Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent

Second order coupling between excited atoms and surface polaritons

Casimir-Polder interactions between an atom and a macroscopic body are typically regarded as due to the exchange of virtual photons. This is strictly true only at zero temperature. At finite temperature, real-photon exchange can provide a significant contribution to the overall dispersion interaction. Here we describe a new resonant two-photon process between an atom and a planar interface. We derive a second order effective Hamiltonian to explain how atoms can couple resonantly to the surface polariton modes of the dielectric medium. This leads to second-order energy exchanges which we compare with the standard nonresonant Casimir-Polder energy.Comment: 7 pages, 2 figure

Scaling laws for rotating Rayleigh-Bénard convection

Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and is compared with experimental results, as well as predictions from multiple scale perturbation theory. We find that the time scaling law agrees with the theoretical prediction, which is in contradiction to experimental results. We also have looked at the scaling of defect lengths and defect glide velocities. We find a separation of scales in defect diameters perpendicular and parallel to the rolls as expected, but the scaling laws for the two different lengths are in contradiction to theory. The defect velocity scaling law agrees with our theoretical prediction from multiple scale perturbation theory

Traveling waves in rotating Rayleigh-Bénard convection: Analysis of modes and mean flow

Numerical simulations of the Boussinesq equations with rotation for realistic no-slip boundary conditions and a finite annular domain are presented. These simulations reproduce traveling waves observed experimentally. Traveling waves are studied near threshhold by using the complex Ginzburg-Landau equation (CGLE): a mode analysis enables the CGLE coefficients to be determined. The CGLE coefficients are compared with previous experimental and theoretical results. Mean flows are also computed and found to be more significant as the Prandtl number decreases (from sigma=6.4 to sigma=1). In addition, the mean flow around the outer radius of the annulus appears to be correlated with the mean flow around the inner radius

Direct Measurement of intermediate-range Casimir-Polder potentials

We present the first direct measurements of Casimir-Polder forces between solid surfaces and atomic gases in the transition regime between the electrostatic short-distance and the retarded long-distance limit. The experimental method is based on ultracold ground-state Rb atoms that are reflected from evanescent wave barriers at the surface of a dielectric glass prism. Our novel approach does not require assumptions about the potential shape. The experimental data confirm the theoretical prediction in the transition regime.Comment: 4 pages, 3 figure

Numerical relativity simulation of GW150914 beyond general relativity

We produce the first astrophysically-relevant numerical binary black hole gravitational waveform in a higher-curvature theory of gravity beyond general relativity. We simulate a system with parameters consistent with GW150914, the first LIGO detection, in order-reduced dynamical Chern-Simons gravity, a theory with motivations in string theory and loop quantum gravity. We present results for the leading-order corrections to the merger and ringdown waveforms, as well as the ringdown quasi-normal mode spectrum. We estimate that such corrections may be discriminated in detections with signal to noise ratio $\gtrsim 180-240$, with the precise value depending on the dimension of the GR waveform family used in data analysis.Comment: 7 pages + appendices, 8 figures, Updated to match Phys. D. Rev articl

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

Nonequilibrium thermal Casimir-Polder forces

We study the nonequilibrium Casimir-Polder force on an atom prepared in an incoherent superposition of internal energy-eigenstates, which is placed in a magnetoelectric environment of nonuniform temperature. After solving the coupled atom--field dynamics within the framework of macroscopic quantum electrodynamics, we derive a general expression for the thermal Casimir-Polder force.Comment: 5 page

Black Hole Area in Brans-Dicke Theory

We have shown that the dynamics of the scalar field $\phi (x)= ``G^{-1}(x)"$ in Brans-Dicke theories of gravity makes the surface area of the black hole horizon {\it oscillatory} during its dynamical evolution. It explicitly explains why the area theorem does not hold in Brans-Dicke theory. However, we show that there exists a certain non-decreasing quantity defined on the event horizon which is proportional to the black hole entropy for the case of stationary solutions in Brans-Dicke theory. Some numerical simulations have been demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory.Comment: 12 pages, latex, 5 figures, epsfig.sty, some statements clarified and two references added, to appear in Phys. Rev.