Short-scan interferometric interrogation and multiplexing of fibre Bragg grating sensors

We describe an interferometric technique for the demodulation of serial fibre Bragg grating sensor arrays, yielding absolute measurement of the individual grating mean wavelengths. The composite beam reflected from the array illuminates a scanning Michelson interferometer but, in contrast to spectral measurement by Fourier Transform Spectroscopy, our technique requires an OPD scan far shorter than the coherence length of the grating reflections. The technique is based on the high-resolution measurement of the phases of the complex analytic signals and of the relationship of these phases to interferometric delay. The analytic signals are derived via the Hilbert transform, allowing frequency domain filtering of individual signals within the signal processing. The technique has yielded a resolution of 0.007 nm for an OPD scan of 1.2 mm.     

Note on a versatile Liapunov functional: applicability to an elliptic equation

A novel, very effective Liapunov functional was used in previous papers to derive decay and asymptotic stability estimates (with respect to time) in a variety of thermal and thermo‐mechanical contexts. The purpose of this note is to show that the versatility of this functional extends to certain non‐linear elliptic boundary value problems in a right cylinder, the axial co‐ordinate in this context replacing the time variable in the previous one. A steady‐state temperature problem is considered with Dirichlet boundary conditions, the condition on the boundary being independent of the axial co‐ordinate. The functional is used to obtain an estimate of the error committed in approximating the temperature field by the two‐dimensional field induced by the boundary condition on the lateral surface. Copyright © 2002 John Wiley & Sons, Ltd.     

Asymptotic behaviour of solutions to semi-linear elliptic equations on the half-cylinder

Various, but closely related, forms of a Phragmén-Lindelöf principle are established for certain classes of semi-linear elliptic equations (including systems) defined on a half-cylinder. For example, it is shown that under either homogeneous Dirichlet or Neumann lateral boundary conditions, the smooth solution either fails to exist globally, or when it does exist globally it must tend asymptotically to zero with increasingly large distance along the cylinder from the base. For uniformly elliptic equations, the decay to zero is at least exponential. The method employed relies upon cross-sectional estimates and is additionally applicable to both the finite and whole cylinder. In the latter case, global existence fails for all non-trivial solutions.Dedicated to Prof. Klaus Kirchgässner on the occasion of his sixtieth birthday     

Dispersion of birefringence and differential group delay in polarization-maintaining fiber

We present an interferometric technique for measurement of the dispersion of birefringence in polarization-maintaining fibers. The approach yields measurements over a broad spectral range from analysis of single interferograms obtained in a tandem inteferometer. The technique is demonstrated to measure first-, second-, and third-order dispersion of the differential propagation constant, corresponding to differential group delay (DGD) and its dispersion to second order; measurements are immune to asymmetry in the interferomgram that is being processed. The technique is further applied to measurement of the temperature dependence of DGD and its first-order dispersion.     

The fundamental integral for small deformations superposed on finite triaxial extension of a neo-Hookean material

Résumé Nous considérons un matériau élastique néo-hookéen qui remplit l'espace entier et qui subit une forte déformation homogène et élastique. Nous trouvons le champ élastique additionnel induit par une petite charge concentrée agissant dans le sens d'une des extensions principales. Nous exprimons la solution en fonctions potentielles.