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

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

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

On the feasibility of studying vortex noise in 2D superconductors with cold atoms

We investigate the feasibility of using ultracold neutral atoms trapped near a thin superconductor to study vortex noise close to the Kosterlitz-Thouless-Berezinskii transition temperature. Alkali atoms such as rubidium probe the magnetic field produced by the vortices. We show that the relaxation time $T_1$ of the Zeeman sublevel populations can be conveniently adjusted to provide long observation times. We also show that the transverse relaxation times $T_2$ for Zeeman coherences are ideal for studying the vortex noise. We briefly consider the motion of atom clouds held close to the surface as a method for monitoring the vortex motion.Comment: 4 pages, 1 figur

Coincident count rates in absorbing dielectric media

A study of the effects of absorption on the nonlinear process of parametric down conversion is presented. Absorption within the nonlinear medium is accounted for by employing the framework of macroscopic QED and the Green tensor quantization of the electromagnetic field. An effective interaction Hamiltonian, which describes the nonlinear interaction of the electric field and the linear noise polarization field, is used to derive the quantum state of the light leaving a nonlinear crystal. The signal and idler modes of this quantum state are found to be a superpositions of the electric and noise polarization fields. Using this state, the expression for the coincident count rates for both Type I and Type II conversion are found. The nonlinear interaction with the noise polarization field were shown to cause an increase in the rate on the order of 10^{-12} for absorption of 10% per cm. This astonishingly small effect is found to be negligible compared to the decay caused by linear absorption of the propagating modes. From the expressions for the biphoton amplitude it can be seen the maximally entangled states can still be produced even in the presence of strong absorption.Comment: Updated to journal version. 10 Pages, 8 figure

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

Quantification and localization of the liquid zone of partially remelted M2 tool steel using X-ray microtomography and scanning electron microscopy

The authors warmly thank Luc Morhain and Marc Wary (Arts et Métiers ParisTech CER Metz) for their technical support.Thixoforming of steels poses challenges due to the high temperatures involved and the lack of understanding of thermomechanical behavior. The volume fractions of the liquid and solid phases in the semi-solid state are the most important parameters for such a form-ing process, as they affect the viscosity and hence the flow behavior of the material. Two-dimensional observations might not always be sufficient, as the size distribution and the connectivity of phases cannot be obtained from associated measurements, which can only be determined by three-dimensional (3-D) investigation. This paper presents the first application of high-energy X-ray microtomography to the microstructure of steel in the semi-solid state. The microstructure of M2 high-speed tool steel was studied in both as-received and heated-and-quenched states. From the reconstructed images, 3-D information could be obtained and was compared with scanning elec-tron microscopy and energy dispersive spectrometry observations. The volume fraction and the location of liquid phase in the semi-solid state were determined in particular, and the continuous solid skeleton was investigated

Casimir forces from a loop integral formulation

We reformulate the Casimir force in the presence of a non-trivial background. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials take place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued.Comment: references added, text clarified in place

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