A multipoint quasi-distributed optical fiber pH sensor

This paper reports the development and characterisation of a multipoint quasi-distributed optical fiber sensor for pH measurement. The system is based on a 170 m length of 200 μm core diameter plastic cladding silica fiber where sections of cladding have been removed and replaced with dye immobilised sol-gel glass to form sensing points. Evanescent wave excitation of a dye, immobilised within 2 mm long sections of cladding, enables the pH value of any spillage material to be determined by optical time domain reflectometry along the length of the fiber. The results suggest a spatial resolution of better than 2.5 meters for this fiber system and indicate that this arrangement could form the basis of a practical sensor/actuator system for chemical spillage, provided that suitable dye/analyte combinations are available.     

Solving singular convolution equations using the inverse Fast Fourier Transform

The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.     

Dynamics of Self-Organized and Self-Assembled Structures,by Rashmi C. Desai and Raymond Kapral

The arrival of the first hard X-ray free electron laser facilities promises new advances in structural dynamics and nanoscale imaging that will have impact across the sciences. This introductory review is intended to cover the basic physics behind this potential and illustrate the current state-of-the-art by discussing a number of recent findings from the LCLS facility at the Stanford Linear Accelerator Centre (SLAC). We concentrate on the new science using these light sources rather than the new light source technology itself, although a brief introduction to the operation of LCLS is given. Emphasis is placed upon the new regime of high intensity X-ray matter interaction physics with ultrashort X-ray pulses. We discuss how the unique combination of X-ray parameters will open new opportunities for time resolved structural studies and how the high brightness enables a new class of coherent diffraction X-ray imaging. The potential importance of this new imaging method in the study of nanostructures and biological systems at the sub-cellular and molecular level will be outlined.     

Adaptive optics in astronomy

Since Galileo’s first observations in 1609, telescopes have grown dramatically in size. Larger telescopes collect more light, allowing astronomers to detect fainter sources and to look further back in time towards the birth of the universe. The angular resolution of these telescopes, however, has been limited by turbulence in the earth’s atmosphere. This limitation can be dramatically reduced with the use of adaptive optics (AO) to measure and correct the blurring introduced by atmospheric turbulence. AO is now routinely used for science observations on the world’s largest telescopes and is providing a much more detailed view of our universe.     

A nonlinear Hamiltonian structure for the Euler equations

The Euler equations for inviscid incompressible fluid flow have a Hamiltonian structure in Eulerian coordinates, the Hamiltonian operator, though, depending on the vorticity. Conservation laws arise from two sources. One parameter symmetry groups, which are completely classified, yield the invariance of energy and linear and angular momenta. Degeneracies of the Hamiltonian operator lead in three dimensions to the total helicity invariant and in two dimensions to the area integrals reflecting the point-wise conservation of vorticity. It is conjectured that no further conservation laws exist, indicating that the Euler equations are not completely integrable, in particular, do not have soliton-like solutions.     

Quantum integrability of Beltrami-Laplace operator as geodesic equivalence

Given two Riemannian metrics on a closed connected manifold , we construct self-adjoint differential operators such that if the metrics have the same geodesics then the operators commute with the Beltrami-Laplace operator of the first metric and pairwise commute. If the operators commute and if they are linearly independent, then the metrics have the same geodesics. Received: 11 February 2000; in final form: 20 August 2000/ Published online: 17 May 2001     

Apollonian isometries of planar domains are Möbius mappings

The Apollonian metric is a generalization of the hyperbolic metric, defined in a much larger class of open sets. Beardon introduced the metric in 1998, and asked whether its isometries are just the Möbius mappings. In this article we show that this is the case in all open subsets of the plane with at least three boundary points.