Light level control in birefringent fibres through thermal stress effects caused by the absorption of broadside incident light: a single-ended fibre-optic system

In this paper, light level control is demonstrated using optically induced thermal stress effects in a polarization-maintaining optical fibre. The controlling light beam is absorbed by a blackened segment of the fibre and produces local heating. Light control is demonstrated in the single-ended sensor configuration, which displays a response that cannot be explained from phase delays only, but requires the addition of the coupled mode theory.     

Surface structure and composition of the missing-row reconstruction of VC0.8(1 1 0): A LEED, GIXRD and photoemission study

Low energy electron diffraction, grazing incidence X-ray diffraction and photoemission were used to decipher the detailed structural arrangement and chemical composition of the surface region of a transition metal carbide, VC_0.8(1 1 0). In agreement with previous scanning tunneling microscopy (STM) studies, we find that the surface reconstructs with a ridge-and-valley grating structure along the direction resulting from {0 0 1} faceting for the (3 × 1) and the (4 × 1) phases.Both superstructures terminate on the vacuum side with a nearly stoïchiometric VC region due to C segregation, in contrast with the conclusions drawn from this previous STM study. However, the present experiments clearly show that these phases are metastable, and slow cooling results in a (1 × 1) surface, which is highly C depleted, similarly to the (1 0 0) face.     

Influence of the β‐crystalline phase on the mechanical properties of unfilled and calcium carbonate‐filled polypropylene: Ductile cracking and impact behavior

The β‐crystalline form of isotactic poly(propylene) (PP) has been long recognized to have a greater mechanical absorption capacity than the α‐crystalline form. This is of major importance for improving impact properties and crack resistance of injection‐molding parts. Unfilled PP samples together with calcium carbonate‐filled PP samples having various β/α‐phase ratios, with nearly constant morphological parameters, have been investigated from the standpoint of ductile crack propagation and impact behavior. The presence of the β‐crystalline phase turned out to improve both properties. The β spherulites are notably more prone to craze initiation than α spherulites that display a propensity for cracking. Subsequent crack propagation appears to be faster in the latter ones. The plastic zone ahead from the crack tip broadens, and the specific plastic energy increases with increasing β‐phase content. The lower elastic limit of the β phase is likely to promote the early crazing. However, the suspected higher density of tie molecules in β spherulites provides more numerous and stiffer microfibrils. The impact strength of PP is also improved by the presence of β crystals as a result of greater energy‐absorption capabilities. However, filled samples turned out insensitive to the β phase. A discussion is made about the origins of the β‐phase‐induced improvement of the mechanical properties. The possible role of the β → α transition is also explained. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 31–42, 2002     

Small-signal amplification of period-doubling bifurcations in smooth iterated maps

Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.     

Simultaneous approximation on two subsets of an open Riemann surface

Given functions f₁ and f₂ meromorphic, respectively, on subsets E₁ and E₂ of a Riemann surface R, we seek a function meromorphic on all of R, which simultaneously approximates f₁ on E₁ and f₂ on E₂.     

Rational approximation and universality for a quasilinear parabolic equation

Approximation theorems, analogous to results known for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for one of the simplest examples of a nonlinear partial differential equation, Burgers’ equation.     

On the definition of the resonance with examples two-channel models

In an exactly solvable model of separable potentials a two channel scattering problem is solved in l = 0 state. The location and the width of a resonance are then defined in three different ways and the resonance parameters so extracted are then compared. This problem is of interest vis-a-vis the Δ(3, 3) resonance parameters.     

Approximation by harmonic functions on closed subsets of Riemann surfaces

Given continuous functionsu and ∈ on a closed subsetF of a Riemann surface, we seek a harmonic functionv on the surface (possibly with logarithmic singularities) such that |u−v|<∈ onF. Research supported in part by NSERC—Canada and FCAR—Quebec.