Numerical continuation of degenerate homoclinic orbits in planar systems

In this paper we develop numerical algorithms for the continuationof degenerate homoclinic connections in planar systems. We considerthe case where the equilibrium point has zero trace and twocases of higher-order degeneracies. The method we propose isable to continue homoclinic connections of order up to codimension-four.Application of the algorithm to four examples supports its validityand demonstrates its usefulness.     

Quantification routines for adsorption studies in static secondary ion mass spectrometry and the effect of ionisation probability

It is shown that the usual method of quantification of surface composition in static secondary ion mass spectrometry (SSIMS), which is purely comparative in nature, is unsuitable for adsorption studies by SSIMS. This is because of the effect of the ionisation efficiency and ion stability of a particular ion produced from a molecule adsorbed on the surface of a substrate. The established routine results in a non-linear relationship between calculated relative surface coverage and the ion selected to characterise the adsorbate. The application of a new normalisation routine to time-of-flight secondary ion mass spectrometry (ToF-SIMS) data has been used to account for this discrepancy, and also takes into account the effect of a possible contribution from the clean substrate to the ion selected to characterise the adsorbate molecule. This routine is suggested only for use with organic secondary ions, where the ionisation potential of such ions is of a comparable magnitude, and should prove particularly useful in the application of surface analysis techniques to adsorption studies.     

Gas-phase deprotonation of arylalkylamines. A collision-induced dissociation study

The collision-induced dissociation (CID) of deprotonated arylalkylamines of general formula R(1)C(6)H(4)CHR(2)CH(2)NR(3)(2) (where R(1) = H, OH, F or NO(2); R(2) = H or OH; R(3) = H or CH(3)) generated by negative chemical ionization with H(2)O and D(2)O as ionizing reagents, is discussed. The negative chemical ionization mass spectra show that, in the absence of a hydroxy group in the aromatic ring, deprotonation takes place at the benzylic position whereas the proton is lost from the OH group when present. The nitro compound forms only M(-.) ions. The CID spectra of the deprotonated molecules show that fragmentations are strongly dependent on the structural features of the molecules, namely the presence or absence of substituents in the aromatic ring or aliphatic chain. Copyright 1999 John Wiley & Sons, Ltd.     

The onset of coulomb explosions in polyatomic molecules

With the development of high intensity femtosecond lasers, the ionisation and dissociation dynamics of molecules has become an area of considerable interest. Using the technique of femtosecond laser mass spectrometry (FLMS), the molecules carbon disulphide, pyrimidine, toluene, cyclohexanone and benzaldehyde are studied with pulse widths of 50 fs in the near infrared (IR) wavelength region (790 nm). Results are presented and contrasted for laser beam intensities around 10(15) and 10(16) W cm(-2). For the lower intensities, the mass spectra yield dominant singly charged parent ions. Additionally, the appearance of doubly charged parent ions is evident for carbon disulphide, toluene and benzaldehyde with envelopes of doubly charged satellite species existing in these local regions. Carbon disulphide also reveals a small triply charged component. Such atomic-like features are thought to be a strong fingerprint of FLMS at these intensities. However, upon increasing the laser intensity to approximately 10(16) W cm(-2), parent ion dominance decreases and the appearance of multiply charged atomic species occurs, particularly carbon. This phenomenon has been attributed to Coulomb explosions in which the fast absorption of many photons may produce transient highly ionised parent species which can subsequently blow apart. Copyright 1999 John Wiley & Sons, Ltd.     

Uniform molecular analysis using femtosecond laser mass spectrometry

The potential of femtosecond laser time-of-flight mass spectrometry (FLMS) for uniform quantitative analysis of molecules has been investigated. Various samples of molecular gases and vapours have been studied, using ultra-fast ( approximately 50 fs) laser pulses with very high intensity (up to 1.6 x 10(16) Wcm(-2)) for non-resonant multiphoton ionisation/tunnel ionisation. Some of these molecules have high ionisation potentials, requiring up to ten photons for non-resonant ionisation. The relative sensitivity factors (RSF) have been determined as a function of the laser intensity and it has been demonstrated that for molecules with very different masses and ionisation potentials, uniform ionisation has been achieved at the highest laser intensities. Quantitative laser mass spectrometry of molecules is therefore a distinct possibility. Copyright 1999 John Wiley & Sons, Ltd.     

1H spin-lattice relaxation and observation of interfacial material in solid polyethylenes

The ¹H NMR laboratory- and rotating-frame (LF,RF) spin-lattice relaxation (SLR) behaviour in solid polyethylenes is reviewed in light of the two region spin diffusion coupled model. Highly crystalline high-density materials show single T¹ values indicative of the fast diffusion limit whilst RFSLR is close to the slow diffusion limit, allowing direct determination of the dimensions of the crystalline and disordered regions. The LFSLR and RFSLR of the HDPE's suggest the existence of an interfacial material which the SLR behaviour includes as part of the crystalline region in contrast to XRD and DSC. ¹³C CPMAS measurements of ¹H RFSLR in a LLDPE provide an additional insight into this problem. The ¹H RFSLR is best represented by a superposition of two exponentials, measured by either ¹H or ¹³C NMR. The ¹H RFSLR, measured at different chemical shifts in the ¹³C NMR spectrum, provides direct evidence of the interfacial material. The possible use of spin-locking at angles other than 90° in the rotating frame to scale the spin diffusion rates is reviewed and its possible utility for LLDPE materials explored.     

Cosheaves and connectedness in formal topology

The localic definitions of cosheaves, connectedness and local connectedness are transferred from impredicative topos theory to predicative formal topology. A formal topology is locally connected (has base of connected opens) iff it has a cosheaf π₀ together with certain additional structure and properties that constrain π₀ to be the connected components cosheaf. In the inductively generated case, complete spreads (in the sense of Bunge and Funk) corresponding to cosheaves are defined as formal topologies. Maps between the complete spreads are equivalent to homomorphisms between the cosheaves. A cosheaf is the connected components cosheaf for a locally connected formal topology iff its complete spread is a homeomorphism, and in this case it is a terminal cosheaf.A new, geometric proof is given of the topos-theoretic result that a cosheaf is a connected components cosheaf iff it is a “strongly terminal” point of the symmetric topos, in the sense that it is terminal amongst all the generalized points of the symmetric topos. It is conjectured that a study of sites as “formal toposes” would allow such geometric proofs to be incorporated into predicative mathematics.     

Nanostructures in Physical Materials Chemistry: An Exploratory Laboratory

The blend of nanotechnology and material science is often beyond the scope of undergraduate laboratories. Through undergraduate research, graphite-intercalated compounds have been incorporated in the production of carbon-based nanostructures. Based on this work a series of exploratory exercises were designed for the undergraduate physical chemistry laboratory emphasizing nanostructure material science. This rapidly expanding area of science and technology can be introduced at an undergraduate level using a high temperature oven to produce nanostructure samples that are analyzed by Raman spectroscopy, scanning electron microscopy, and transmission electron microscopy at research university laboratories, infrared spectroscopy, and a bomb calorimeter. In these experiments we use samples of pure graphite, fluorinated graphite, and lanthanum oxide to induce the formation of nanostructures. An overview of fullerenes, nanotubes, boron nitride and Si nanostructures, other carbon forms, graphite-intercalated compounds, and the storage of hydrogen in nanotubes are provided in an appendix. Several extensions of the laboratory are proposed.     

100 mK bolometers for the submillimetre common-user bolometer array (scuba) I. Design and construction

We describe the design and construction of bolometric detectors for SCUBA - the Submillimetre Common-User Bolometer Array for the James Clerk Maxwell Telescope in Hawaii. The instrument contains 131 individual detectors, in two arrays, optimized for the submillimetre atmospheric transmission windows. The detectors are cooled by dilution refrigeration to a temperature of 100 mK, so that the receiver performance will be limited by photon noise from the sky and telescope background in all wavebands. A future paper will describe the performance of the detectors with reference to typical data obtained during the laboratory commissioning period.     

Thermoset polyester as an alternative material for microchip electrophoresis/electrochemistry

Microchip CE coupled with electrochemical detection (MCE-EC) is a good method for the direct detection of many small molecule analytes because the technique is sensitive and readily miniaturized. Polymer materials are being increasingly used with MCE due to their affordability and ease of fabrication. While PDMS has become arguably the most widely used material in MCE-EC due to the simplicity of microelectrode incorporation, it suffers from a lack of separation efficiency, lower surface stability, and a tendency for analyte sorption. Other polymers, such as poly(methylmethacrylate) (PMMA) and poly(carbonate) (PC), have higher separation efficiencies but require more difficult fabrication techniques for electrode incorporation. In this report, thermoset polyester (TPE) was characterized as an alternative material for MCE-EC. TPE microchips were characterized in their native and plasma oxidized forms and after coating with polyelectrolyte multilayers (PEMs). TPE provides higher separation efficiencies when compared to PDMS microchips, while still using simple fabrication protocols. In this work, separation efficiencies as high as 295,000 N/m were seen when using TPE MCE-EC devices. Furthermore, the EOF was higher and more consistent as a function of pH for both native and plasma-treated TPE than PDMS. Finally, TPE is amenable to modification using simple PEM coatings as another way to control surface chemistry and surface charge.