Lyapunov Instability of the Boundary-Driven Chernov–Lebowitz Model for Stationary Shear Flow

We report on the computation of full Lyapunov spectra of the boundary-driven Chernov–Lebowitz model for stationary planar shear flow. The Lyapunov exponents are calculated with a recently developed formalism for systems with elastic hard collisions. Although the Chernov–Lebowitz model is strictly energy conserving, any phase-space volume is subjected to a contraction due to the reflection rules of the hard disks colliding with the walls. Consequently, the sum of Lyapunov exponents is negative. As expected for an inhomogeneously driven system, the Lyapunov spectra do not obey the conjugate pairing rule. The external driving makes the system less chaotic, which is reflected in a decrease of the Kolmogorov–Sinai entropy if the driving is increased.     

Lyapunov Modes in Hard-Disk Systems

We consider simulations of a two-dimensional gas of hard disks in a rectangular container and study the Lyapunov spectrum near the vanishing Lyapunov exponents. To this spectrum are associated eigen-directions, called Lyapunov modes. We carefully analyze these modes and show how they are naturally associated with vector fields over the container. We also show that the Lyapunov exponents, and the coupled dynamics of the modes (where it exists) follow linear laws, whose coefficients only depend on the density of the gas, but not on aspect ratio and very little on the boundary conditions.     

Optical and fibre-optic sensors for vapours of polar solvents

An optical sensor is described which continuously measures the concentration of vapours of polar organic solvents such as alcohols, ethers, esters and ketones, but does not respond to hydrocarbons and chlorinated hydrocarbons. The detection is based on reversible decolorization of the blue thermal printer paper used in graphic plotters. Two sensing principles are exploited. In the first, a sensor sheet is placed in a flow-through cell. An LED acts as a source of yellow light and a phototransistor measures the light transmitted. In the second, the sensing membrane is placed at the end of a bifurcated fibre-optic and its diffuse reflectance is measured. The sensitivity of the devices towards various kinds of vapours has been studied and the detection limits vary from 10 to 1000 ppm for some of the most common technical solvents.     

Fractal dimension of steady nonequilibrium flows

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces. For both kinds of nonequilibrium systems, it is demonstrated numerically that external isothermal boundaries can drive the otherwise purely Newtonian flow onto a multifractal attractor with a phase-space information dimension significantly less than that of the corresponding equilibrium flow. Thus the Gibbs' entropy of such nonequilibrium flows can diverge.     

Charged and neutral particle multiplicity in π−p and π−n interactions at 40 GeV/c

Data on the multiplicity of charged particles and π⁰ mesons in π^?p and π^?n interactions are presented and compared to various models. The average π⁰ multiplicity tends to increase with increasing number of charged particles.     

Implementation of a design of experiments to study the influence of the background electrolyte on separation and detection in non-aqueous capillary electrophoresis-mass spectrometry

Non-aqueous capillary electrophoresis (NACE) background electrolytes are most often composed of a mixture of methanol and acetonitrile (ACN) with soluble ammonium salts added as electrolyte. In this study on NACE-MS, we used a mixture of glacial acetic acid and ACN giving rise to an acidic background electrolyte (BGE) with a very low dielectric constant. Impressive changes in selectivity and resolution were observed for structurally closely related indole alkaloids including diastereomers upon addition of ammonium formate as electrolyte and upon variation of the solvent ratio. In order to obtain best separation and MS detection conditions and to reveal the influence of the parameters of the BGE on separation and detection and vice versa of the MS parameters on separation, an optimization strategy was employed using a design of experiments in a central composite design with response surface methodology. It was proven that at high electroosmotic flow conditions capillary electrophoretic separations and thus optimization can be realized without interference from the coupling to an MS system. Several significantly interacting parameters were revealed, which are not accessible with classical univariate optimization approaches. With this optimization, alkaloid mixtures from a plant extract of Mitragyna speciosa, containing a large number of diastereomeric compounds were successfully separated.     

Fibre-optic fluorescing sensor for ammonia

The fluorescing sensor is based on the change in fluorescence intensity of a buffered pH indicator solution entrapped in silicone rubber. Exposure to ammonia increases the pH of the trapped solution; this increases the fluorescence intensity, which is monitored via an optical fibre bundle. Ammonium chloride in 0.001 M sodium hydroxide, or the indicators themselves, can serve as buffers. Effects of sensor preparation and buffer composition on response time, reversibility and sensitivity are discussed.     

Lyapunov instability of two-dimensional fluids: Hard dumbbells

We generalize Benettin's classical algorithm for the computation of the full Lyapunov spectrum to the case of a two-dimensional fluid composed of linear molecules modeled as hard dumbbells. Each dumbbell, two hard disks of diameter sigma with centers separated by a fixed distance d, may translate and rotate in the plane. We study the mixing between these qualitatively different degrees of freedom and its influence on the full set of Lyapunov exponents. The phase flow consists of smooth streaming interrupted by hard elastic collisions. We apply the exact collision rules for the differential offset vectors in tangent space to the computation of the Lyapunov exponents, and of time-averaged offset-vector projections into various subspaces of the phase space. For the case of a homogeneous mass distribution within a dumbbell we find that for small enough d/sigma, depending on the density, the translational part of the Lyapunov spectrum is decoupled from the rotational part and converges to the spectrum of hard disks. (c) 1998 American Institute of Physics.     

Multi-analyte quantification in bioprocesses by Fourier-transform-infrared spectroscopy by partial least squares regression and multivariate curve resolution

This paper presents the quantification of Penicillin V and phenoxyacetic acid, a precursor, inline during Pencillium chrysogenum fermentations by FTIR spectroscopy and partial least squares (PLS) regression and multivariate curve resolution – alternating least squares (MCR-ALS). First, the applicability of an attenuated total reflection FTIR fiber optic probe was assessed offline by measuring standards of the analytes of interest and investigating matrix effects of the fermentation broth. Then measurements were performed inline during four fed-batch fermentations with online HPLC for the determination of Penicillin V and phenoxyacetic acid as reference analysis. PLS and MCR-ALS models were built using these data and validated by comparison of single analyte spectra with the selectivity ratio of the PLS models and the extracted spectral traces of the MCR-ALS models, respectively. The achieved root mean square errors of cross-validation for the PLS regressions were 0.22 g L⁻¹ for Penicillin V and 0.32 g L⁻¹ for phenoxyacetic acid and the root mean square errors of prediction for MCR-ALS were 0.23 g L⁻¹ for Penicillin V and 0.15 g L⁻¹ for phenoxyacetic acid. A general work-flow for building and assessing chemometric regression models for the quantification of multiple analytes in bioprocesses by FTIR spectroscopy is given.