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.     

MRI velocimetry and lattice-Boltzmann simulations of viscous flow of a Newtonian liquid through a dual porosity fibre array.

Viscous flow through fibrous porous media has considerable importance in a number of industrial processes including, in particular, resin transfer molding. In this paper magnetic resonance flow imaging techniques are used to visualize flow of a Newtonian liquid through a dual porosity structure. Of particular interest in these studies is the transition in the flow as the liquid moves from the open region into the fiber array. The ability of lattice-Boltzmann simulations to predict the visualized flow fields is presented and discussed.     

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.     

Real-time measurement of bubbling phenomena in a three-dimensional gas-fluidized bed using ultrafast magnetic resonance imaging

Ultrafast magnetic resonance imaging has been applied for the first time to measure simultaneously both the rise velocities and coalescence of bubbles, and the dynamics of the solid phase in a gas-solid two-phase flow. Here, we consider the hydrodynamics within a gas-fluidized bed of particles of diameter 0.5 mm contained within a column of internal diameter 50 mm; gas velocities in the range of 0.18-0.54 m/s were studied. The data are of sufficient temporal and spatial resolution that bubble size and the evolution of bubble size and velocity following coalescence events are determined.     

Rapid measurement of transient velocity evolution using GERVAIS

Rapid velocity measurements using GERVAIS (Gradient Echo Rapid Velocity and Acceleration Imaging Sequence), an EPI (Echo Planar Imaging) based technique capable of measuring velocity over an observation time of several milliseconds, are performed on a wide-gap Couette Rheo-NMR cell for the first time. A variable delay time between a control signal to initiate a transition in flow and the start of the measurement sequence is incorporated to allow investigation of the transient evolution of the velocity field following a step change in rotation rate. Both the commencement and the cessation of imposed shear stress are investigated for (i) a shear banding micellar solution of CPyCl (cetylpyridiniumchloride)/NaSal (sodium salicylate) in brine and (ii) a low molecular weight PDMS (polydimethylsiloxane) oil. With respect to the micellar solution, an elastic shear wave is seen to propagate across the cell following the commencement of shear stress whilst an oscillatory ‘recoil’ is observed following the cessation of shear stress; neither of these phenomena were observed for the PDMS oil which exhibited a purely viscous response as expected for an incompressible Newtonian fluid. This technique has potential applications across a wide range of transient rheological investigations, particularly with respect to optically opaque materials.     

Rapid measurement of dispersion and velocity in freezing drops using magnetic resonance methods

Magnetic resonance (MR) methods are used to provide both rapid real-time dispersion and spatially resolved velocity measurements within suspended drops undergoing freezing. Two-mm-diameter drops composed of water, sucrose solution, oil-in-water emulsion or oil-in-sucrose-solution emulsion drops are thus studied. Dispersion measurements have been shown to give valuable insights into the transport processes and solidification behaviour of the freezing drops. It was possible to detect drop nucleation/recalescence, rupture and solution freeze concentration. Limited convection of unfrozen material, due to crystal growth, was detected. The spatial distribution of the velocity within freezing drops revealed the rotation of the water drops but not of drops composed of the other materials studied. Rapid increases in velocity were observed following nucleation, which were dampened down during subsequent heat-transfer-governed droplet freezing.