Spiral Defect Chaos in Large Aspect Ratio Rayleigh-Benard Convection

We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number of approximately 1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.Comment: Preprint of experimental paper submitted to Phys. Rev. Lett. May 12 1993. Text is preceeded by many TeX macros. Figures 1 and 2 are rather lon

Power-Law Behavior of Power Spectra in Low Prandtl Number Rayleigh-Benard Convection

The origin of the power-law decay measured in the power spectra of low Prandtl number Rayleigh-Benard convection near the onset of chaos is addressed using long time numerical simulations of the three-dimensional Boussinesq equations in cylindrical domains. The power-law is found to arise from quasi-discontinuous changes in the slope of the time series of the heat transport associated with the nucleation of dislocation pairs and roll pinch-off events. For larger frequencies, the power spectra decay exponentially as expected for time continuous deterministic dynamics.Comment: (10 pages, 6 figures

Quasiperiodic waves at the onset of zero Prandtl number convection with rotation

We show the possibility of quasiperiodic waves at the onset of thermal convection in a thin horizontal layer of slowly rotating zero-Prandtl number Boussinesq fluid confined between stress-free conducting boundaries. Two independent frequencies emerge due to an interaction between a stationary instability and a self-tuned wavy instability in presence of coriolis force, if Taylor number is raised above a critical value. Constructing a dynamical system for the hydrodynamical problem, the competition between the interacting instabilities is analyzed. The forward bifurcation from the conductive state is self-tuned.Comment: 9 pages of text (LaTex), 5 figures (Jpeg format

Whirling Hexagons and Defect Chaos in Hexagonal Non-Boussinesq Convection

We study hexagon patterns in non-Boussinesq convection of a thin rotating layer of water. For realistic parameters and boundary conditions we identify various linear instabilities of the pattern. We focus on the dynamics arising from an oscillatory side-band instability that leads to a spatially disordered chaotic state characterized by oscillating (whirling) hexagons. Using triangulation we obtain the distribution functions for the number of pentagonal and heptagonal convection cells. In contrast to the results found for defect chaos in the complex Ginzburg-Landau equation and in inclined-layer convection, the distribution functions can show deviations from a squared Poisson distribution that suggest non-trivial correlations between the defects.Comment: 4 mpg-movies are available at http://www.esam.northwestern.edu/~riecke/lit/lit.html submitted to New J. Physic

Principle of Maximum Entropy Applied to Rayleigh-B\'enard Convection

A statistical-mechanical investigation is performed on Rayleigh-B\'enard convection of a dilute classical gas starting from the Boltzmann equation. We first present a microscopic derivation of basic hydrodynamic equations and an expression of entropy appropriate for the convection. This includes an alternative justification for the Oberbeck-Boussinesq approximation. We then calculate entropy change through the convective transition choosing mechanical quantities as independent variables. Above the critical Rayleigh number, the system is found to evolve from the heat-conducting uniform state towards the convective roll state with monotonic increase of entropy on the average. Thus, the principle of maximum entropy proposed for nonequilibrium steady states in a preceding paper is indeed obeyed in this prototype example. The principle also provides a natural explanation for the enhancement of the Nusselt number in convection.Comment: 13 pages, 4 figures; typos corrected; Eq. (66a) corrected to remove a double counting for $k_{\perp}=0$; Figs. 1-4 replace

Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in- and outlet. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system's length. They do, however, depend on the axial boundary conditions, the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that one of linear front propagation. PACS:47.54.+r,47.20.Ky,47.32.-y,47.20.FtComment: 15 pages (LateX-file), 8 figures (Postscript

A Standard Siren Measurement of the Hubble Constant from GW170817 without the Electromagnetic Counterpart

We perform a statistical standard siren analysis of GW170817. Our analysis does not utilize knowledge of NGC 4993 as the unique host galaxy of the optical counterpart to GW170817. Instead, we consider each galaxy within the GW170817 localization region as a potential host; combining the redshifts from all of the galaxies with the distance estimate from GW170817 provides an estimate of the Hubble constant, H 0. Considering all galaxies brighter than $0.626{L}_{B}^{\star }$ as equally likely to host a binary neutron star merger, we find ${H}_{0}={77}_{-18}^{+37}$ km s−1 Mpc−1 (maximum a posteriori and 68.3% highest density posterior interval; assuming a flat H 0 prior in the range $\left[10,220\right]$ km s−1 Mpc−1). We explore the dependence of our results on the thresholds by which galaxies are included in our sample, and we show that weighting the host galaxies by stellar mass or star formation rate provides entirely consistent results with potentially tighter constraints. By applying the method to simulated gravitational-wave events and a realistic galaxy catalog we show that, because of the small localization volume, this statistical standard siren analysis of GW170817 provides an unusually informative (top 10%) constraint. Under optimistic assumptions for galaxy completeness and redshift uncertainty, we find that dark binary neutron star measurements of H 0 will converge as $40 \% /\sqrt{(N)}$, where N is the number of sources. While these statistical estimates are inferior to the value from the counterpart standard siren measurement utilizing NGC 4993 as the unique host, ${H}_{0}={76}_{-13}^{+19}$ km s−1 Mpc−1 (determined from the same publicly available data), our analysis is a proof-of-principle demonstration of the statistical approach first proposed by Bernard Schutz over 30 yr ago

Increasing the Astrophysical Reach of the Advanced Virgo Detector via the Application of Squeezed Vacuum States of Light

Current interferometric gravitational-wave detectors are limited by quantum noise over a wide range of their measurement bandwidth. One method to overcome the quantum limit is the injection of squeezed vacuum states of light into the interferometer’s dark port. Here, we report on the successful application of this quantum technology to improve the shot noise limited sensitivity of the Advanced Virgo gravitational-wave detector. A sensitivity enhancement of up to 3.2±0.1  dB beyond the shot noise limit is achieved. This nonclassical improvement corresponds to a 5%–8% increase of the binary neutron star horizon. The squeezing injection was fully automated and over the first 5 months of the third joint LIGO-Virgo observation run O3 squeezing was applied for more than 99% of the science time. During this period several gravitational-wave candidates have been recorded