Van der Waals contribution to the inelastic atom-surface scattering

A calculation of the inelastic scattering rate of Xe atoms on Cu(111) is presented. We focus in the regimes of low and intermediate velocities, where the energy loss is mainly associated to the excitation electron-hole pairs in the substrate. We consider trajectories parallel to the surface and restrict ourselves to the Van der Waals contribution. The decay rate is calculated within a self-energy formulation. The effect of the response function of the substrate is studied by comparing the results obtained with two different approaches: the Specular Reflection Model and the Random Phase Approximation. In the latter, the surface is described by a finite slab and the wave functions are obtained from a one-dimensional model potential that describes the main features of the surface electronic structure while correctly retains the image-like asymptotic behaviour. We have also studied the influence of the surface state on the calculation, finding that it represents around 50% of the total probability of electron-hole pairs excitation.Comment: 7 pages, 4 figure

Ab initio study of the double row model of the Si(553)-Au reconstruction

Using x-ray diffraction Ghose et al. [Surf. Sci. {\bf 581} (2005) 199] have recently produced a structural model for the quantum-wire surface Si(553)-Au. This model presents two parallel gold wires located at the step edge. Thus, the structure and the gold coverage are quite different from previous proposals. We present here an ab initio study using density functional theory of the stability, electronic band structure and scanning tunneling microscopy images of this model.Comment: Submitted to Surface Science on December 200

Kato's square root problem in Banach spaces

Let $L$ be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces $L^{p}(R^{n};X)$ of $X$-valued functions on $R^n$. We characterize Kato's square root estimates $\|\sqrt{L}u\|_{p} \eqsim \|\nabla u\|_{p}$ and the $H^{\infty}$-functional calculus of $L$ in terms of R-boundedness properties of the resolvent of $L$, when $X$ is a Banach function lattice with the UMD property, or a noncommutative $L^{p}$ space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case $X=C$, we get a new approach to the $L^p$ theory of square roots of elliptic operators, as well as an $L^{p}$ version of Carleson's inequality.Comment: 44 page

INSA scientific activities in the space astronomy area

Support to Astronomy operations is an important and long-lived activity within INSA. Probably the best known (and traditional) INSA activities are those related with real-time spacecraft operations: Ground station maintenance and operation (Ground station engineers and operators); spacecraft and payload real-time operation (spacecraft and instruments controllers); computing infrastructure maintenance (operators, analysts) and general site services.In this paper, we'll show a different perspective, probably not so well-known, presenting some INSA recent activities at the European Space Astronomy Centre (ESAC) and NASA Madrid Deep Space Communication Complex (MDSCC) directly related to scientific operations. Basic lines of activity involved include: Operations support for science operations; system and software support for real time systems; technical administration and IT support; R \& D activities, radioastronomy (at MDSCC and ESAC) and scientific research projects. This paper is structured as follows: first, INSA activities in two ESA cornerstone astrophysics missions, XMM-Newton and Herschel, will be outlined. Then, our activities related to Science infrastructure services, represented by the Virtual Observatory (VO) framework and the Science Archives development facilities are briefly shown. Radio Astronomy activities will be described afterwards, and finally, a few research topics in which INSA scientists are involved will be also described.Comment: 6 pages. Highlights of Spanish Astrophysics V Proceedings of the VIII Scientific Meeting of the Spanish AstronomicalSociety (SEA) held in Santander, 7-11 July, 200

Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in L^p

Perturbed Hodge-Dirac operators and their holomorphic functional calculi, as investigated in the papers by Axelsson, Keith and the second author, provided insight into the solution of the Kato square-root problem for elliptic operators in $L^2$ spaces, and allowed for an extension of these estimates to other systems with applications to non-smooth boundary value problems. In this paper, we determine conditions under which such operators satisfy conical square function estimates in a range of $L^p$ spaces, thus allowing us to apply the theory of Hardy spaces associated with an operator, to prove that they have a bounded holomorphic functional calculus in those $L^p$ spaces. We also obtain functional calculi results for restrictions to certain subspaces, for a larger range of $p$. This provides a framework for obtaining $L^p$ results on perturbed Hodge Laplacians, generalising known Riesz transform bounds for an elliptic operator $L$ with bounded measurable coefficients, one Sobolev exponent below the Hodge exponent, and $L^p$ bounds on the square-root of $L$ by the gradient, two Sobolev exponents below the Hodge exponent. Our proof shows that the heart of the harmonic analysis in $L^2$ extends to $L^p$ for all $p \in (1,\infty)$, while the restrictions in $p$ come from the operator-theoretic part of the $L^2$ proof. In the course of our work, we obtain some results of independent interest about singular integral operators on tent spaces, and about the relationship between conical and vertical square functions.Comment: 45 pages; mistake correcte