Oseledets' Splitting of Standard-like Maps

For the class of differentiable maps of the plane and, in particular, for standard-like maps (McMillan form), a simple relation is shown between the directions of the local invariant manifolds of a generic point and its contribution to the finite-time Lyapunov exponents (FTLE) of the associated orbit. By computing also the point-wise curvature of the manifolds, we produce a comparative study between local Lyapunov exponent, manifold's curvature and splitting angle between stable/unstable manifolds. Interestingly, the analysis of the Chirikov-Taylor standard map suggests that the positive contributions to the FTLE average mostly come from points of the orbit where the structure of the manifolds is locally hyperbolic: where the manifolds are flat and transversal, the one-step exponent is predominantly positive and large; this behaviour is intended in a purely statistical sense, since it exhibits large deviations. Such phenomenon can be understood by analytic arguments which, as a by-product, also suggest an explicit way to point-wise approximate the splitting.Comment: 17 pages, 11 figure

Magpie: towards a semantic web browser

Web browsing involves two tasks: finding the right web page and then making sense of its content. So far, research has focused on supporting the task of finding web resources through ‘standard’ information retrieval mechanisms, or semantics-enhanced search. Much less attention has been paid to the second problem. In this paper we describe Magpie, a tool which supports the interpretation of web pages. Magpie offers complementary knowledge sources, which a reader can call upon to quickly gain access to any background knowledge relevant to a web resource. Magpie automatically associates an ontologybased semantic layer to web resources, allowing relevant services to be invoked within a standard web browser. Hence, Magpie may be seen as a step towards a semantic web browser. The functionality of Magpie is illustrated using examples of how it has been integrated with our lab’s web resources

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Electron surface layer at the interface of a plasma and a dielectric wall

We study the potential and the charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the charge bound to the wall is modelled as a quasi-stationary electron surface layer which satisfies Poisson's equation and minimizes the grand canonical potential of the wall-thermalized excess electrons constituting the wall charge. Based on an effective model for a graded interface taking into account the image potential and the offset of the conduction band to the potential just outside the dielectric, we specifically calculate the potential and the electron distribution for magnesium oxide, silicon dioxide and sapphire surfaces in contact with a helium discharge. Depending on the electron affinity of the surface, we find two vastly different behaviors. For negative electron affinity, electrons do not penetrate into the wall and an external surface charge is formed in the image potential, while for positive electron affinity, electrons penetrate into the wall and a space charge layer develops in the interior of the dielectric. We also investigate how the electron surface layer merges with the bulk of the dielectric.Comment: 15 pages, 9 figures, accepted versio

Synergistic Formation of Radicals by Irradiation with Both Vacuum Ultraviolet and Atomic Hydrogen: A Real-Time In Situ Electron Spin Resonance Study

We report on the surface modification of polytetrafluoroethylene (PTFE) as an example of soft- and bio-materials that occur under plasma discharge by kinetics analysis of radical formation using in situ real-time electron spin resonance (ESR) measurements. During irradiation with hydrogen plasma, simultaneous measurements of the gas-phase ESR signals of atomic hydrogen and the carbon dangling bond (C-DB) on PTFE were performed. Dynamic changes of the C-DB density were observed in real time, where the rate of density change was accelerated during initial irradiation and then became constant over time. It is noteworthy that C-DBs were formed synergistically by irradiation with both vacuum ultraviolet (VUV) and atomic hydrogen. The in situ real-time ESR technique is useful to elucidate synergistic roles during plasma surface modification.Comment: 14 pages, 4 figure

Auger de-excitation of metastable molecules at metallic surfaces

We study secondary electron emission from metallic surfaces due to Auger de-excitation of diatomic metastable molecules. Our approach is based on an effective model for the two active electrons involved in the process -- a molecular electron described by a linear combination of atomic orbitals when it is bound and a two-center Coulomb wave when it is not and a metal electron described by the eigenfunctions of a step potential -- and employs Keldysh Green's functions. Solving the Dyson equation for the retarded Green's function by exponential resummation we are able to treat time-nonlocal self-energies and to avoid the wide-band approximation.Results are presented for the de-excitation of \NitrogenDominantMetastableState\ on aluminum and tungsten and discussed in view of previous experimental and theoretical investigations. We find quantitative agreement with experimental data for tungsten indicating that the effective model captures the physics of the process quite well. For aluminum we predict secondary electron emission due to Auger de-excitation to be one to two orders of magnitude smaller than the one found for resonant charge-transfer and subsequent auto-detachment.Comment: 15 pages, 9 figures, revised version using an improved single-electron basi

Electron heating mechanisms in dual frequency capacitive discharges

We discuss electron heating mechanisms in the sheath regions of dual-frequency capacitive discharges, with the twin aims of identifying the dominant mechanisms and supplying closed-form expressions from which the heating power can be estimated. We show that the heating effect produced by either Ohmic or collisionless heating is much larger when the discharge is excited by a superposition of currents at two frequencies than if either current had acted alone. This coupling effect occurs because the lower frequency current, while not directly heating the electrons to any great extent, strongly affects the spatial structure of the discharge in the sheath regions

Algebraic varieties with automorphism groups of maximal rank

We confirm, to some extent, the belief that a projective variety X has the largest number (relative to the dimension of X) of independent commuting automorphisms of positive entropy only when X is birational to a complex torus or a quotient of a torus. We also include an addendum to an early paper though it is not used in the present paper.Comment: Mathematische Annalen (to appear