Variational symmetries and Lagrangian multiforms

Letters in Mathematical Physics - By considering the closure property of a Lagrangian multiform as a conservation law, we use Noether’s theorem to show that every variational symmetry of a...     

The synthesis and evaluation of unsymmetrical dimeric X-ray contrast agents

Novel dimeric iodinated contrast agents with low osmolality have been prepared and evaluated with the aim of improving the already good safety profile of such agents. The aim of low osmolality was achieved, and the viscosity of these dimeric agents was also found to be beneficially lower than current dimeric agents in clinical use.     

Identification of geometric parameters influencing the flow-induced vibration of a two-layer self-oscillating computational vocal fold model

Simplified models have been used to simulate and study the flow-induced vibrations of the human vocal folds. While it is clear that the models' responses are sensitive to geometry, it is not clear how and to what extent specific geometric features influence model motion. In this study geometric features that played significant roles in governing the motion of a two-layer (body-cover), two-dimensional, finite element vocal fold model were identified. The model was defined using a flow solver based on the viscous, unsteady, Navier-Stokes equations and a solid solver that allowed for large strain and deformation. A screening-type design-of-experiments approach was used to identify the relative importance of 13 geometric parameters. Five output measures were analyzed to assess the magnitude of each geometric parameter's effect on the model's motion. The measures related to frequency, glottal width, flow rate, intraglottal angle, and intraglottal phase delay. The most significant geometric parameters were those associated with the cover--primarily the pre-phonatory intraglottal angle--as well as the body inferior angle. Some models exhibited evidence of improved model motion, including mucosal wave-like motion and alternating convergent-divergent glottal profiles, although further improvements are still needed to more closely mimic human vocal fold motion.     

Picosecond pulses from a cryogenically cooled, composite amplifier using Yb:YAG and Yb:GSAG

A cryogenic Yb amplifier using two laser materials, Gd3Sc2Al3O12 and Y3Al5O12 (YAG), has been used to obtain 70 W average power at 5 kHz pulse repetition frequency; the output was compressed to 1.6 ps, compared with an input compressible to 1.4 ps. The gain broadening obtained by combining two media enables shorter pulses than using Yb:YAG alone but retains the power-scaling advantages of cryogenic Yb:YAG.     

Selective spreading and jetting of electrically driven dielectric films

We study the electrically driven spreading of dielectric liquid films in wedge-shaped gaps across which a potential difference is applied. Our experiments are in a little-studied regime where, throughout the dynamics, the electrical relaxation time is long compared to the time for charge to be convected by the fluid motion. We observe that at a critical normal electric field the hump-shaped leading edge undergoes an instability in the form of a single Taylor cone and periodic jetting ensues, after which traveling waves occur along the trailing thin film. We propose a convection-dominated mechanism for charge transport to describe the observed dynamics and rationalize the viscosity dependence of the self-excited dynamics.     

A high-resolution NMR probe in which the coil and preamplifier are cooled with liquid helium. 1984

In a well designed NMR spectrometer, the noise originates predominantly from the resistance of the receiver coil. Significant improvements in sensitivity can be achieved by cooling the coil to cryogenic temperatures, provided that a preamplifier can be designed to match the coil’s performance. A probe is described in which the coil and preamplifier are cooled with liquid helium, but the sample is maintained at room temperature. Carbon-l3 spectra at 45 MHz demonstrate improved sensitivity over conventional probes at the same field.     

Diborane: High resolution infrared rovibration studies of 11B2H6 and 11B2D6

Ground state rotation and quartic distortion constants were obtained for ¹¹B₂D₆ from the analysis of high resolution (～0.05 cm^?1) Fourier transform infrared spectra. The bands studied comprised the ν₁₇, ν₁₈ type A, and ν₁₄, ν₉ + ν₁₅ type C bands of ¹¹B₂H₆ and the ν₁₆, ν₁₇, ν₁₈ type A, ν₈ type B, and ν₁₄ type C bands of ¹¹B₂D₆. In the case of ¹¹B₂H₆, the authors' ground state data were combined with those of Lafferty et al. obtained from a previous study (J. Mol. Spectrosc.33, 345–367 (1970)) at comparable resolution of the ν₁₆ type A and ν₈ type B fundamentals. Information on the ground state rotational energy manifold of ¹¹B₂H₆ was accumulated up to J = 23, K_a = 18, and of ¹¹B₂D₆ up to J = 32, K_a = 22. This permitted rather precise determination of the distortion constants Δ_J⁰, Δ_JK⁰, Δ_K⁰, although δ_J⁰ and δ_K⁰ proved to be too small (< 10^?7 cm^?1) and were constrained to values calculated from the force field. Sets of upper state parameters were determined for all vibrational levels studied. Although these appear to be essentially unperturbed globally, several localized perturbations were observed and identified.     

Possibilities for refining an object program compiled with an ALGOL translator

The paper discusses possible improvements in connection with compilation of computer programs. Four different areas are mentioned where contributions should be possible: The language, the computer, the compiler, and the programmer. Although many of the points are quite general, ALGOL 60 is specifically taken into account.This paper was presented at the NordSAM conference in Stockholm, Aug. 1964.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Sample path Large Deviations and optimal importance sampling for stochastic volatility models

Sample path Large Deviation Principles (LDP) of the Freidlin–Wentzell type are derived for a class of diffusions, which govern the price dynamics in common stochastic volatility models from Mathematical Finance. LDP are obtained by relaxing the non-degeneracy requirement on the diffusion matrix in the standard theory of Freidlin and Wentzell. As an application, a sample path LDP is proved for the price process in the Heston stochastic volatility model.