Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

Attachment of glycosaminoglycan oligosaccharides to thiol-derivatised gold surfaces

Glycosaminoglycan oligosaccharides have been attached to thiol-derivatised gold surfaces, via the formation of mercury-sugar adducts at the non-reducing end, representing a new method of generating versatile glycoconjugates incorporating this class of biologically and medically important carbohydrate.     

Low-temperature growth of single-crystalline ZnO tubes on sapphire(0001) substrates

Single-crystalline ZnO tubes were grown on sapphire(0001) substrates by metalorganic chemical vapor deposition at 400 °C. The growth temperature was much lower than that (900–1100 °C) used in previous reports. The tubes were grown along the substrate normal and were characterized by hexagon-shaped cross sections. All of the tubes possessed the same epitaxial relationships with respect to the substrate. Growth pressure was found to play an important role in the formation of ZnO tubes. PACS 61.46.+w; 78.67.-n; 81.15.Gh     

Beyond Schmittel and Myers-Saito cyclizations: rearrangements of 4-heteroatom-1,2-hexa-diene-5-ynes

The thermal rearrangements of 4-heteroatom-1,2-hexadiene-5-ynes (2) were studied at the BLYP/6-311+G//BLYP/6-31G level of theory. Cyclization of 2 to heteroatom-containing cyclopentadienyl structures (6) competes with the Claisen-type rearrangement to acyclic, allenic structures. Cyclizations to cyclobutene (4)- and cyclohexadiene (8)-derived heterocycles are not feasible as a result of high reaction barriers and lower-lying alternative pathways. [structure: see text]     

Fonctions séparément harmoniques,un théorème de type Terada

Given D a domain in , G an open set in and E a subset of D verifying the harmonic analogue of Local Polynomial Condition of Leja at some point in D. We prove that if f(x, y) is a complex function defined on D × G such that– f(x, ) is harmonic on G for every fixed x E,– f(, y) is harmonic on D for every fixed y G,then f is harmonic in (x, y) on D × G.     

A study of fused silica micro/nano patterning by focused-ion-beam

A dual-beam scanning electron microscopy (SEM)/focused-ion-beam (FIB) system was used to pattern fused silica substrates coated with a 15 nm thin Cr layer. The dimensions of fabricated features together with their surface morphology and profiles were investigated by SEM and atomic force microscopy (AFM). The study demonstrated that with the increase of the ion beam fluence the sputtering rate of the fused silica decreased non-linearly. Also, it was found that initially the sputtering rate increased with the increase of the beam current, after reaching a maximum value, it started decreasing when further beam current increment was performed. Compared with unprocessed areas, the surface finish of the features fabricated by FIB exhibited a significant improvement, and the ion fluence influence on the surface roughness of trenches with low aspect ratios could be considered as negligible. Using a fine beam probe, nano-gratings in the form of grooves with a width down to 54 nm and an aspect ratio higher than three were fabricated. The study showed that FIB machining could be an alternative technology to e-beam lithography for producing fused silica templates for UV nanoimprinting.     

Simultaneous measurement of anomalous group-velocity dispersion and nonlinear coefficient in optical fibers using soliton-effect compression

We present a novel and simple method to measure both the value of the second-order dispersion coefficient and the nonlinear coefficient in optical fibers. This method is based on the higher-order soliton-effect pulse compression phenomenon and is valid for dispersion values greater than 0.5 ps/km/nm. A non-zero dispersion-shifted fiber, a standard single-mode fiber and a highly-dispersive highly-nonlinear fiber have been measured using this method.     

Hydrogenated Graphene and Hydrogenated Silicene: Computational Insights

Density functional calculations are performed to study the energetic, structural, and electronic properties of graphene and silicene functionalized with hydrogen. Our calculations predict that H atoms bind much more strongly to silicene than to graphene. The adsorbed H atoms tend to cooperatively stabilize each other leading to a two‐dimensional nucleation and growth mechanism. The different structural and electronic modifications induced by H in fully functionalized graphene and silicene (known as graphane and silicane) are also explained. Finally, the electronic properties of defective graphane with multiple hydrogen vacancies are investigated. Engineering the vacancies in graphane offers a way to modify the electronic properties of this material.     

A computational study of hybrid approaches of metaheuristic algorithms for the cell formation problem

In this paper we solve the 0–1 cell formation problem where the number of cells is fixed a priori and where the objective is to maximize the overall efficiency of a production system by grouping together machines providing service to similar parts into a subsystem (denoted cell). Three different methods are introduced and compared numerically. The first local search method is an implementation of simulated annealing (SA) where the definition of the neighbourhood is specific to the application and requires using a diversification and intensification strategies. The second local search method is an adaptive simulated annealing method where the neighbourhood is selected randomly at each iteration. The procedure is adaptive in the sense that the probability of selecting a neighbourhood is updated during the process. The third method is a hybrid method (HM) of a population-based method and a local search method. To improve the solution obtained with HM, we apply a SA method afterward. The best variants are very efficient to solve the 35 benchmark problems commonly used in the literature.