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.     

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.     

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.     

Determination of loads applied perpendicularly to the outer boundary of a ring using coefficients of influence

A procedure is explained to determined the amount of several pairs of diametrical loads applied to the outside boundary of a ring when stresses at selected points of the inside or outside boundaries are known. Coefficients of influence are used, following an approach similar to the one presented in a previous paper. Examples of application are given and the possible increase in precision is shown when the number of points of measurements is larger than the number of loads to be determined.     

Stresses in square slabs,with different edge geometries,when bonded on one face to a rigid plate and shrunk

An approximately square epoxy slab (≈14 in. ×≈14 in. ×1 in.) with four different edge geometries was bonded to a rigid plate on one of its faces. In the process of “freezing” photoelastic effects, a state of restrained shrinkage developed. Slices removed from the slab were used to determine the concentration factors corresponding to the four geometries.     

A shadow-moiré method with continuously variable sensitivity

This paper presents a shadow moiré method whereby the isostathmics (contours of surface depth) can be studied with continuously variable sensitivity. In the method the sensitivity is varied by simply rotating the grating in front of the object surface. Equations interpreting the isostathmics are derived, and an experimental demonstration is included.     

Identification of isochromatic fringes

In simple cases of static-photoelastic analysis, the numbering of the isochromatic fringes does not present unusual difficulties. In more complex cases, in particular wave propagation, the problem may be so difficult that few investigators attempt the analysis. In this paper guidelines to number the isochromatic fringes are presented. Advantage is taken of some topological properties as well as of the time and space derivatives of these isochromatic fringes. Several examples are discussed to illustrate the use of the guidelines. It is observed that under most conditions the guidelines are sufficient to number the whole field of isochromatics on photographs taken with the commonly used monochromatic light.     

Temperature and time influence in the stress freezing of the epoxy Hysol 4290

Disks of the photoelastic epoxy known as Hysol 4290 have been subjected to constant load at various temperature levels and the birefringence has been recorded as time elapsed (creep test). Also disks of the same material were loaded at the critical temperature and then cooled, each to a different temperature level and, after they reached thermal equilibrium, the loading was removed while the temperature was maintained constant (recovery test). The effect of time on the fringe value is given for both groups of tests using the temperature as a parameter. Finally, tensile specimens have been subjected to various loads at the critical temperature and fringe response and failure recorded. The results obtained may be useful for the design of experiments and, in some cases, to shorten the time required to conduct a three-dimensional photoelasticity investigation using the “freezing” method.