Collision and escape orbits in a generalized Hénon–Heiles model

The motion of a material point of unit mass in a field determined by a generalized Hénon–Heiles potential $U=A{q}_1^2+B{q}_2^2+C{q}_1^2{q}_2+D{q}_2^3$, with $(q_1,q_2)=$ standard Cartesian coordinates and $(A,B,C,D)\in {(0,\infty )}^2\times R^2$, is addressed for two limit situations: collision and escape. Using McGehee-type transformations, the corresponding collision and infinity boundary manifolds pasted on the phase space are determined. These are fictitious manifolds, but, due to the continuity with respect to initial data, their flow determines the near by orbit behaviour.The dynamics on the collision and infinity manifolds is fully described. The topology of the flow on the collision manifold is independent of the parameters. In the full phase space, while spiraling collision orbits are present, most of the orbits avoid collision. The topology of the flow on the infinity manifold changes as the ratio between $C$ and $D$ varies. More precisely, there are two symmetric pitchfork bifurcations along the line $2C?3D=0$, due to the reshaping of the potential along the bifurcation line. Besides rectilinear and spiraling orbits, the near-escape dynamics includes oscillatory orbits, for which angular momentum alternates sign.     

A New Method for Estimating the Distribution of Scan Statistics for a Two-Dimensional Poisson Process

A method for estimating the distribution of scan statistics with high precisìon was introduced in Haiman (2000). Using that method sharp bounds for the errors were also established. This paper is concerned with the application of the method in Haiman (2000) to a two-dimensional Poisson process. The method involves the estimation by simulation of the conditional (fixed number of points) distribution of scan statistics for the particular rectangle sets of size 2 × 2, 2 × 3, 3 × 3, where the unit is the (1 × 1) dimension of the squared scanning window. In order to perform these particular estimations, we develop and test a perfect simulation algorithm. We then perform several numerical applications and compare our results with results obtained by other authors.     

Polylactic acid (PLA)/Silver-NP/VitaminE bionanocomposite electrospun nanofibers with antibacterial and antioxidant activity

The antibacterial property of silver nanoparticles (Ag-NPs) and the antioxidant activity of Vitamin E have been combined by incorporation of these two active components within polylactic acid (PLA) nanofibers via electrospinning (PLA/Ag-NP/VitaminE nanofibers). The morphological and structural characterizations of PLA/Ag-NP/VitaminE nanofibers were performed by Scanning Electron Microscopy (SEM), Transmission Electron Microscopy and X-ray diffraction. The average fiber diameter was 140 ± 60 nm, and the size of the Ag-NP was 2.7 ± 1.5 nm. PLA/Ag-NP/VitaminE nanofibers inhibited growth of Escherichia coli, Listeria monocytogenes and Salmonella typhymurium up to 100 %. The amount of released Ag ions from the nanofibers immersed in aqueous solution was determined by Inductively Coupled Plasma Mass Spectrometry, and it has been observed that the release of Ag ions was kept approximately constant after 10 days of immersion. The antioxidant activity of PLA/Ag-NP/VitaminE nanofibers was evaluated according to DPPH (2,2-diphenyl-1-picrylhydrazyl) method and determined as 94 %. The results of the tests on fresh apple and apple juice indicated that the PLA/Ag/VitaminE nanofiber membrane actively reduced the polyphenol oxidase activity. The multifunctional electrospun PLA nanofibers incorporating Ag-NP and Vitamin E may be quite applicable in food packaging due to the extremely large surface area of nanofibers along with antibacterial and antioxidant activities. These materials could find application in food industry as a potential preservative packaging for fruits and juices.     

Microfabrication techniques using focused ion beams and emergent applications.

The application of focused ion beam (FIB) machining in several technologies aimed at microstructure fabrication is presented. These emergent applications include the production of micromilling tools for machining of metals and the production of microsurgical tools. An example of the use of microsurgical manipulators in a circulatory system measurement is presented. The steps needed to transform the laboratory fabrication of these tools and manipulators into a routine FIB production process are discussed. The ion milling of three-dimensional cavities by the exact solution of a mathematical model of the FIB deflection is demonstrated. A good agreement between the model calculation and the ion beam control has been obtained for parabolic and cosine cross-section features with planes of symmetry.     

Intercalation of halogen fluorides into graphite

IF₇ intercalates into graphite accompanied by the partial fluorination of the graphite host. The intercalated species was identified as IF₅ by IR and ¹⁹F nmr spectroscopies. Mass spectrometric analyses of the gases evolved from the intercalate showed only IF₅ and fluorocarbons. Iodine pentafluoride intercalates only in the presence of HF, yielding a compound with the stoichiometry C₈IF₅ and no fluorination of the graphite host. Careful elimination of even traces of HF resulted in no intercalation. Evolved gas analysis showed that the only species recovered from the intercalation was IF₅. The remaining interhalogens, ClF₅, ClF₃, BrF₅ and BrF₃ all intercalate into graphite with extensive fluorination of the lattice. In the case of these four compounds, the intercalate proved to be more difficult to characterize, e.g. stoichiometry was often variable, and ¹⁹F nmr yielded resonances that did not agree with any known halogen fluorides. Thermal decomposition of these intercalates showed little or no gas evolution until relatively high temperatures were reached, whereupon Cl₂ or Br₂ was evolved, followed by fluorocarbons.     

Sur la compatibilité des copolymères statistiques binaires et ternaires d'acrylonitrile,d'acétate de vinyle et d'α-méthylstyrène

A comparison has been made between (a) mixtures of the binary copolymers of acrylonitrile with vinyl acetate and with α-methyl styrene and (b) the ternary copolymer. The two products have been characterized for thermal and mechanical behaviour. For each pair of copolymers, a study has been made of compatibility in establishing the type of mixture and the variation of properties with composition.     

Efficient NIR‐Light Emission from Solid‐State Complexes of Boron Difluoride with 2′‐Hydroxychalcone Derivatives

This article describes a series of nine complexes of boron difluoride with 2′‐hydroxychacone derivatives. These dyes were synthesized very simply and exhibited intense NIR emission in the solid state. Complexation with boron was shown to impart very strong donor–acceptor character into the excited state of these dyes, which further shifted their emission towards the NIR region (up to 855 nm for dye 5 b , which contained the strongly donating triphenylamine group). Strikingly, these optical features were obtained for crystalline solids, which are characterized by high molecular order and tight packing, two features that are conventionally believed to be detrimental to luminescence in organic crystals. Remarkably, the emission of light from the π‐stacked molecules did not occur at the expense of the emission quantum yield. Indeed, in the case of pyrene‐containing dye 4 , for example, a fluorescence quantum yield of about 15 % with a fluorescence emission maximum at 755 nm were obtained in the solid state. Moreover, dye 3 a and acetonaphthone‐based compounds 1 b , 2 b , and 3 b showed no evidence of degradation as solutions in CH₂Cl₂ that contained EtOH. In particular, solutions of brightly fluorescent compound 3 a (brightness: ε×Φ_f=45 000 M ^?1 cm^?1) could be stored for long periods without any detectable changes in its optical properties. All together, these new dyes possess a set of very interesting properties that make them promising solid‐state NIR fluorophores for applications in materials science.