Variational bound on energy dissipation in turbulent shear flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits structure, namely a pronounced minimum at intermediate Reynolds numbers, and recovers the Busse bound in the asymptotic regime. The most notable feature is a bifurcation of the minimizing wavenumbers, giving rise to simple scaling of the optimized variational parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz file from [email protected]

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Characterization of reconnecting vortices in superfluid helium

When two vortices cross, each of them breaks into two parts and exchanges part of itself for part of the other. This process, called vortex reconnection, occurs in classical as well as superfluids, and in magnetized plasmas and superconductors. We present the first experimental observations of reconnection between quantized vortices in superfluid helium. We do so by imaging micron-sized solid hydrogen particles trapped on quantized vortex cores (Bewley GP, Lathrop DP, Sreenivasan KR, 2006, Nature, 441:588), and by inferring the occurrence of reconnection from the motions of groups of recoiling particles. We show the distance separating particles on the just-reconnected vortex lines grows as a power law in time. The average value of the scaling exponent is approximately 1/2, consistent with the scale-invariant evolution of the vortices

Velocity Statistics Distinguish Quantum Turbulence from Classical Turbulence

By analyzing trajectories of solid hydrogen tracers, we find that the distributions of velocity in decaying quantum turbulence in superfluid $^4$He are strongly non-Gaussian with $1/v^3$ power-law tails. These features differ from the near-Gaussian statistics of homogenous and isotropic turbulence of classical fluids. We examine the dynamics of many events of reconnection between quantized vortices and show by simple scaling arguments that they produce the observed power-law tails.Comment: 4 pages, 4 figure

Algorithm engineering for optimal alignment of protein structure distance matrices

Protein structural alignment is an important problem in computational biology. In this paper, we present first successes on provably optimal pairwise alignment of protein inter-residue distance matrices, using the popular Dali scoring function. We introduce the structural alignment problem formally, which enables us to express a variety of scoring functions used in previous work as special cases in a unified framework. Further, we propose the first mathematical model for computing optimal structural alignments based on dense inter-residue distance matrices. We therefore reformulate the problem as a special graph problem and give a tight integer linear programming model. We then present algorithm engineering techniques to handle the huge integer linear programs of real-life distance matrix alignment problems. Applying these techniques, we can compute provably optimal Dali alignments for the very first time

Elastic turbulence in curvilinear flows of polymer solutions

Following our first report (A. Groisman and V. Steinberg, \sl Nature $\bf 405$, 53 (2000)) we present an extended account of experimental observations of elasticity induced turbulence in three different systems: a swirling flow between two plates, a Couette-Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had high ratio of width of the region available for flow to radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high molecular weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. Those include: (i)randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales; (ii) significant increase in the rates of momentum and mass transfer (compared to those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms, and parameter dependence of the elastic turbulence are compared with those of the conventional high Re hydrodynamic turbulence in Newtonian fluids.Comment: 23 pages, 26 figure

Statistics of extremal intensities for Gaussian interfaces

The extremal Fourier intensities are studied for stationary Edwards-Wilkinson-type, Gaussian, interfaces with power-law dispersion. We calculate the probability distribution of the maximal intensity and find that, generically, it does not coincide with the distribution of the integrated power spectrum (i.e. roughness of the surface), nor does it obey any of the known extreme statistics limit distributions. The Fisher-Tippett-Gumbel limit distribution is, however, recovered in three cases: (i) in the non-dispersive (white noise) limit, (ii) for high dimensions, and (iii) when only short-wavelength modes are kept. In the last two cases the limit distribution emerges in novel scenarios.Comment: 15 pages, including 7 ps figure

Polymorphisms in the WNK1 gene are asociated with blood pressure variation and urinary potassium excretion

WNK1 - a serine/threonine kinase involved in electrolyte homeostasis and blood pressure (BP) control - is an excellent candidate gene for essential hypertension (EH). We and others have previously reported association between WNK1 and BP variation. Using tag SNPs (tSNPs) that capture 100% of common WNK1 variation in HapMap, we aimed to replicate our findings with BP and to test for association with phenotypes relating to WNK1 function in the British Genetics of Hypertension (BRIGHT) study case-control resource (1700 hypertensive cases and 1700 normotensive controls). We found multiple variants to be associated with systolic blood pressure, SBP (7/28 tSNPs min-p = 0.0005), diastolic blood pressure, DBP (7/28 tSNPs min-p = 0.002) and 24 hour urinary potassium excretion (10/28 tSNPs min-p = 0.0004). Associations with SBP and urine potassium remained significant after correction for multiple testing (p = 0.02 and p = 0.01 respectively). The major allele (A) of rs765250, located in intron 1, demonstrated the strongest evidence for association with SBP, effect size 3.14 mmHg (95%CI:1.23–4.9), DBP 1.9 mmHg (95%CI:0.7–3.2) and hypertension, odds ratio (OR: 1.3 [95%CI: 1.0–1.7]).We genotyped this variant in six independent populations (n = 14,451) and replicated the association between rs765250 and SBP in a meta-analysis (p = 7×10−3, combined with BRIGHT data-set p = 2×10−4, n = 17,851). The associations of WNK1 with DBP and EH were not confirmed. Haplotype analysis revealed striking associations with hypertension and BP variation (global permutation p10 mmHg reduction) and risk for hypertension (OR<0.60). Our data indicates that multiple rare and common WNK1 variants contribute to BP variation and hypertension, and provide compelling evidence to initiate further genetic and functional studies to explore the role of WNK1 in BP regulation and EH

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev.

Perfect-fluid cylinders and walls - sources for the Levi-Civita space-time

The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of the metric components, is chosen. The solutions are either static fluid cylinders or walls depending on whether or not one of the spatial coordinates is periodic. Cylinder and wall sources are generated and matched to the vacuum (Levi--Civita) space--time. A match to a cylinder source is achieved for -\frac{1}{2}<\si<\frac{1}{2}, where \si is the mass per unit length in the Newtonian limit \si\to 0, and a match to a wall source is possible for |\si|>\frac{1}{2}, this case being without a Newtonian limit; the positive (negative) values of \si correspond to a positive (negative) fluid density. The range of \si for which a source has previously been matched to the Levi--Civita metric is 0\leq\si<\frac{1}{2} for a cylinder source.Comment: 22 pages, LaTeX, one included figure. Revised version: three (non-perfect-fluid) interior solutions are added, one of which falsifies the original conjecture in Sec. 4, and the circular geodesics of the Levi-Civita space-time are discussed in a footnot