic Ginzburg-Landau system with XPM. We first derive conditions for the existence of bounded dynamics, approximating the absorbing set for solutions. We use this to then determine conditions for amplitude death of a single wavefunction. We also construct exact plane wave solutions, and determine conditions for their modulational instability. In a degenerate limit where dispersion and nonlinearity balance, we reduce our system to a saturable nonlinear Schr\"odinger system with XPM parameters, and we demonstrate the existence and behavior of spatially heterogeneous stationary solutions in this limit. Using numerical simulations we verify the aforementioned analytical results, while also demonstrating other interesting emergent features of the dynamics, such as spatiotemporal chaos in the presence of modulational instability. In other regimes, coherent patterns including uniform states or banded structures arise, corresponding to certain stable stationary states. For sufficiently large yet equal XPM parameters, we observe a segregation of wavefunctions into different regions of the spatial domain, while when XPM parameters are large and take different values, one wavefunction may decay to zero in finite time over the spatial domain (in agreement with the amplitude death predicted analytically). While saturation will often regularize the dynamics, such transient dynamics can still be observed - and in some cases even prolonged - as the saturability of the media is increased, as the saturation may act to slow the timescale.Comment: 36 page

Production of cold fragments in nucleus-nucleus collisions in the Fermi-energy domain

The reaction mechanism of nucleus-nucleus collisions at projectile energies around the Fermi energy is investigated with emphasis on the production of fragmentation-like residues. The results of simulations are compared to experimental mass distributions of elements with Z = 21 - 29 observed in the reactions 86Kr+124,112Sn at 25 AMeV. The model of incomplete fusion is modified and a component of excitation energy of the cold fragment dependent on isospin asymmetry is introduced. The modifications in the model of incomplete fusion appear consistent with both overall model framework and available experimental data. A prediction is provided for the production of very neutron-rich nuclei using a secondary beam of 132Sn where e.g. the reaction 132Sn+238U at 28 AMeV appears as a possible alternative to the use of fragmentation reactions at higher energies.Comment: LaTeX, 15 pages, 5 figures, minor modifications, accepted for publication in Nuclear Physics

The health care burden and societal impact of acute otitis media in seven European countries: results of an Internet survey

This paper estimates medical resource use, direct costs, and productivity losses and costs (indirect costs) during episodes of acute otitis media (AOM) in young children. A 24-item Internet questionnaire was developed for parents in Belgium (Flanders), France, Germany, Italy, The Netherlands, Spain, and the United Kingdom (UK) to report health care resource use and productivity losses during the most recent episode of AOM in their child, younger than 5 years. The percentage who did not seek medical help for AOM was considerable in The Netherlands (28.3%) and the UK (19.7%). Antibiotic use was high, ranging from 60.8% (Germany) to 87.1% (Italy). Total costs per AOM episode ranged from D 332.00 (The Netherlands) to D 752.49 (UK). Losses in productivity accounted for 61% (France) to 83% (Germany) of the total costs. AOM poses a significant medical and economic burden to society

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200, and it decreases to about 20% for Re=2500. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.Comment: 11 pages, 26 (sub)figure

Fractal Stability Border in Plane Couette Flow

We study the dynamics of localised perturbations in plane Couette flow with periodic lateral boundary conditions. For small Reynolds number and small amplitude of the initial state the perturbation decays on a viscous time scale $t \propto Re$. For Reynolds number larger than about 200, chaotic transients appear with life times longer than the viscous one. Depending on the type of the perturbation isolated initial conditions with infinite life time appear for Reynolds numbers larger than about 270--320. In this third regime, the life time as a function of Reynolds number and amplitude is fractal. These results suggest that in the transition region the turbulent dynamics is characterised by a chaotic repeller rather than an attractor.Comment: 4 pages, Latex, 4 eps-figures, submitted to Phys. Rev. Le