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 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. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic 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.     

Iridium-Catalyzed Silylation of Five-Membered Heteroarenes: High Sterically Derived Selectivity from a Pyridyl-Imidazoline Ligand

The steric effects of substituents on five-membered rings are less pronounced than those on six-membered rings because of the difference in bond angles. Thus, the regioselectivities of reactions of five-membered heteroarenes that occur with selectivities dictated by steric effects, such as the borylation of C−H bonds, have been poor in many cases. We report that the silylation of five-membered-ring heteroarenes occurs with high sterically derived regioselectivity when catalyzed by the combination of [Ir(cod)(OMe)]₂ (cod=1,5-cyclooctadiene) and a phenanthroline ligand or a new pyridyl-imidazoline ligand that further increases the regioselectivity. The silylation reactions with these catalysts produce high yields of heteroarylsilanes from functionalization at the most sterically accessible C−H bonds of these rings under conditions that the borylation of C−H bonds with previously reported catalysts formed mixtures of products or products that are unstable. The heteroarylsilane products undergo cross-coupling reactions and substitution reactions with ipso selectivity to generate heteroarenes that bear halogen, aryl, and perfluoroalkyl substituents.     

Purification,Characterization, and Structural Studies of a Sulfatase from Pedobacter yulinensis

Sulfatases are ubiquitous enzymes that hydrolyze sulfate from sulfated organic substrates such as carbohydrates, steroids, and flavones. These enzymes can be exploited in the field of biotechnology to analyze sulfated metabolites in humans, such as steroids and drugs of abuse. Because genomic data far outstrip biochemical characterization, the analysis of sulfatases from published sequences can lead to the discovery of new and unique activities advantageous for biotechnological applications. We expressed and characterized a putative sulfatase (PyuS) from the bacterium Pedobacter yulinensis. PyuS contains the (C/S)XPXR sulfatase motif, where the Cys or Ser is post-translationally converted into a formylglycine residue (FGly). His-tagged PyuS was co-expressed in Escherichia coli with a formylglycine-generating enzyme (FGE) from Mycobacterium tuberculosis and purified. We obtained several crystal structures of PyuS, and the FGly modification was detected at the active site. The enzyme has sulfatase activity on aromatic sulfated substrates as well as phosphatase activity on some aromatic phosphates; however, PyuS did not have detectable activity on 17α-estradiol sulfate, cortisol 21-sulfate, or boldenone sulfate.     

Transition to turbulence in a shear flow

We analyze the properties of a 19-dimensional Galerkin approximation to a parallel shear flow. The laminar flow with a sinusoidal shape is stable for all Reynolds numbers Re. For sufficiently large Re additional stationary flows occur; they are all unstable. The lifetimes of finite amplitude perturbations shows a fractal dependence on amplitude and Reynolds number. These findings are in accord with observations on plane Couette flow and suggest a universality of this transition scenario in shear flows.     

Magnetic alignment in nominally non-magnetic hexagonal metal hydrides: NMR

Powders of three hexagonal metal-hydrides or -deuterides are found to align in 4.4–8.3 T magnetic fields used for NMR. The field-alignment is unexpected, since all three systems have very small susceptibilities, as demonstrated by sharp NMR lines. The extent of alignment runs from nearly complete to barely detectable in ZrBe₂(H,D)_x, LuD₃, and YD₃, respectively. The preferred alignment direction in ZrBe₂(H,D)_x is with the crystallites’ c-axis perpendicular to B, while the c-axis and B tend to be parallel in LuD₃ and YD₃. The susceptibilities χ_|| and χ are determined from bulk magnetization measurements in aligned ZrBe₂H_1.4 powder. The alignment must be considered for proper analysis of NMR spectra in these and related materials.     

Noise correlations in shear flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions. Received 26 February 2002 / Received in final form 11 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bruno.eckhardt@physik.uni-marburg.de RID="b" ID="b"Also at: Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India