Rubber elasticity in relation to polyester networks

The equation of rubber elasticity has been applied to the dynamic shear modulus of styreneunsaturated polyester networks. Due to the non-ideal nature of the networks, the apparent front factor approached the theoretical value of 0.5 only when the crosslink density was low. At higher crosslink densities, it has been found that either the non-Gaussian theory of Smith or the steric interaction approach of Blanchard and Wooton satisfactorily describes the results.     

Molecular rearrangement and cluster formation in the secondary ion mass spectra (SIMS) of fluoride salts

Secondary ion clusters with mass greater than 700 amu, e.g., K(KF)₁₂⁺ and up to 27 atoms, e.g., Na(NaF)₁₃⁺, have been observed in the static SIMS spectra of MF (M = Li, Na, K), NaBF₄, and KPF₆. The long series of detected cluster ions of the type M(MF)_n⁺ indicates that there is a high degree of stability associated with these clusters. The observation of such clusters in the NaBF₄ and KPF₆ spectra suggest that there is significant molecular rearrangement occurring in the secondary ion emission process from such salts. The secondary ion Intensities provide a crude fit to the Saha-Eggert equation, yielding an electron temperature of ~12,000 K. The data are consistent with the plasma model of surface ionization in which rearrangement and cluster formation occur in the plasma.     

Molecular photoionization cross-sections and their dependence on excitation energy

A general formula for the photoionization cross-section of a linear molecule in terms of atomic subshell cross-sections and diffraction effects is given. Example calculations are carried out for line intensities of CO and N₂ as a function of incident photon energy from threshold up to the soft X-ray region. The importance of associating CNDO coefficients to orthogonal Slater AO's is pointed out. General rules for dependence of photoionization cross-sections on excitation energy are discussed.     

Multipoint boundary value problems with discontinuities II. Convergence of the initial value adjusting method

In this paper we give a proof for convergence of the initial value adjusting method, described in detail in part I, based on Kantorovich's theorem. Under standard assumptions on the dynamics, boundary conditions, and initial approximations, a quadratic convergence rate is obtained.     

L p Results for the Pompeiu Problem with Moments on the Heisenberg Group

This article extends previous results on the Pompeiu problem with moments. On the Heisenberg group the results previously considered for L²(H_n) have been extended to the function spaces L^p(H_n) for 1 p . In the case of L(H_n), the conclusions recover differential conditions comparable to those observed in the Euclidean space Cⁿ.     

Self-starting passive harmonic mode-locked femtosecond Yb3+-doped fiber laser at 1030 nm

We demonstrate, for the first time to our knowledge, a self-starting passive harmonic mode-locked femtosecond Yb3+-doped fiber laser with a scalable repetition rate of up to 585 MHz and >45 dB of supermode suppression. Pulse-to-pulse jitter of approximately 14 ps is measured by optical cross correlation at the ninth harmonic, and radiofrequency (RF) spectrum measurements show that certain correlations exist between pulses in harmonic mode. Our results suggest that one of the proposed passive harmonic mode-locking mechanisms may be dominant for this laser.     

Modification of statistical threading in two-component pseudorotaxane melts using the amphiphilic approach and variations in the confinement geometry

Recently we described a coarse-grained model of poly(ethylene oxide) and then employed that model to study the amount of spontaneous threading of cyclic molecules by linear chains in the melt [C. A. Helfer, G. Xu, W. L. Mattice, and C. Pugh, Macromolecules 36, 10071 (2003)]. Since the amount of statistical threading at equilibrium is small, there is interest in identifying physical changes in the system that will increase the threading. We now use that coarse-grained model to investigate the effect on threading of various hypothetical (but feasible) modifications to the two-component system of macrocycles and linear chains in the melt, and different confinement geometries, that can bring about correlations in the arrangement of the rings. Our work follows on the concept of an amphiphilic approach [C. Pugh, J.-Y. Bae, J. R. Scott, and C. L. Wilkins, Macromolecules 30, 8139 (1997)] for increasing the statistical threading in homopolyrotaxane melts. We investigate whether introducing such correlations in the macrocycles can increase the spontaneous threading. This paper shows that some of our modifications can yield more than double the amount of threading seen in purely statistical mixing.     

Cavity-enhanced absorption: detection of nitrogen dioxide and iodine monoxide using a violet laser diode

We present an application of cavity-enhanced absorption spectroscopy with an off-axis alignment of the cavity formed by two spherical mirrors and with time integration of the cavity-output intensity for detection of nitrogen dioxide (NO₂) and iodine monoxide (IO) radicals using a violet laser diode at λ=404.278 nm. A noise-equivalent (1σ≡ root-mean-square variation of the signal) fractional absorption for one optical pass of 4.5×10^-8 was demonstrated with a mirror reflectivity of ∼0.99925, a cavity length of 0.22 m and a lock-in-amplifier time constant of 3 s. Noise-equivalent detection sensitivities towards nitrogen dioxide of 1.8×10¹⁰ molecule cm^-3 and towards the IO radical of 3.3×10⁹ molecule cm^-3 were achieved in flow tubes with an inner diameter of 4 cm for a lock-in-amplifier time constant of 3 s. Alkyl peroxy radicals were detected using chemical titration with excess nitric oxide (RO₂+NO→RO+NO₂). Measurement of oxygen-atom concentrations was accomplished by determining the depletion of NO₂ in the reaction NO₂+O→NO+O₂. Noise-equivalent concentrations of alkyl peroxy radicals and oxygen atoms were 3×10¹⁰ molecule cm^-3 in the discharge-flow-tube experiments. Received: 4 February 2003 / Revised version: 10 March 2003 / Published online: 12 May 2003 RID="*" ID="*"Corresponding author. Fax: +44-1865/275-410, E-mail: vlk@physchem.ox.ac.uk     

Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space

We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean curvature 1 surfaces in hyperbolic 3-space, and we give an overview of recent results on these surfaces. We include computer graphics of a number of examples.