Characterization of the domain chaos convection state by the largest Lyapunov exponent

Using numerical integrations of the Boussinesq equations in rotating cylindrical domains with realistic boundary conditions, we have computed the value of the largest Lyapunov exponent lambda1 for a variety of aspect ratios and driving strengths. We study in particular the domain chaos state, which bifurcates supercritically from the conducting fluid state and involves extended propagating fronts as well as point defects. We compare our results with those from Egolf et al., [Nature 404, 733 (2000)], who suggested that the value of lambda1 for the spiral defect chaos state of a convecting fluid was determined primarily by bursts of instability arising from short-lived, spatially localized dislocation nucleation events. We also show that the quantity lambda1 is not intensive for aspect ratios Gamma over the range 20<Gamma<40 and that the scaling exponent of lambda1 near onset is consistent with the value predicted by the amplitude equation formalism

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

Numerical simulations of neutron star-black hole binaries in the near-equal-mass regime

Simulations of neutron star-black hole (NSBH) binaries generally consider black holes with masses in the range $(5-10)M_\odot$, where we expect to find most stellar mass black holes. The existence of lower mass black holes, however, cannot be theoretically ruled out. Low-mass black holes in binary systems with a neutron star companion could mimic neutron star-neutron (NSNS) binaries, as they power similar gravitational wave (GW) and electromagnetic (EM) signals. To understand the differences and similarities between NSNS mergers and low-mass NSBH mergers, numerical simulations are required. Here, we perform a set of simulations of low-mass NSBH mergers, including systems compatible with GW170817. Our simulations use a composition and temperature dependent equation of state (DD2) and approximate neutrino transport, but no magnetic fields. We find that low-mass NSBH mergers produce remnant disks significantly less massive than previously expected, and consistent with the post-merger outflow mass inferred from GW170817 for moderately asymmetric mass ratio. The dynamical ejecta produced by systems compatible with GW170817 is negligible except if the mass ratio and black hole spin are at the edge of the allowed parameter space. That dynamical ejecta is cold, neutron-rich, and surprisingly slow for ejecta produced during the tidal disruption of a neutron star : $v\sim (0.1-0.15)c$. We also find that the final mass of the remnant black hole is consistent with existing analytical predictions, while the final spin of that black hole is noticeably larger than expected -- up to $\chi_{\rm BH}=0.84$ for our equal mass case

On the Casimir entropy between 'perfect crystals'

We give a re-interpretation of an `entropy defect' in the electromagnetic Casimir effect. The electron gas in a perfect crystal is an electromagnetically disordered system whose entropy contains a finite Casimir-like contribution. The Nernst theorem (third law of thermodynamics) is not applicable.Comment: 10 pages, 2 figures, proceedings of "Quantum Field Theory under the influence of external boundary conditions" QFExt (Oklahoma, Sep 2009

Casimir-Polder interaction of fullerene molecules with surfaces

We calculate the thermal Casimir--Polder potential of C60 and C70 fullerene molecules near gold and silicon nitride surfaces, motivated by their relevance for molecular matter wave interference experiments. We obtain the coefficients governing the asymptotic power laws of the interaction in the thermal, retarded and nonretarded distance regimes and evaluate the full potential numerically. The interaction is found to be dominated by electronic transitions, and hence independent of the internal temperature of the molecules. The contributions from phonon transitions, which are affected by the molecular temperature, give rise to only a small correction. Moreover, we find that the sizeable molecular line widths of thermal fullerenes may modify the nonretarded interaction, depending on the model used. Detailed measurements of the nonretarded potential of fullerene thus allow one to distinguish between different theories of incorporating damping.Comment: 9 pages, 8 figures, 9 table

Implementation of Monte-Carlo transport in the general relativistic SpEC code

Neutrino transport and neutrino-matter interactions are known to play an important role in the evolution of neutron star mergers, and of their post-merger remnants. Neutrinos cool remnants, drive post-merger winds, and deposit energy in the low-density polar regions where relativistic jets may eventually form. Neutrinos also modify the composition of the ejected material, impacting the outcome of nucleosynthesis in merger outflows and the properties of the optical/infrared transients that they power (kilonovae). So far, merger simulations have largely relied on approximate treatments of the neutrinos (leakage, moments) that simplify the equations of radiation transport in a way that makes simulations more affordable, but also introduces unquantifiable errors in the results. To improve on these methods, we recently published a first simulation of neutron star mergers using a low-cost Monte-Carlo algorithm for neutrino radiation transport. Our transport code limits costs in optically thick regions by placing a hard ceiling on the value of the absorption opacity of the fluid, yet all approximations made within the code are designed to vanish in the limit of infinite numerical resolution. We provide here an in-depth description of this algorithm, of its implementation in the SpEC merger code, and of the expected impact of our approximations in optically thick regions. We argue that the latter is a subdominant source of error at the accuracy reached by current simulations, and for the interactions currently included in our code. We also provide tests of the most important features of this code

On the importance of discharge variability in the morphodynamic modeling of rivers

River morphodynamics and sediment transportRiver morphology and morphodynamic

Reducing orbital eccentricity in binary black hole simulations

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but non-zero orbital eccentricities. In this paper the quasi-equilibrium initial-data method is extended to allow non-zero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency and radial velocities to minimize the orbital eccentricity, and the resulting ($\sim 5$ orbit) evolutions are compared with those of quasi-circular initial data. Evolutions of the quasi-circular data clearly show eccentric orbits, with eccentricity that decays over time. The precise decay rate depends on the definition of eccentricity; if defined in terms of variations in the orbital frequency, the decay rate agrees well with the prediction of Peters (1964). The gravitational waveforms, which contain $\sim 8$ cycles in the dominant l=m=2 mode, are largely unaffected by the eccentricity of the quasi-circular initial data. The overlap between the dominant mode in the quasi-circular evolution and the same mode in the low-eccentricity evolution is about 0.99.Comment: 27 pages, 9 figures; various minor clarifications; accepted to the "New Frontiers" special issue of CQ