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

Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

The response of pipe flow to physically realistic, temporally and spatially continuous(periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to input output transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient

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

Flow non-normality-induced transient growth in superposed Newtonian and non-Newtonian fluid layers

In recent years non-normality and transient growths have attracted much interest in fluid mechanics. Here, we investigate these topics with reference to the problem of interfacial instability in superposed Newtonian and non-Newtonian fluid layers. Under the hypothesis of the lubrication theory, we demonstrate the existence of significant transient growths in the parameter space region where the dynamical system is asymptotically stable, and show how they depend on the main physical parameters. In particular, the key role of the density ratio is highlighte

Functional characterisation of the mammalian NDR1 and NDR2 protein kinases and their regulation by the mammalian Ste20-like kinase MST3

Protein modification is a common regulatory mechanism in order to transduce a signal from one molecule to another. One of the best-studied protein modifications is phosphorylation. The enzymes that are capable of transferring phosphate groups onto other proteins are called protein kinases. Depending on the acceptor group, kinases can be distinguished into tyrosine, serine/threonine and dual-specificity kinases. This work describes the characterisation of human and mouse NDR1 and NDR2 kinases, members of the AGC group of serine/threonine kinases. The NDR protein kinase family is highly conserved between yeast and human, and several members have been shown to be involved in the regulation of cell morphology and the control of cell cycle progression. For example, the yeast NDR kinases Sid2p (Schizosaccharomyces pombe) and Dbf2p (Saccharomyces cerevisiae) are central components of the septation-initiation network and the mitosis exit network, respectively. The closest yeast relatives Cbk1p and Orb6p, members of the regulation of Ace2p transcription and morphogenesis network and Orb6 signalling pathways, are implicated in the coordination of cell cycle progression and cell morphology. This study, as well as studies using worms and flies, provide evidence that not only NDR is conserved, but also the NDR signalling pathway and regulation. Similar to yeast, NDR kinase activation is regulated by phosphorylation at the activation segment phosphorylation site and the hydrophobic motif phosphorylation site. This phosphorylation is regulated by a conserved signaling module consisting of MOB proteins and a STE20–like kinase. Here we show that the STE20-like kinase MST3 activates NDR by phosphorylation specifically at the hydrophobic motif in vitro and in vivo. Furthermore, MOB1A binding is important for the release of autoinhibition and full kinase activation. The data also indicate that NDR is part of a feedback mechanism, which induces cleavage and nuclear translocation of MST3. The data presented here also show that NDR1 and NDR2 are differentially expressed, but regulated in a similar manner. Mouse Ndr1 mRNA is mainly expressed in spleen, thymus and lung, whereas Ndr2 mRNA is more ubiquitously expressed, with the highest levels in the gastrointestinal tract. Both, NDR1 and NDR2, are activated by S100B protein and okadaic acid stimulated phosphorylation; NDR1 and NDR2 are also indistinguishable in the biochemical assays used: membrane targetting, phosphorylation by MST3, and activation by MOB. Further, this work describes the generation and initial characterisation of a mouse model for NDR1 deficiency. Protein analysis using NDR1 knockout mouse embryonic fibroblasts suggest a compensation of the loss of NDR1 by upregulation of NDR2 expression

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

Synthesis and Quantitative Structure–Activity Relationship of Imidazotetrazine Prodrugs with Activity Independent of O6-Methylguanine-DNA-methyltransferase, DNA Mismatch Repair and p53.

The antitumor prodrug Temozolomide is compromised by its dependence for activity on DNA mismatch repair (MMR) and the repair of the chemosensitive DNA lesion, O6-methylguanine (O6-MeG), by O6-methylguanine-DNA-methyltransferase (EC 2.1.1.63, MGMT). Tumor response is also dependent on wild-type p53. Novel 3-(2-anilinoethyl)-substituted imidazotetrazines are reported that have activity independent of MGMT, MMR and p53. This is achieved through a switch of mechanism so that bioactivity derives from imidazotetrazine-generated arylaziridinium ions that principally modify guanine-N7 sites on DNA. Mono- and bi-functional analogs are reported and a quantitative structure-activity relationship (QSAR) study identified the p-tolyl-substituted bi-functional congener as optimized for potency, MGMT-independence and MMR-independence. NCI60 data show the tumor cell response is distinct from other imidazotetrazines and DNA-guanine-N7 active agents such as nitrogen mustards and cisplatin. The new imidazotetrazine compounds are promising agents for further development and their improved in vitro activity validates the principles on which they were designed

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

Serological markers of extracellular matrix remodeling predict transplant‐free survival in primary sclerosing cholangitis

BACKGROUND: Primary sclerosing cholangitis is a progressive liver disease with a remarkably variable course. Biomarkers of disease activity or prognostic models predicting outcome at an individual level are currently not established. AIM: To evaluate the prognostic utility of four biomarkers of basement membrane and interstitial extracellular matrix remodeling in patients with primary sclerosing cholangitis. METHODS: Serum samples were available from 138 large‐duct primary sclerosing cholangitis patients (of which 102 [74%] with IBD) recruited 2008‐2012 and 52 ulcerative colitis patients (controls). The median follow‐up time was 2.2 (range 0‐4.3) years. Specific biomarkers of type III and V collagen formation (PRO‐C3 and PRO‐C5, respectively) and type III and IV collagen degradation (C3M and C4M, respectively) were assessed. The Enhanced Liver Fibrosis test, including procollagen type III N‐terminal peptide, tissue inhibitor of metalloproteinase‐1 and hyaluronic acid was assessed for comparison. RESULTS: All markers were elevated in primary sclerosing cholangitis compared to ulcerative colitis patients (P < 0.001). PRO‐C3 showed the largest difference between the two groups with a threefold increase in primary sclerosing cholangitis compared to ulcerative colitis patients. Patients with high baseline serum levels of all markers, except C3M, had shorter survival compared to patients with low baseline serum levels (P < 0.001). Combining PRO‐C3 and PRO‐C5 the odds ratio for predicting transplant‐free survival was 47 compared to the Enhanced Liver Fibrosis test's odds ratio of 11. CONCLUSIONS: Extracellular matrix remodeling is elevated in primary sclerosing cholangitis patients compared to ulcerative colitis patients. Furthermore, the interstitial matrix marker PRO‐C3 was identified as a potent prognostic marker and an independent predictor of transplant‐free survival in primary sclerosing cholangitis