Search results for "Planar"
showing 10 items of 412 documents
A density problem for Sobolev spaces on Gromov hyperbolic domains
2017
We prove that for a bounded domain $\Omega\subset \mathbb R^n$ which is Gromov hyperbolic with respect to the quasihyperbolic metric, especially when $\Omega$ is a finitely connected planar domain, the Sobolev space $W^{1,\,\infty}(\Omega)$ is dense in $W^{1,\,p}(\Omega)$ for any $1\le p<\infty$. Moreover if $\Omega$ is also Jordan or quasiconvex, then $C^{\infty}(\mathbb R^n)$ is dense in $W^{1,\,p}(\Omega)$ for $1\le p<\infty$.
Gray coding cubic planar maps
2016
International audience; The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize beta-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps. (C) 2015 Elsevier B.V. All rights reserved.
Optimization of fluorescence enhancement for silicon-based microarrays
2008
An optical technique for the enhancement of fluorescence detection sensitivity on planar samples is presented. Such a technique is based on the simultaneous optimization of excitation and light collection by properly combining interference and reflectance from the sample holder. Comparative tests have been performed in microarray applications, by evaluating the proposed solution against commercial glass-based devices, using popular labeling dyes, such as Cy3 and Cy5. The proposed technique is implemented on a substrate built with standard silicon technology and is therefore well suited for integrated micro total analysis systems (microTAS) applications.
Difficulties of density functional theory in predicting the torsional potential of 2,2?-bithiophene
1998
The internal rotation of 2,2′-bithiophene was investigated within the density functional theory (DFT) approach. Fully optimized DFT torsional potentials are compared with Moller–Plesset (MP2) results which predict a fourfold potential with s-cis- and s-trans-gauche minima. DFT calculations fail in describing the energetics of the internal rotation because they favor planar vs. perpendicular conformers. Gradient-corrected functionals provide torsional potentials where the gauche minima have almost vanished and the s-ciss-trans interconversion barriers are twice as high as the barriers obtained at the MP2 level. The use of local functionals augments the shortcomings of the DFT approach. The g…
Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments
2012
Theoretical descriptions of static properties of polymer brushes are reviewed, with an emphasis on monodisperse macromolecules grafted to planar, cylindrical, or spherical substrates. Blob concepts and resulting scaling relations are outlined, and various versions of the self-consistent field theory are summarized: the classical approximation and the strong stretching limit, as well as the lattice formulation. The physical justification of various inherent assumptions is discussed, and computer simulation results addressing the test of the validity of these approximations are reviewed. Also, alternative theories, such as the single chain mean field theory and the density functional theory, …
A theoretical approach of the propagation through geometrical constraints in cardiac tissue
2007
International audience; The behaviour of impulse propagation in the presence of non-excitable scars and boundaries is a complex phenomenon and induces pathological consequences in cardiac tissue. In this article, a geometrical con¯guration is considered so that cardiac waves propagate through a thin strand, which is connected to a large mass of cells. At this interface, waves can slow down or even be blocked depending on the width of the strand. We present an analytical approach leading to determine the blockade condition, by introducing planar travelling wavefront and circular stationary wave. Eventually, the in°uence of the tissue geometry is examined on the impulse propagation velocity.
Fabrication of a planar micro Penning trap and numerical investigations of versatile ion positioning protocols
2009
We describe a versatile planar Penning trap structure, which allows one to dynamically modify the trapping configuration almost arbitrarily. The trap consists of 37 hexagonal electrodes, each with a circumcircle diameter of 300 μm, fabricated in a gold-on-sapphire lithographic technique. Every hexagon can be addressed individually, thus shaping the electric potential. The fabrication of such a device with clean room methods is demonstrated. We illustrate the variability of the device by a detailed numerical simulation of a lateral and a vertical transport and simulate trapping in racetrack and artificial crystal configurations. The trap may be used for ions or electrons, as a versatile cont…
Random quasi-phase matching in congruent lithium tantalate waveguides by proton exchange
2012
A report is presented on broadband second-harmonic generation in the range between 930 and 970 nm using random quasi-phase matching in a planar waveguide fabricated by soft proton exchange in congruent lithium tantalate. Bulk and waveguide measurements are compared, outlining the averaging role of guided-wave modes and their interactions with respect to spectral acceptance and near-field profile.
Planar Mappings of Finite Distortion
2010
We review recent results on planar mappings of finite distortion. This class of mappings contains all analytic functions and quasiconformal mappings.
On the orientational analysis of planar fibre systems from digital images
2002
The orientational characteristics of fibres in digital images are studied. The fibres are modelled by a planar Boolean model whose typical grain is a thick (coloured) fibre. The aim is to make stereological inference on the rose of directions of the unobservable central fibres from observations made on a digital image of the thick fibres. For central fibres, the relation between the rose of directions and the point intensity, observed on a sampling line, is known. We derive, under regularity conditions, the relation between the unobservable point intensity and the scaled variogram observed on the line in a binary and a greyscale image. Using such a relation, it is possible to draw inference…