On the wrinkling of a pre-stressed annular thin film in tension

Asymptotic properties of the neutral stability curves for a linear boundary eigenvalue problem which models the wrinkling instability of an annular thin film in tension are considered. The film is subjected to imposed radial displacement fields on its inner and outer boundaries and, when these loads are sufficiently large, the film is susceptible to wrinkling. The critical values at which this onset occurs are dictated by the solution of a fourth-order ordinary differential eigensystem whose eigenvalue λ is a function of μ(?1), a quantity inversely proportional to the non-dimensional bending stiffness of the film, and n, the number of half-waves of the wrinkling pattern that sets in around the annular domain. Previously, Coman and Haughton [2006. Localised wrinkling instabilities in radially stretched annular thin films. Acta Mech. 185, 179-200] employed the compound matrix method together with a WKB technique to characterise the form of λ(μ,n) which essentially is related to a turning point in a reduced eigenproblem. The asymptotic analysis conducted therein pertained to the case when this turning point was not too close to the inner edge of the annulus. However, in the thin film limit μ→∞, the wrinkling load and the preferred instability mode are given by a modified eigenvalue problem that involves a turning point asymptotically close to the inner rim. Here WKB and boundary-layer asymptotic methods are used to examine these issues and comparisons with direct numerical simulations made.     

Interference of white light in tandem configuration of birefringent crystal and sensing birefringent fiber

Spectral interference of white-light beams propagating through a tandem configuration of birefringent crystal and sensing birefringent fiber is analyzed theoretically and experimentally. The spectral interference law is expressed analytically under the condition of a Gaussian response function of a spectrometer taking into account the dispersion of birefringence in the crystal and in the fiber. Two types of spectral interferograms are modeled knowing dispersion characteristics of the sensing fiber and using a quartz crystal of the positive or a calcite crystal of the negative birefringence. The theoretical analysis is accompanied by two experiments employing a highly birefringent fiber and a birefringent quartz crystal of two suitable thicknesses. Within both experiments the spectral interference fringes are resolved in accordance with the theory with phases dependent on the fiber length.     

Secondary bifurcations and localisation in a three-dimensional buckling model

This paper revisits the effect of secondary bifurcations on the post-buckling response of a simple 3D system of elastically restrained beams, first discussed by Luongo in [19]. Our main objective is to show how to construct a uniform asymptotic expression for the localised buckling patterns experienced by this model. The governing equation is formulated as a fourth-order eigenvalue problem with non-constant coefficients and then a complex WKB technique is employed to yield the localised instability patterns. Numerical simulations supporting the analytical findings are included as well.     

Quantum flux-based resonances in solitonic vortices

Working with the Nielsen–Olesen Lagrangian in static cylindric coordinates, we derive the system of coupled field equations and perform a first-order perturbative approach, pointing out an interesting contribution connected to the London–Heitler current. For an r,θ-depending scalar boson, evolving in a constant or zero magnetic field we get, besides the flux quantization and the Landau energy levels, a less expected structure of the scalar modes whose radial and azimuthal parts are decoupled by the presence of the quantized magnetic flux.     

MISTRAL: A new program for precise atomic mass determinations of nuclides far from stability

The MISTRAL project (Mass measurements at ISolde using a Transmission RAdiofrequency spectrometer on-Line) is scheduled to begin experiments towards the end of 1996. With high resolution (10⁵), potentially high accuracy (5×10^–7) and excellent sensitivity (10 s^–1), the MISTRAL spectrometer promises to provide needed mass measurements in regions of very-short lived nuclei. The spectrometer operation principles are described and a discussion concerning the interest in using highly charged ions is presented.CSNSM, Orsay; IAP, Bucharest; PPE Division, CERN; GSI, Darmstadt; University of Mainz; McGill University, Montreal; IPN, Orsay; Chalmers University, Göteborg; University of Giessen and the ISOLDE Collaboration.     

Elastic scattering of 86 MeV9Li and 55 MeV6He on208Pb

The cross sections of elastically scattered⁹Li and⁶He on²⁰⁸Pb were measured. The scattered particles were detected by an annular CR-39 solid state nuclear track detector and the monitoring was done with a triple telescope of silicon detectors. The classical and optical model analyses of the measured elastic cross sections have been carried out. It was shown that the peripheral⁹Li interaction region has a rather high transparency. Strong dynamical polarization of⁹Li ions in the process of scattering is suggested.     

Central intertwining lifting,maximum entropy and their permanence

The central intertwining lifting is used to establish a maximum principle for the commutant lifting theorem. This maximum principle is used to prove that the central intertwining lifting is also a maximal entropy solution for the commutant lifting theorem, when T is a unilateral shift of finite multiplicity. The maximum principle is based on the residual spaces for intertwining liftings, and is motivated by Robinson's minimum energy delay principle for outer functions. A permanence property for the central intertwining lifting is also given.     

Amperometric Detection of 4‐Chlorophenol on Two Types of Expanded Graphite Based Composite Electrodes

The assessment of an expanded graphite‐Ag‐zeolite‐epoxy composite (EG‐Z‐Ag‐Epoxy) electrode for the determination of 4‐chlorophenol (4‐CP) is described and compared to the corresponding expanded graphite‐epoxy composite (EG‐Epoxy) electrode. Cyclic voltammetry was used to characterize the electrochemical behavior and determination of 4‐CP at both electrodes in 0.1 M Na₂SO₄ and 0.1 M NaOH supporting electrolytes. A substantial enhancement of sensitivity for the determination of 4‐CP at the EG‐Z‐Ag‐Epoxy electrode was reached by applying a chemical preconcentration step prior to voltammetric quantification. Also, under these last conditions the lowest limit of detection of 1 μM illustrates the analytical versatility of this electrode in a concentration range where aquatic 4‐chlorophenol pollution is known to occur.     

Simultaneous Determination of Acetaminophen and Ascorbic Acid at an Unmodified Boron‐Doped Diamond Electrode by Differential Pulse Voltammetry in Buffered Media

A boron‐doped diamond electrode (BDDE) was used for the simultaneous anodic determination of L ‐ascorbic acid (AA) and acetaminophen (AC) in aqueous buffered media by differential pulse voltammetry (DPV). Linear calibration plots of anodic current peaks versus concentration were obtained for both analytes in the concentration range 0.01–0.1 mM with very high correlation coefficients. RSD of 2–3% and high sensitivities were obtained from DPV data in single and dicomponent systems. The potential applicability of the DPV technique associated with standard addition was illustrated by simultaneous determination of AA and AC in real sample solutions made up from pharmaceutical products.     

Soft Null Hypotheses: A Case Study of Image Enhancement Detection in Brain Lesions

This work is motivated by a study of a population of multiple sclerosis (MS) patients using dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) to identify active brain lesions. At each visit, a contrast agent is administered intravenously to a subject and a series of images are acquired to reveal the location and activity of MS lesions within the brain. Our goal is to identify the enhancing lesion locations at the subject level and lesion enhancement patterns at the population level. We analyze a total of 20 subjects scanned at 63 visits (～30Gb), the largest population of such clinical brain images. After addressing the computational challenges, we propose possible solutions to the difficult problem of transforming a qualitative scientific null hypothesis, such as “this voxel does not enhance,” to a well-defined and numerically testable null hypothesis based on the existing data. We call such procedure “soft null” hypothesis testing as opposed to the standard “hard null” hypothesis testing. This problem is fundamentally different from: (1) finding testing statistics when a quantitative null hypothesis is given; (2) clustering using a mixture distribution; or (3) setting a reasonable threshold with a parametric null assumption. Supplementary materials are available online.