Turbulence transition and the edge of chaos in pipe flow

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.Comment: 4 pages, 5 figure

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

Tree Diversity Drives Forest Stand Resistance to Natural Disturbances

Purpose of review Forests are frequently exposed to natural disturbances, which are likely to increase with global change, and may jeopardize the delivery of ecosystem services. Mixed-species forests have often been shown to be more productive than monocultures, but it is unclear whether this results from mixed stands being in part more resistant to various biotic and abiotic disturbance factors. This review investigates the relationships between tree diversity and stand resistance to natural disturbances and explores the ecological mechanisms behind the observed relationships.Recent findings Mixed forests appear to be more resistant than monocultures to small mammalian herbivores, soil-borne fungal diseases and specialized insect herbivores. Admixing broadleaves to conifers also increases the resistance to fire and windstorms when compared to pure conifer stands. However, mixed forests may be more affected by drought depending on the species in the mixture.Summary Overall, our findings suggest that mixed forests are more resistant to natural disturbances that are relatively small-scale and selective in their effect. However, benefits provided by mixtures are less evident for larger-scale disturbances. Higher tree diversity translates into increased resistance to disturbances as a result of ecological trait complementarity among species, reduction of fuel and food resources for herbivores, enhancement of diversion or disruption processes, and multi-trophic interactions such as predation or symbiosis.To promote resistance, the selection of tree species with different functional characteristics appears more important than increasing only the number of species in the stand. Trees with different levels of susceptibility to different hazards should be intermixed in order to reduce the amount of exposed resources and to generate barriers against contagion.However, more research is needed to further improve associational resistance in mixed forests, through a better understanding of the most relevant spatial and temporal scales of species interactions and to optimize the overall provision of ecosystem services

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.Comment: for the proceedings of statphys 2

Immunization with HIV protease peptides linked to syngeneic erythrocytes

New potent vaccine adjuvants are desirable for increasing the efficacy of novel vaccine modalities such as DNA and peptides. We therefore tested if syngeneic erythrocytes could serve as delivery vectors for selected HIV peptides and compared the potency of these constructs to immunization with peptides in phosphate buffered saline or in incomplete Freunds adjuvant. Immunization of mice with peptides in a low dose (5 ng) coupled to erythrocytes induced a weak immune response in mice. These peptides alone (5 μg) gave no immune responses, while formulating the peptides (50 μg) in IFA induced strong homologous immunity as well as prominent cross reactivity to a related mutant epitope. Thus, vaccine delivery using syngeneic erythrocytes, although attractive for clinical use, might be of limited value due to the low amount of antigen that can be loaded per erythrocyte

Lifetime statistics in transitional pipe flow

Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties of these decaying states within direct numerical simulations for Reynolds numbers up to 2200 and in pipes with lengths equal to 5, 9 and 15 times the diameter. We show that the choice of the ensemble of initial conditions affects the short time parts of lifetime distributions, but does not change the characteristic decay rate for long times. Comparing lifetimes for pipes of different length we notice a linear increase in the characteristic lifetime with length, which reproduces the experimental results when extrapolated to 30 diameters, the length of an equilibrium turbulent puff at these Reynolds numbers.Comment: 10 pages, 11 figure

Travelling waves in pipe flow

A family of three-dimensional travelling waves for flow through a pipe of circular cross section is identified. The travelling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.Comment: 4 pages, 5 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

Quasielastic 12C(e,e'p) Reaction at High Momentum Transfer

We measured the 12C(e,e'p) cross section as a function of missing energy in parallel kinematics for (q,w) = (970 MeV/c, 330 MeV) and (990 MeV/c, 475 MeV). At w=475 MeV, at the maximum of the quasielastic peak, there is a large continuum (E_m > 50 MeV) cross section extending out to the deepest missing energy measured, amounting to almost 50% of the measured cross section. The ratio of data to DWIA calculation is 0.4 for both the p- and s-shells. At w=330 MeV, well below the maximum of the quasielastic peak, the continuum cross section is much smaller and the ratio of data to DWIA calculation is 0.85 for the p-shell and 1.0 for the s-shell. We infer that one or more mechanisms that increase with $\omega$ transform some of the single-nucleon-knockout into multinucleon knockout, decreasing the valence knockout cross section and increasing the continuum cross section.Comment: 14 pages, 7 figures, Revtex (multicol, prc and aps styles), to appear in Phys Rev