A quantization property for static Ginzburg‐Landau vortices

For any critical point of the complex Ginzburg‐Landau functional in dimension 3, we prove that, for large coupling constants, ; if the energy of this critical point on a ball of a given radius r is relatively small compared to r log , then the ball of half‐radius contains no vortex (the modulus of the solution is larger than ½). We then show how this property can be applied to describe limiting vortices as ε → 0. © 2001 John Wiley & Sons, Inc.     

Industrial perspective on focused electron beam-induced processes

After a short overview of the historical developments of the technique of gas-assisted focused electron beam-induced processing (mostly deposition and etching), this paper deals with the applications of this technology to photolithographic mask repair. A commented list of results is shown on different mask types, for different types of defects, and at different node generations. The scope of this article is double: summarize the state of the art in a fast-paced highly specific industrial environment driven by “Moore’s law” and feedback to academic researchers some technologically relevant directions for further investigations.     

Calabi-Yau manifolds — Motivations and constructions

The possible ways of compacitification of theE ₈ E ₈ Superstring theory to four dimensions are reviewed. The phenomenological need forN=1 supersymmetry is argued (on quite general grounds) to favour the choice of a Calabi-Yau manifold for the compact internal manifold. The massless spectrum after compactification is derived in full detail revealing, beside the usual particles, others that may have great phenomenological impact. The technical aspects of the construction of such manifolds are examined and the methods of calculation of the relevant topological properties are given. A big family of such constructions, giving rise to many new Calabi-Yau manifolds, is presented and its relevance to the search of a phenomenologically acceptable solution is discussed.This work was supported by the National Science Foundation     

Bayesian estimation of bandwidth in semiparametric kernel estimation of unknown probability mass and regression functions of count data

This work takes advantage of semiparametric modelling which improves significantly in many situations the estimation accuracy of the purely nonparametric approach. Herein for semiparametric estimations of probability mass function (pmf) of count data, and an unknown count regression function (crf), the kernel used is a binomial one and the bandiwdth selection is investigated by developing Bayesian approaches. About the latter, Bayes local and global bandwidth approaches are used to establish data-driven selection procedures in semiparametric framework. From conjugate beta prior distributions of the smoothing parameter and under the squared errors loss function, Bayes estimate for pmf is obtained in closed form. This is not available for the crf which is computed by the Markov Chain Monte Carlo technique. Simulation studies demonstrate that both proposed methods perform better than the classical cross-validation procedures, in particular the smoothing quality and execution times are optimized. All applications are made on real data sets.     

2,2′-Bis(arylamino)-1,1′-biaryls as Building Blocks for the Synthesis of Dibenzo[d,f][1,3]diazepines,Dibenzo[d,f][1,3]diazepinones,and Dibenzo[c,e][1,2,7]thiadiazepine 6-Oxides

The iron-catalyzed oxidative C−C homocoupling of diarylamines affords 2,2′-bis(arylamino)-1,1′-biaryls which represent crucial synthetic building blocks for an access to a range of seven-membered heterocyclic ring systems. Reaction with paraformaldehyde, diphenyl carbonate, and diphenyl sulfite as efficient 1,1-dielectrophiles led to dibenzo[d,f][1,3]diazepines, dibenzo[d,f][1,3]diazepinones, and dibenzo[c,e][1,2,7]thiadiazepine 6-oxides. The synthetic procedures enable short and practical routes to these 1,3-diazepine derivatives under mild reaction conditions and with a high tolerance of various functional groups.     

Application of Static Charge Transfer within an Ionic‐Liquid Force Field and Its Effect on Structure and Dynamics

The effects of linear scaling of the atomic charges of a reference potential on the structure, dynamics, and energetics of the ionic liquid 1,3‐dimethylimidazolium chloride are investigated. Diffusion coefficients that span over four orders of magnitude are observed between the original model and a scaled model in which the ionic charges are ±0.5 e. While the three‐dimensional structure of the liquid is less affected, the partial radial distribution functions change markedly—with the positive result that for ionic charges of ±0.7 e, an excellent agreement is observed with ab initio molecular dynamics data. Cohesive energy densities calculated from these partial‐charge models are also in better agreement with those calculated from the ab initio data. We postulate that ionic‐liquid models in which the ionic charges are assumed to be ±1 e overestimate the intermolecular attractions between ions, which results in overstructuring, slow dynamics, and increased cohesive energy densities. The use of scaled‐charge sets may be of benefit in the simulation of these systems—especially when looking at properties beyond liquid structure—thus providing an alternative to computationally expensive polarisable force fields.     

Granular structure of self-assembled PAA/PAH and PSS/PAH nascent films imaged in situ by LC-AFM

Liquid cell atomic force microscopy (LC-AFM) is used to image self-assembled polyelectrolyte films eliminating any drying effects on the film structure. Weak/weak and strong/weak polyelectrolyte films are formed by the alternated deposition of poly(acrylic acid) [PAA]/poly(allylamine hydrochloride) [PAH], and poly(sodium 4-styrene sulfonate) [PSS]/PAH, respectively, forming a granular surface structure. Number and area of grains (GN, GA) are used to characterize the surface of these films during their build up process. We show that hydrophilic PAA increases GA and decreases GN, while these parameters follow an opposite behavior with PSS. In both cases, GA and GN always have a simple inverse relationship, and then grain surface coverage (GS=GNGA) is nearly constant and independent of polyelectrolyte nature and the substrates used here, but also in the published data as well. The drying of the weak/weak film was also imaged after natural and forced solvent evaporation, and the surface structure is strongly affected, although the GS values keep roughly the same value found for wet films. The set of these results indicates that GS may be considered as a constant parameter during the build-up for the self-nascent assembled polyelectrolytes. The granular structure is still maintained after glucose oxidase adsorption on these films with comparable GS values.     

Poly[μ‐2‐aminopyrazine‐κ2N1:N4‐μ‐cyanido‐copper(I)]: a three‐dimensional network from laboratory powder diffraction data

In the title compound, [Cu(CN)(C₄H₅N₃)]_n or [Cu(μ‐CN)(μ‐PyzNH₂)]_n (PyzNH₂ is 2‐aminopyrazine), the Cu^I center is tetrahedrally coordinated by two cyanide and two PyzNH₂ ligands. The Cu^I–cyano links give rise to [Cu–CN]_∞ chains running along the c axis, which are bridged by bidentate PyzNH₂ ligands. The three‐dimensional framework can be described as being formed by two interpenetrated three‐dimensional honeycomb‐like networks, both made of 26‐membered rings of composition [Cu₆(μ‐CN)₂(μ‐PyzNH₂)₄].