Superelements for the finite element solution of two-dimensional elliptic problems with boundary singularities

A novel singular superelement (SSE) formulation has been developed to overcome the loss of accuracy encountered when applying the standard finite element schemes to two-dimensional elliptic problems possessing a singularity on the boundary arising from an abrupt change of boundary conditions or a reentrant corner. The SSE consists of an inner region over which the known analytic form of the solution in the vicinity of the singular point is utilized, and a transition region in which blending functions are used to provide a smooth transition to the usual linear or quadratic isoparametric elements used over the remainder of the domain. Solution of the finite element equations yield directly the coefficients of the asymptotic series, known as the flux/stress intensity factors in linear heat transfer or elasticity theories, respectively. Numerical examples using the SSE for the Laplace equation and for computing the stress intensity factors in the linear theory of elasticity are given, demonstrating that accurate results can be attained for a moderate computational effort.     

Low melting point agarose as a protection layer in photolithographic patterning of aligned binary proteins

A novel photolithography method to build aligned patterns of two different proteins is presented. Chessboard patterns of 125 microm x 125 microm squares are constructed on a silicon dioxide substrate, using standard photoresist chemistries in combination with low-temperature oxygen plasma etching. Low-melting-point agarose (LMPA) is used to protect underlying protein layers and, at the appropriate stage, the digestive enzyme GELase (EPICENTRE) is used to selectively remove the prophylactic LMPA layers. Two antibodies, mouse-IgG and human-IgG, were immobilized and patterned by this procedure. The patterned antibodies maintained the specificity of their antigen-antibody binding, as demonstrated by fluorescence microscopy. In addition, normalized fluorescence intensity profiles illustrate that the patterned proteins layers are uniform (standard deviations below 0.05). Finally, a trypsin activity test was conducted to probe the effect of the patterning protocol on immobilized enzymes; the results imply that this photolithographic process using LMPA as a protection layer preserves 70% of immobilized enzyme activity.     

Co-Assembly between Fmoc Diphenylalanine and Diphenylalanine within a 3D Fibrous Viscous Network Confers Atypical Curvature and Branching

Supramolecular polymer co-assembly is a useful approach to modulate peptide nanostructures. However, the co-assembly scenario where one of the peptide building blocks simultaneously forms a hydrogel is yet to be studied. Herein, we investigate the co-assembly formation of diphenylalanine (FF), and Fmoc-diphenylalanine (FmocFF) within the 3D network of FmocFF hydrogel. The overlapping peptide sequence between the two building blocks leads to their co-assembly within the gel state modulating the nature of the FF crystals. We observe the formation of branched microcrystalline aggregates with an atypical curvature, in contrast to the FF assemblies obtained from aqueous solution. Optical microscopy reveal the sigmoidal kinetic growth profile of these aggregates. Microfluidics and ToF-SIMS experiments exhibit the presence of co-assembled structures of FF and FmocFF in the crystalline aggregates. Molecular dynamics simulation was used to decipher the mechanism of co-assembly formation.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.     

Edge singularities and structure of the 3-D Williams expansion

The elastic solution in a vicinity of a re-entrant wedge can be described by a Williams like expansion in terms of powers of the distance to a point on the edge. This expansion has a particular structure due to the invariance of the problem by translation parallel to the edge. We show here that some terms, so-called primary solutions, derive directly from solutions to the 2-D corner problem posed in the orthogonal cross section of the domain. The others, baptized shadow functions, derive of the primary solutions by integration along the axis parallel to the edge. This 3-D Williams expansion is shown to be equivalent to the edge expansion proposed by Costabel et al. [M. Costabel, M. Dauge, Z. Yosibash, A quasidual function method for extracting edge stress intensity functions, SIAM J. Math. Anal. 35 (5) (2004) 1177–1202]. To cite this article: T. Apel et al., C. R. Mecanique 336 (2008).     

Functional polymers. XVI. Synthesis and polymerization of 2(2-hydroxy-5-isopropenylphenyl)-2H-benzotriazole and a new synthesis of 2(2-hydroxy-5-vinylphenyl)2H-benzotriazole

2(2-Hydroxy-5-isopropenylphenyl)2H-benzotriazole was synthesized in 40% overall yield starting from o-nitroaniline. Diazotization in aqueous hydrochloric acid gave o-nitrophenyl diazonium chloride which was condensed with p-hydroxyacetophenone; the azo compound was reduced to 2(2-hydroxy-5-acetylphenyl) 2H-benzotriazole with zinc powder in sodium hydroxide solution and the 2-hydroxy group of the compound was acetylated. Treatment of the acetyl compound with methyl Grignard reagent resulted in the methylation of the 5-acetyl group to 2[2-acetoxy-5(2-hydroxy-2-propyl)phenyl]2H-benzotriazole which was then dehydrated with potassium hydrogen sulfate to the desired 2(2-hydroxy-5-isopropenylphenyl)2H-benzotriazole. This monomer did not homopolymerize, but was copolymerized readily with styrene, methyl methacrylate, and n-butyl acrylate with azobisisobutyronitrile as the initiator. 2(2-Acetoxy-5-acetylphenyl)2H-benzotriazole was also reduced with sodium borohydride to form 2[2-acetoxy-5-(1-hydroxyethyl)phenyl]2H-benzotriazole which was dehydrated and hydrolyzed to the known 2(2-hydroxy-5-vinylphenyl)-2H-benzotriazole. This route provides a novel and simpler synthesis of 2(2-hydroxy-5-vinylphenyl)2H-benzotriazole.     

Plasma jets produced by low energy laser pulse interaction with planar and cratered targets

Laser experiments of the plasma jet formation using nanosecond laser pulses with low energy, i.e., <20 J, are presented. Planar and cratered gadolinium and aluminum targets are irradiated with laser intensities of several 10¹⁴ W/cm². Spatially-resolved time-integrated X-ray spectra were recorded in the spectral range from 7 to 10 Å. A jet-like structure is obtained from aluminum targets with a preformed crater, which is not seen in planar target irradiation. For gadolinium, a jet is observed from both planar and preformed cratered targets, suggesting that the collimation is dominated by radiative cooling. A radiation-hydrodynamics code coupled to a non-LTE ionization code was used to model the plasma. The calculated plasma emission was found to be consistent with the experimental results.     

Triply Existentially Complete Triangle‐Free Graphs

A triangle‐free graph G is called k‐existentially complete if for every induced k‐vertex subgraph H of G, every extension of H to a ‐vertex triangle‐free graph can be realized by adding another vertex of G to H. Cherlin  11 , 12 asked whether k‐existentially complete triangle‐free graphs exist for every k. Here, we present known and new constructions of 3‐existentially complete triangle‐free graphs.     

Sequent Systems for Negative Modalities

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics.