Competition between Spiral-Defect Chaos and Rolls in Rayleigh-Benard Convection

We present experimental results for pattern formation in Rayleigh-Benard convection of a fluid with a Prandtl number, Pr~ 4. We find that the spiral-defect-chaos (SDC) attractor which exists for Pr~1 has become unstable. Gradually increasing the temperature difference from below to well above its critical value no longer leads to SDC. A sudden jump of temperature difference from below to above onset causes convection to grow from thermal fluctuations and does yield SDC. However, the SDC is a transient; it coarsens and forms a single cell-filling spiral which then drifts toward the cell wall and disappears.Comment: 9 pages(RevTeX), 5 jpg figures, To appear as Rapid Communication in PR

Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity

We describe three apparatus, known as the large, medium, and small apparatus, used for high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600 was reached for Gamma = 0.43. Measurements were made with both Aluminum and Copper top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N_infinity for plates with infinite conductivity was estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 - exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Gamma for the large apparatus and showed a small Gamma-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.Comment: 35 pages, 11 figures. Under consideration for publication in Phys. of Fluid

Extensive Scaling and Nonuniformity of the Karhunen-Lo\`eve Decomposition for the Spiral-Defect Chaos State

By analyzing large-aspect-ratio spiral-defect-chaos (SDC) convection images, we show that the Karhunen-Lo\`eve decomposition (KLD) scales extensively for subsystem-sizes larger than 4d (d is the fluid depth), which strongly suggests that SDC is extensively chaotic. From this extensive scaling, the intensive length \xi_KLD is computed and found to have a different dependence on the Rayleigh number than the two-point correlation length \xi_2. Local computations of \xi_KLD reveal a substantial spatial nonuniformity of SDC that extends over radii 18d< r < 45d in a \Gamma=109 aspect-ratio cell.Comment: 10 pages single-spaced (total), 3 figues, 2 table

Effect of the Centrifugal Force on Domain Chaos in Rayleigh-B\'enard convection

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects rotating Rayleigh-B\'enard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly-stationary nearly-radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency $f\sim\epsilon^\mu$ with $\mu\simeq1$ as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, $\mu$ and the domain size closely agreed with experiment.Comment: 8 pages, 11 figure

Metabolic response of human osteoarthritic cartilage to biochemically characterized collagen hydrolysates

The most frequent disease of the locomotor system is osteoarthritis (OA), which, as a chronic joint disease, might benefit more from nutrition than acute illnesses. Collagen hydrolysates (CHs) are peptidic mixtures that are often used as nutraceuticals for OA. Three CHs were characterized biochemically and pharmacologically. Our biophysical (MALDI-TOF-MS, NMR, AFM) and fluorescence assays revealed marked differences between CHs of fish (Peptan® F 5000, Peptan® F 2000) and porcine (Mobiforte®) origin with respect to the total number of peptides and common peptides between them. Using a novel dual radiolabeling procedure, no CH modulated collagen biosynthesis in human knee cartilage explants. Peptan® F 2000 enhanced the activities of the aggrecanase ADMATS4 and ADMATS5 in vitro without loss of proteoglycan from cartilage explants; the opposite effect was observed with Mobiforte®. Interleukin (IL)-6, matrix metalloproteinase (MMP)-1, -3 and -13 levels were elevated in explants that were treated with Mobiforte® and Peptan® F 5000, but not with Peptan® F 2000. In conclusion, the heterogeneous peptide composition and disparate pharmacological effects between CHs suggest that the effect of a CH preparation cannot be extrapolated to other formulations. Thus, the declaration of a CH as a safe and effective nutraceutical requires a thorough examination of its pleiotropic effects

Confinement of the Sun's interior magnetic field: some exact boundary-layer solutions

High-latitude laminar confinement of the Sun's interior magnetic field is shown to be possible, as originally proposed by Gough and McIntyre (1998) but contrary to a recent claim by Brun and Zahn (A&A 2006). Mean downwelling as weak as 2x10^-6cm/s -- gyroscopically pumped by turbulent stresses in the overlying convection zone and/or tachocline -- can hold the field in advective-diffusive balance within a confinement layer of thickness scale ~ 1.5Mm ~ 0.002 x (solar radius) while transmitting a retrograde torque to the Ferraro-constrained interior. The confinement layer sits at the base of the high-latitude tachocline, near the top of the radiative envelope and just above the `tachopause' marking the top of the helium settling layer. A family of exact, laminar, frictionless, axisymmetric confinement-layer solutions is obtained for uniform downwelling in the limit of strong rotation and stratification. A scale analysis shows that the flow is dynamically stable and the assumption of laminar flow realistic. The solution remains valid for downwelling values of the order of 10^-5cm/s but not much larger. This suggests that the confinement layer may be unable to accept a much larger mass throughput. Such a restriction would imply an upper limit on possible internal field strengths, perhaps of the order of hundreds of gauss, and would have implications also for ventilation and lithium burning. The solutions have interesting chirality properties not mentioned in the paper owing to space restrictions, but described at http://www.atmos-dynamics.damtp.cam.ac.uk/people/mem/papers/SQBO/solarfigure.htmlComment: 6 pages, 3 figures, to appear in conference proceedings: Unsolved Problems in Stellar Physic

Long GRBs from binary stars: runaway, Wolf-Rayet progenitors

The collapsar model for long gamma-ray bursts requires a rapidly rotating Wolf-Rayet star as progenitor. We test the idea of producing rapidly rotating Wolf-Rayet stars in massive close binaries through mass accretion and consecutive quasi-chemically homogeneous evolution; the latter had previously been shown to provide collapsars below a certain metallicity threshold for single stars. The binary channel presented here may provide a means for massive stars to obtain the high rotation rates required to evolve quasi-chemically homogeneous and fulfill the collapsar scenario. Moreover, it suggests that a possibly large fraction of long gamma-ray bursts occurs in runaway stars.Comment: To appear in the proceedings of the conference "Unsolved problems in stellar physics" - Cambridge, July 200