A characterization of Dirac morphisms

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.Comment: 18 pages; restricted to the even-dimensional cas

A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

A spinorial energy functional: critical points and gradient flow

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.Comment: Small changes, final versio

Para to Ortho transition of metallic dimers on Si(001)

Extensive electronic structure calculations are performed to obtain the stable geometries of metals like Al, Ga and In on the Si(001) surface at 0.5 ML and 1 ML coverages. Our results coupled with previous theoretical findings explain the recent experimental data in a comprehensive fashion. At low coverages, as shown by previous works, `Para' dimers give the lowest energy structure. With increasing coverage beyond 0.5 ML, `Ortho' dimers become part of low energy configurations leading toward a `Para' to `Ortho' transition at 1 ML coverage. For In mixed staggered dimers (`Ortho' and `Para') give the lowest energy configuration. For Ga, mixed dimers are non-staggered, while for Al `Para' to `Ortho' transition of dimers is complete. Thus at intermediate coverages between 0.5 and 1 ML, the `Ortho' and `Para' dimers may coexist on the surface. Consequently, this may be an explanation of the fact that the experimental observations can be successfully interpreted using either orientation. A supported zigzag structure at 0.5 ML, which resembles ${\rm (CH)_x}$, does not undergo a dimerization transition, and hence stays semi-metallic. Also, unlike ${\rm (CH)_x}$ the soliton formation is ruled out for this structure.Comment: 8 pages, 6 figure

Investigating Off-shell Stability of Anti-de Sitter Space in String Theory

We propose an investigation of stability of vacua in string theory by studying their stability with respect to a (suitable) world-sheet renormalization group (RG) flow. We prove geometric stability of (Euclidean) anti-de Sitter (AdS) space (i.e., $\mathbf{H}^n$) with respect to the simplest RG flow in closed string theory, the Ricci flow. AdS space is not a fixed point of Ricci flow. We therefore choose an appropriate flow for which it is a fixed point, prove a linear stability result for AdS space with respect to this flow, and then show this implies its geometric stability with respect to Ricci flow. The techniques used can be generalized to RG flows involving other fields. We also discuss tools from the mathematics of geometric flows that can be used to study stability of string vacua.Comment: 29 pages, references added in this version to appear in Classical and Quantum Gravit

Possible detection of phase changes from the non-transiting planet HD 46375b by CoRoT

The present work deals with the detection of phase changes in an exoplanetary system. HD 46375 is a solar analog known to host a non-transiting Saturn-mass exoplanet with a 3.0236 day period. It was observed by the CoRoT satellite for 34 days during the fall of 2008. We attempt to identify at optical wavelengths, the changing phases of the planet as it orbits its star. We then try to improve the star model by means of a seismic analysis of the same light curve and the use of ground-based spectropolarimetric observations. The data analysis relies on the Fourier spectrum and the folding of the time series. We find evidence of a sinusoidal signal compatible in terms of both amplitude and phase with light reflected by the planet. Its relative amplitude is Delta Fp/F* = [13.0, 26.8] ppm, implying an albedo A=[0.16, 0.33] or a dayside visible brightness temperature Tb ~ [1880,2030] K by assuming a radius R=1.1 R_Jup and an inclination i=45 deg. Its orbital phase differs from that of the radial-velocity signal by at most 2 sigma_RV. However, the tiny planetary signal is strongly blended by another signal, which we attribute to a telluric signal with a 1 day period. We show that this signal is suppressed, but not eliminated, when using the time series for HD 46179 from the same CoRoT run as a reference. This detection of reflected light from a non-transiting planet should be confirmable with a longer CoRoT observation of the same field. In any case, it demonstrates that non-transiting planets can be characterized using ultra-precise photometric lightcurves with present-day observations by CoRoT and Kepler. The combined detection of solar-type oscillations on the same targets (Gaulme et al. 2010a) highlights the overlap between exoplanetary science and asteroseismology and shows the high potential of a mission such as Plato.Comment: 4 pages, 6 figure

Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition

In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\Omega))$ and L^\infty((0,T)\times\o), where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.Comment: 45page

Shelf morphology as an indicator of sedimentary regimes: a synthesis from a mixed siliciclastic-carbonate shelf on the eastern Brazilian margin

Modern shelf morphology is the result of the interplay between short and long term sedimentary processes. The relation between rates of sediment supply/carbonate growth and accommodation space creation will not only control coastal transgression and regression, but will also define the shelf sedimentary regimes acting to shape the seabed. Herein, shelf morphology and sedimentology are investigated in order to discuss how these characteristics can be representative of distinct sedimentary regimes. The study area is the eastern Brazilian shelf where coastal transgression and regression coexist with the most important coral reef system of the South Atlantic. A compilation of existing published and unpublished data was carried out in order to produce morphological and faciological maps and compare the mapped features with high-resolution seismic and sonographic data. The results show three major regions or morphological compartments: Abrolhos Shelf, Doce River Shelf and the Paleovalleys Shelf. In terms of shelf sedimentary domain, rhodolith beds predominate over the outer shelf along the entire area, coralline reefs are present along the northern Abrolhos inner shelf and a significant terrigenous mud deposit is observed associated to the Doce River adjacent inner shelf beds. The rest of the shelf is composed by bioclastic or terrigenous mud sand and gravel. Terrigenous sedimentation is always restricted to the shoreface or inner shelf shallower areas and carbonate sands and gravels are predominant elsewhere. The Abrolhos shelf shows two distinct sectors; the northern area is a typical mixed sediment environment that has a supply regime along the coast/shoreface, mainly due to longshore transport and a carbonate regime along the inner and outer shelf. The southern shelf morphology and sedimentation are controlled by the antecedent topography and is typically a accommodation regime shelf with associated rhodolith beds. The Doce river shelf is a supply regime environment with the formation of a 5 to 8m thick regressive deposit with downlapping clinoforms. Southward from the Doce river shelf, a significant shift in sedimentary regime is observed as the morphology becomes very irregular with associated hardbottoms and unfilled paleovalleys. This sector of the shelf (Paleovalley shelf) is characterized by an accommodation regime. The interpretation shows that the entire study area can be defined as a mixed sedimentation shelf, showing supply and accommodation regimes. Shelf morphology worked as an indicator of these changes. Carbonate/terrigenous deposition during a highstand/regressive phase coeval along the eastern Brazilian shelf, either laterally and across shelf. This lateral/along coast variation in sediment supply and carbonate production leads to distinct lateral facies and geometry. These spatial changes in morphology and facies, with coexistence of carbonate and siliciclastic sedimentation, are very important for the correlation and interpretation of the geological record, especially stratigraphic surfaces and sequence units