Nonlinear fiber-optic strain sensor based on four-wave mixing in microstructured optical fiber

We demonstrate a nonlinear fiber-optic strain sensor, which uses the shifts of four-wave mixing Stokes and anti-Stokes peaks caused by the strain-induced changes in the structure and refractive index of a microstructured optical fiber. The sensor thus uses the inherent nonlinearity of the fiber and does not require any advanced postprocessing of the fiber. Strain sensitivity of -0.23 pm/με is achieved experimentally and numerical simulations reveal that for the present fiber the sensitivity can be increased to -4.46 pm/με by optimizing the pump wavelength and power.     

Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions

It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.     

A spectrokinetic study of CH2I and CH2IO2 radicals

The UV absorption spectrum and kinetics of CH₂I and CH₂IO₂ radicals have been studied in the gasphase at 295 K using a pulse radiolysis UV absorption spectroscopic technique. UV absorption spectra of CH₂I and CH₂IO₂ radicals were quantified in the range 220–400 nm. The spectrum of CH₂I has absorption maxima at 280 nm and 337.5 nm. The absorption cross-section for the CH₂I radicals at 337.5 nm was (4.1 ± 0.9) × 10^?18 cm² molecule^?1. The UV spectrum of CH₂IO₂ radicals is broad. The absorption cross-section at 370 nm was (2.1 ± 0.5) × 10^?18 cm² molecule^?1. The rate constant for the self reaction of CH₂I radicals, k = 4 × 10^?11 cm³ molecule^?1 s^?1 at 1000 mbar total pressure of SF₆, was derived by kinetic modelling of experimental absorbance transients. The observed self-reaction rate constant for CH₂IO₂ radicals was estimated also by modelling to k = 9 × 10^?11 cm³ molecule^?1 s^?1. As part of this work a rate constant of (2.0 ± 0.3) × 10^?10 cm³ molecule^?1 s^?1 was measured for the reaction of F atoms with CH₃I. The branching ratios of this reaction for abstraction of an I atom and a H atom were determined to (64 ± 6)% and (36 ± 6)%, respectively. © 1994 John Wiley & Sons, Inc.     

The use of reflection as symmetry operation in connection with Peierls' argument

It is shown that Peierls' argument can be extended to prove the coexistence of states which can be transformed into each other only by reflection, inversion or rotation. This makes Peierls' argument applicable to the repulsive lattice gas on a large class of lattices, as well as many models for liquid crystals, ferroelectrics etc. It is specifiquely shown how the argument can be applied to a lattice gas with nearest neighbour repulsion on the hexagonal lattice and the diamond lattice.     

High resolution study of the reactions 54, 56, 58Fe(16O, 12C)58, 60, 62Ni and a comparison with (6Li,d) α-transfer spectroscopy

Spectra and angular distributions for the reactions ^{54, 56, 58}Fe(¹⁶O, ¹²C)^{58, 60, 62}Ni (E_x = 0.0–4.5 MeV) have been measured at 50 MeV with an energy resolution of 45–80 keV using a Q3D spectrograph. The selectivity of the (¹⁶O, ¹²C) reaction is found to be very similar to the (⁶Li, d) reaction. The close correspondence recently noted between the (⁶Li, d) spectra and levels strongly excited in (t, p) and (³He, n) two-nucleon transfer reactions is also observed to be present for the (¹⁶O, ¹²C) reaction. Relative α spectroscopic factors for (¹⁶O, ¹²C) and (⁶Li, d) obtained in a DWBA analysis assuming direct one-step α-cluster transfer are in very good quantitative agreement. Unnatural parity states, whose excitation is forbidden in the DWBA α-cluster approximation, are observed to be very weakly populated. These results, together with previous work on s-d shell and Ni targets, strongly suggest that the spectroscopic information provided by the (¹⁶O, ¹²C) and (⁶Li, d) reactions is essentially the same and that this information may be reliably extracted by DWBA analysis.     

Convergence of fourier methods for Navier-Stokes equations

The Fourier-Galerkin method is used to simulate fluid flows in two and three dimensions, on domains with periodic boundary conditions. It is proved that the numerical solution converges towards the solution of Navier-Stokes equations. The rate of convergence depends on the smoothness of the mathematical solution. Finally, it is shown that the Fourier-Galerkin method can be interpreted as a projection method. This observation may lead to more sophisticated convergence proofs.     

Location of the Zeros of the Grand Partition Function of Certain Classes of Lattice Gases

It is proved that there exist lattices in any dimension such that the grand partition function of the corresponding repulsive lattice gas has all the zeros in the fugacity on the negative real axis. The argument also furnishes a new proof of the Lee-Yang circle theorem.     

Some positive definite functions on sets and their application to the Ising model

Consideration of correlation inequalities for Ising ferromagnets with arbitrary spins has led to the discovery of a class of positive definite functions on sets. These functions are linear combinations of the functions which enter into Muirhead's Theorem. We prove these functions to be positive definite and also show how they can be applied to the Ising problem to prove Griffiths second inequality for arbitrary spins.