On the Sensitivity of 3-D Thermal Convection Codes to Numerical Discretization: A Model Intercomparison

Fully 3-D numerical simulations of thermal convection in a spherical shell have become a standard for studying the dynamics of pattern formation and its stability under perturbations to various parameter values. The question arises as to how does the discretization of the governing equations affect the outcome and thus any physical interpretation. This work demonstrates the impact of numerical discretization on the observed patterns, the value at which symmetry is broken, and how stability and stationary behavior is dependent upon it. Motivated by numerical simulations of convection in the Earth\u27s mantle, we consider isoviscous Rayleigh-Bénard convection at infinite Prandtl number, where the aspect ratio between the inner and outer shell is 0.55. We show that the subtleties involved in development mantle convection models are considerably more delicate than has been previously appreciated, due to the rich dynamical behavior of the system. Two codes with different numerical discretization schemes: an established, community-developed, and benchmarked finite element code (CitcomS) and a novel spectral method that combines Chebyshev polynomials with radial basis functions (RBF) are compared. A full numerical study is investigated for the following three cases. The first case is based on the cubic (or octahedral) initial condition (spherical harmonics of degree ℓ =4). How variations in the behavior of the cubic pattern to perturbations in the initial condition and Rayleigh number between the two numerical discrezations is studied. The second case investigates the stability of the dodecahedral (or icosahedral) initial condition (spherical harmonics of degree ℓ = 6). Although both methods converge first to the same pattern, this structure is ultimately unstable and systematically degenerates to cubic or tetrahedral symmetries, depending on the code used. Lastly, a new steady state pattern is presented as a combination of order 3 and 4 spherical harmonics leading to a five cell or a hexahedral pattern and stable up to 70 times the critical Rayleigh number. This pattern can provide the basis for a new accuracy benchmark for 3-D spherical mantle convection codes

Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order

Perturbed stationary axisymmetric isolated bodies, e.g. stars, represented by a matter-filled interior and an asymptotically flat vacuum exterior joined at a surface where the Darmois matching conditions are satisfied, are considered. The initial state is assumed to be static. The perturbations of the matching conditions are derived and used as boundary conditions for the perturbed Ernst equations in the exterior region. The perturbations are calculated to second order. The boundary conditions are overdetermined: necessary and sufficient conditions for their compatibility are derived. The special case of perturbations of spherical bodies is given in detail.Comment: RevTeX; 32 pp. Accepted by Phys. Rev. D. Added references and extra comments in introductio

The Character of Z-pole Data Constraints on Standard Model Parameters

Despite the impressive precision of the Z-pole measurements made at LEP and SLC, the allowed region for the principle Standard Model parameters responsible for radiative corrections (the mass of the Higgs, the mass of the top and alpha(Mz)) is still large enough to encompass significant non-linearities. The nature of the experimental constraints therefore depends in an interesting way on the "accidental" relationships among the various measurements. In particular, the fact that the Z-pole measurements favor values of the Higgs mass excluded by direct searches leads us to examine the effects of external Higgsstrahlung, a process ignored by the usual precision electroweak calculations.Comment: 9 pages, 6 figures, REVTeX format; added reference in section IV; added paragraph on widths and a few cosmetic changes to correspond to published versio

Fostering Application Opportunites for the NASA Soil Moisture Active Passive (SMAP) Mission

The NASA Soil Moisture Active Passive (SMAP) Mission will provide global observations of soil moisture and freeze/thaw state from space. We outline how priority applications contributed to the SMAP mission measurement requirements and how the SMAP mission plans to foster applications and applied science

Mesoscopic Phase Coherence in a Quantum Spin Fluid

Mesoscopic quantum phase coherence is important because it improves the prospects for handling quantum degrees of freedom in technology. Here we show that the development of such coherence can be monitored using magnetic neutron scattering from a one-dimensional spin chain Y2BaNiO5, a quantum spin fluid where no classical, static magnetic order is present. In the cleanest samples, the quantum coherence length is 20 nm, almost an order of magnitude larger than the classical antiferromagnetic correlation length of 3 nm. We also demonstrate that the coherence length can be modified by static and thermally activated defects in a quantitatively predictable manner

Stability of sub-surface oxygen at Rh(111)

Using density-functional theory (DFT) we investigate the incorporation of oxygen directly below the Rh(111) surface. We show that oxygen incorporation will only commence after nearly completion of a dense O adlayer (\theta_tot = 1.0 monolayer) with O in the fcc on-surface sites. The experimentally suggested octahedral sub-surface site occupancy, inducing a site-switch of the on-surface species from fcc to hcp sites, is indeed found to be a rather low energy structure. Our results indicate that at even higher coverages oxygen incorporation is followed by oxygen agglomeration in two-dimensional sub-surface islands directly below the first metal layer. Inside these islands, the metastable hcp/octahedral (on-surface/sub-surface) site combination will undergo a barrierless displacement, introducing a stacking fault of the first metal layer with respect to the underlying substrate and leading to a stable fcc/tetrahedral site occupation. We suggest that these elementary steps, namely, oxygen incorporation, aggregation into sub-surface islands and destabilization of the metal surface may be more general and precede the formation of a surface oxide at close-packed late transition metal surfaces.Comment: 9 pages including 9 figure files. Submitted to Phys. Rev. B. Related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Chandra detection of extended X-ray emission from the recurrent nova RS Ophiuchi

Radio, infrared, and optical observations of the 2006 eruption of the symbiotic recurrent nova RS Ophiuchi (RS Oph) showed that the explosion produced non-spherical ejecta. Some of this ejected material was in the form of bipolar jets to the east and west of the central source. Here we describe Xray observations taken with the Chandra X-ray Observatory one and a half years after the beginning of the outburst that reveal narrow, extended structure with a position angle of approximately 300 degrees (east of north). Although the orientation of the extended feature in the X-ray image is consistent with the readout direction of the CCD detector, extensive testing suggests that the feature is not an artifact. Assuming it is not an instrumental effect, the extended X-ray structure shows hot plasma stretching more than 1,900 AU from the central binary (taking a distance of 1.6 kpc). The X-ray emission is elongated in the northwest direction - in line with the extended infrared emission and some minor features in the published radio image. It is less consistent with the orientation of the radio jets and the main bipolar optical structure. Most of the photons in the extended X-ray structure have energies of less than 0.8 keV. If the extended X-ray feature was produced when the nova explosion occurred, then its 1".2 length as of 2007 August implies that it expanded at an average rate of more than 2 mas/d, which corresponds to a flow speed of greater than 6,000 km/s (d/1.6 kpc) in the plane of the sky. This expansion rate is similar to the earliest measured expansion rates for the radio jets.Comment: accepted in Ap

The TWA 3 Young Triple System: Orbits, Disks, Evolution

We have characterized the spectroscopic orbit of the TWA 3A binary and provide preliminary families of probable solutions for the TWA 3A visual orbit as well as for the wide TWA 3A--B orbit. TWA 3 is a hierarchical triple located at 34 pc in the $\sim$10 Myr old TW Hya association. The wide component separation is 1."55; the close pair was first identified as a possible binary almost 20 years ago. We initially identified the 35-day period orbital solution using high-resolution infrared spectroscopy which angularly resolved the A and B components. We then refined the preliminary orbit by combining the infrared data with a re-analysis of our high-resolution optical spectroscopy. The orbital period from the combined spectroscopic solution is $\sim$35 days, the eccentricity is $\sim$0.63, and the mass ratio is $\sim$0.84; although this high mass ratio would suggest that optical spectroscopy alone should be sufficient to identify the orbital solution, the presence of the tertiary B component likely introduced confusion in the blended optical spectra. Using millimeter imaging from the literature, we also estimate the inclinations of the stellar orbital planes with respect to the TWA 3A circumbinary disk inclination and find that all three planes are likely misaligned by at least $\sim$30 degrees. The TWA 3A spectroscopic binary components have spectral types of M4.0 and M4.5; TWA 3B is an M3. We speculate that the system formed as a triple, is bound, and that its properties were shaped by dynamical interactions between the inclined orbits and disk.Comment: Accepted to Ap

Integral Equations for Heat Kernel in Compound Media

By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$ acquires a certain constant value. At the interface of the media the conditions are imposed which demand the continuity of the `temperature' and the `heat flows'. The integration in the equations is spread out only over the interface of the media. As a result the dimension of the initial problem is reduced by 1. The perturbation series for the integral equations derived are nothing else as the multiple scattering expansions for the relevant heat kernels. Thus a rigorous derivation of these expansions is given. In the one dimensional case the integral equations at hand are solved explicitly (Abel equations) and the exact expressions for the regarding heat kernels are obtained for diverse matching conditions. Derivation of the asymptotic expansion of the integrated heat kernel for a compound media is considered by making use of the perturbation series for the integral equations obtained. The method proposed is also applicable to the configurations when the same medium is divided, by a smooth compact surface, into internal and external regions, or when only the region inside (or outside) this surface is considered with appropriate boundary conditions.Comment: 26 pages, no figures, no tables, REVTeX4; two items are added into the Reference List; a new section is added, a version that will be published in J. Math. Phy

The effect of monomer evaporation on a simple model of submonolayer growth

We present a model for thin film growth by particle deposition that takes into account the possible evaporation of the particles deposited on the surface. Our model focuses on the formation of two-dimensional structures. We find that the presence of evaporation can dramatically affect the growth kinetics of the film, and can give rise to regimes characterized by different ``growth'' exponents and island size distributions. Our results are obtained by extensive computer simulations as well as through a simple scaling approach and the analysis of rate equations describing the system. We carefully discuss the relationship of our model with previous studies by Venables and Stoyanov of the same physical situation, and we show that our analysis is more general.Comment: 41 pages including figures, Revtex, to be published in Physical Review