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

Shear-flow transition: the basin boundary

The structure of the basin of attraction of a stable equilibrium point is investigated for a dynamical system (W97) often used to model transition to turbulence in shear flows. The basin boundary contains not only an equilibrium point Xlb but also a periodic orbit P, and it is the latter that mediates the transition. Orbits starting near Xlb relaminarize. We offer evidence that this is due to the extreme narrowness of the region complementary to basin of attraction in that part of phase space near Xlb. This leads to a proposal for interpreting the 'edge of chaos' in terms of more familiar invariant sets.Comment: 11 pages; submitted for publication in Nonlinearit

Liquid Relationship to Possessions

This study investigates consumers' relationship to possessions in the condition of contemporary global nomadism. Prior research argues that consumers form enduring and strong attachments to possessions because of their centrality to identity projects. This role is heightened in life transitions including cross-border movements as possessions anchor consumer's identities either to their homeland or to the host country. This study reexamines this claim via in-depth interviews with elite global nomads, deterritorialized consumers who engage in serial relocation and frequent short-term international mobility. An alternative relationship to possessions characterized by detachment and flexibility emerges, which is termed “liquid.” Three characteristics of a liquid relationship to possessions are identified: temporary situational value, use-value, and immateriality. The study outlines a logic of nomadic consumption, that of instrumentality, where possessions and practices are strategic resources in managing mobility. A liquid perspective on possessions expands current understandings of materiality, acculturation, and globalization

Semiclassical cross section correlations

We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth classical limit the autocorrelation function of such matrix elements has two contributions with relative weights determined by classical dynamics. We show how the random matrix result can be obtained if the operator approaches a projector onto a single initial state. The expressions are verified in calculations for the kicked rotor.Comment: 6 pages, 2 figure

Anomalous power law of quantum reversibility for classically regular dynamics

The Loschmidt Echo M(t) (defined as the squared overlap of wave packets evolving with two slightly different Hamiltonians) is a measure of quantum reversibility. We investigate its behavior for classically quasi-integrable systems. A dominant regime emerges where M(t) ~ t^{-alpha} with alpha=3d/2 depending solely on the dimension d of the system. This power law decay is faster than the result ~ t^{-d} for the decay of classical phase space densities

Reflection of Channel-Guided Solitons at Junctions in Two-Dimensional Nonlinear Schroedinger Equation

Solitons confined in channels are studied in the two-dimensional nonlinear Schr\"odinger equation. We study the dynamics of two channel-guided solitons near the junction where two channels are merged. The two solitons merge into one soliton, when there is no phase shift. If a phase difference is given to the two solitons, the Josephson oscillation is induced. The Josephson oscillation is amplified near the junction. The two solitons are reflected when the initial velocity is below a critical value.Comment: 3 pages, 2 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

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

An experimental evaluation of software redundancy as a strategy for improving reliability

The strategy of using multiple versions of independently developed software as a means to tolerate residual software design faults is suggested by the success of hardware redundancy for tolerating hardware failures. Although, as generally accepted, the independence of hardware failures resulting from physical wearout can lead to substantial increases in reliability for redundant hardware structures, a similar conclusion is not immediate for software. The degree to which design faults are manifested as independent failures determines the effectiveness of redundancy as a method for improving software reliability. Interest in multi-version software centers on whether it provides an adequate measure of increased reliability to warrant its use in critical applications. The effectiveness of multi-version software is studied by comparing estimates of the failure probabilities of these systems with the failure probabilities of single versions. The estimates are obtained under a model of dependent failures and compared with estimates obtained when failures are assumed to be independent. The experimental results are based on twenty versions of an aerospace application developed and certified by sixty programmers from four universities. Descriptions of the application, development and certification processes, and operational evaluation are given together with an analysis of the twenty versions

Quantitative reduction of RyR1 protein caused by a single-allele frameshift mutation in RYR1 ex36 impairs the strength of adult skeletal muscle fibres

Here we characterized a mouse model knocked-in for a frameshift mutation in RYR1 exon 36 (p.Gln1970fsX16) that is isogenic to that identified in one parent of a severely affected patient with recessively inherited multiminicore disease. This individual carrying the RYR1 frameshifting mutation complained of mild muscle weakness and fatigability. Analysis of the RyR1 protein content in a muscle biopsy from this individual showed a content of only 20% of that present in a control individual. The biochemical and physiological characteristics of skeletal muscles from RyR1Q1970fsX16 heterozygous mice recapitulates that of the heterozygous parent. RyR1 protein content in the muscles of mutant mice reached 38% and 58% of that present in total muscle homogenates of fast and slow muscles from wild-type (WT) littermates. The decrease of RyR1 protein content in total homogenates is not accompanied by a decrease of Cav1.1 content, whereby the Cav1.1/RyR1 stoichiometry ratio in skeletal muscles from RyR1Q1970fsX16 heterozygous mice is lower compared to that from WT mice. Electron microscopy (EM) revealed a 36% reduction in the number/area of calcium release units accompanied by a 2.5-fold increase of dyads (triads that have lost one junctional sarcoplasmic reticulum element); both results suggest a reduction of the RyR1 arrays. Compared to WT, muscle strength and depolarization-induced calcium transients in RyR1Q1970fsX16 heterozygous mice muscles were decreased by 20% and 15%, respectively. The RyR1Q1970fsX16 mouse model provides mechanistic insight concerning the phenotype of the parent carrying the RYR1 ex36 mutation and suggests that in skeletal muscle fibres there is a functional reserve of RyR1