A domain-specific embedded language in C++ for lowest-order discretizations of diffusive problems on general meshes

In this work we propose an original implementation of a large family of lowest-order methods for diffusive problems including standard and hybrid finite volume methods, mimetic finite difference-type schemes, and cell centered Galerkin methods. The key idea is to regard the method at hand as a (Petrov–)Galerkin scheme based on possibly incomplete, broken affine spaces defined from a gradient reconstruction and a point value. The resulting unified framework serves as a basis for the development of a FreeFEM-like domain specific language targeted at defining discrete linear and bilinear forms. Both the back-end and the front-end of the language are extensively discussed, and several examples of applications are provided. The overhead of the language is evaluated with respect to a more traditional implementation. A benchmark including the comparison with more classical finite element methods on standard meshes is also proposed.     

Yttrium segregation and intergranular defects in alumina

Intergranular segregation of yttrium is investigated in a rhombohedral twin grain boundary of alumina. The deviation from the twin orientation is compensated by a periodic arrangement of intergranular dislocations. TEM tools (CTEM and HREM, EDXS, EFTEM and EELS/ELNES) have been used to characterize changes in chemical and electronic environments along this twin. Within the experimental limits, no Y is detected in the perfect twin parts. On the other hand, Y segregation occurs very locally in the dislocation cores on about four atomic planes perpendicularly to the GB, which in fact corresponds to the step height associated with the interfacial dislocations. By comparison with an undoped bicrystal, both the dislocation distribution and the Y segregation localization confirm the influence of Y on the dislocation mobility. Furthermore, in the Y-rich defects, high spatial resolution analysis of the energy loss near edge structures (ELNES) of the Al-L₂₃ absorption edge brings some enlightenments about the Al³⁺ cation environment, provided the effects of local radiation damage are fully considered and under control.     

Weil Representation and Metaplectic Groups over an Integral Domain

Given F a locally compact, nondiscrete, non-archimedean field of characteristic ≠ 2 and R an integral domain such that a non-trivial smooth character χ: F → R ^× exists, we construct the (reduced) metaplectic group attached to χ and R. We show that it is in the expected cases a double cover of the symplectic group over F. Finally, we define a faithful infinite dimensional R-representation of the metaplectic group analogue to the Weil representation in the complex case.     

Analysis of a discontinuous galerkin method for heterogeneous diffusion problems with low‐regularity solutions

We study the convergence of the Symmetric Weighted Interior Penalty discontinuous Galerkin method for heterogeneous diffusion problems with low‐regularity solutions only belonging to W^{2, p} with p ∈ (1,2]. In 2d, we infer an optimal algebraic convergence rate. In any space dimension d, we achieve the same result for p > 2 d/( d + 2). We also prove convergence without algebraic rates for exact solutions only belonging to the energy space. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2012     

Bounded enumeration reducibility and its degree structure

We study a strong enumeration reducibility, called bounded enumeration reducibility and denoted by ≤_be, which is a natural extension of s-reducibility ≤_s. We show that ≤_s, ≤_be, and enumeration reducibility do not coincide on the ${\Pi^0_1}$ –sets, and the structure ${\boldsymbol{\mathcal{D}_{\rm be}}}$ of the be-degrees is not elementarily equivalent to the structure of the s-degrees. We show also that the first order theory of ${\boldsymbol{\mathcal{D}_{\rm be}}}$ is computably isomorphic to true second order arithmetic: this answers an open question raised by Cooper (Z Math Logik Grundlag Math 33:537–560, 1987).     

Bent polyynes: ring geometry studied by Raman and IR spectroscopy

Infrared (IR) and Raman spectroscopy have been used to examine the vibrational characteristics of a series of three macrocyclic tetraynes in comparison with an acyclic analog. By changing the length of the alkyl tether of the macrocycles, varying degrees of bending of the tetrayne moiety can be achieved, and the joint use of IR and Raman spectroscopies provides an avenue to probe the impact of bending on the sp‐chain. The spectroscopic data show a general trend toward decreasing activation of Raman bands in the IR spectra, and vice versa, as bending of the polyyne chain is decreased. Density functional theory calculations provide a detailed rationalization of the experimental observations. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating Reduced-Reference Video Quality for Quality-Based Streaming Video

Reduced-reference (RR) video-quality estimators send a small signature to the receiver. This signature comprises the original video content as well as the video stream. RR quality estimation provides reliability and involves a small data payload. While significant in theory, RR estimators have only recently been used in practice for quality monitoring and adaptive system control in streaming-video frameworks. In this paper, we classify RR algorithms according to whether they are based on a) modeling the signal distortion, b) modeling the human visual system, or c) analyzing the video signal source. We review proposed RR techniques for monitoring and controlling quality in streaming video systems.     

Hindering the Oxidation of Silicene with Non‐Reactive Encapsulation

The chemical stability of buckled silicene, i.e., the silicon counterpart of graphene, is investigated then resulting in a low reactivity with O₂ when dosing up to 1000 L and in a progressive oxidation under ambient conditions. The latter drawback is addressed by engineering ad hoc Al‐ and Al₂O₃‐based encapsulations of the silicene layer. This encapsulation design can be generally applied to any silicene configuration, irrespective of the support substrate, and it leads to the fabrication of atomically sharp and chemically intact Al/silicene and Al₂O₃/silicene interfaces that can be functionally used for ex situ characterization as well as for gated device fabrication.