Covariant Lyapunov vectors for rigid disk systems

We carry out extensive computer simulations to study the Lyapunov instability of a two-dimensional hard-disk system in a rectangular box with periodic boundary conditions. The system is large enough to allow the formation of Lyapunov modes parallel to the x-axis of the box. The Oseledec splitting into covariant subspaces of the tangent space is considered by computing the full set of covariant perturbation vectors co-moving with the flow in tangent space. These vectors are shown to be transversal, but generally not orthogonal to each other. Only the angle between covariant vectors associated with immediate adjacent Lyapunov exponents in the Lyapunov spectrum may become small, but the probability of this angle to vanish approaches zero. The stable and unstable manifolds are transverse to each other and the system is hyperbolic.     

Selective and sensitive analysis of 1-nitropyrene in diesel exhaust particulate extract by multidimensional HPLC

Summary A multicolumn (MC) HPLC method for the determination of 1-nitropyrene (1-NP) at trace-levels via on-line reduction to 1-aminopyrene and fluorescence detection is presented. On the first column, packed with a pyrenebutyric acid amide stationary phase, the nitro-derivatives of PAHs are strongly retained and separated from other matrix components. The nitro-PAHs-containing fractions are transferred onto a RP₁₈-column via stepwise gradient elution and finally separated according to their various lipophilicities and sizes. To increase the overall selectivity and sensitivity of the multidimensional method (MD-HPLC system) post-column, on-line reduction of the nitro-PAHs to the respective amino-PAHs via a short catalysis column is performed thus enhancing the sensitivity significantly (to low pg levels). The applicability of this method for the determination of trace amounts of 1-NP in real samples (diesel particulate extracts) is demonstrated.     

Qualitative and quantitative determination of micro-inclusions by automated SEM/EDX analysis

With the help of an automated SEM/EDX analysis system non-metallic micro-inclusions in steel can be detected on a metallographically prepared surface area. The system makes it possible to determine position, size, shape and composition of each particle. Usually more than 1000 inclusions are found on one scan area. Therefore a new offline evaluation method has been developed to classify the large amount of inclusions and calculate specific size and shape data. A summary sheet is created to show the area contents and the mean values of all important properties for each class. Size and XY distributions as well as binary and ternary phase diagrams are drawn to depict the results. The strengths of this analytical technique are demonstrated by evaluation of an LC (low-carbon) steel. Alumina, common spinel, sulfide and oxisulfide inclusions could be identified as dominant inclusion types in LC steel.     

Statistical measures derived from the correlation integrals of physiological time series

In this work correlation integrals are used for the analysis of various EEG signals from rabbits in resting states and under the influence of an anesthetic. The comparison with surrogate data reveals nonlinear dynamics in all of the time series. Our attempt to determine the correlation dimension D(2) by the modified algorithm of Theiler [Phys. Rev. A 34, 2427 (1986)] failed since no saturation is reached with increasing embedding dimension. The hypothesis of low-dimensional chaos turns out to be inconsistent with our results, but we can still distinguish, at least qualitatively, between different states of brain dynamics. A quantitative characterization of the time series is possible by defining correlation parameters P(a) derived from correlation integrals reflecting also autocorrelation of the signal. (c) 1996 American Institute of Physics.     

A new sensing material for optical oxygen measurement,with the indicator embedded in an aqueous phase

A new type of oxygen-sensitive material is obtained by preparing an aqueous emulsion of a solution of an oxygen-sensitive fluorescent dye in a rigid polymer. The fluorescence of this emulsion is related to the oxygen partial pressure, but a Stern-Volmer plot is not linear over the whole pressure range. Aside from high sensitivity and specificity for oxygen, this new type of sensing material has favorable analytical wavelengths allowing the use of low-cost opto-electronic equipment. Since the indicator is embedded in an aqueous environment, the sensor should be capable of monitoring various kinds of reactions occurring in the aqueous phase, for instance enzymatic reactions which are accompanied by production or consumption of oxygen.     

Direct measurement of Lyapunov exponents

Benettin, Calgani and Strelcyn studied the dynamical separation of neighboring phase-space trajectories, determining the corresponding Lyapunov exponents by discrete rescaling of the intertrajectory separation. We incorporate rescaling directly into the equations of motion, preventing Lyapunov instability by using an effective constraint force.     

Ion chromatography of aluminium, gallium and indium using a complexing mobile phase

Summary The elements Al, Ga and In were analyzed by ion chromatography using a complexing mobile phase and a refractive index monitor as detector. Linearities between detector response and concentration were found up to 100 /g or more (with respect to the metal ion), detection limits being below 1 g/g. Additionally, the simultaneous codetermination of simple anions like chloride, nitrate, sulphate and others were investigated along with interferences from other common cations.Dedicated to Prof. Dr. R. Pietsch on the occasion of his 65th birthday on November 9, 1990.     

Nonaqueous capillary electrophoresis-mass spectrometry: a versatile, straightforward tool for the analysis of alkaloids from psychoactive plant extracts

In this study we show that a nonaqueous capillary electrophoresis mass spectrometry (NACE-MS) method carefully optimized by a design of experiment can be applied to a very large number of alkaloids in different plant extracts. It is possible to characterize the pattern of the psychoactive alkaloids in several plant samples and preparations thereof, each presenting different challenges in their analysis. The method is shown to be able to separate structurally closely related substances, diastereomers and further isobaric compounds, to separate members of different alkaloid classes within one run and to tolerate significant matrix load. A comparison with methods presented in the literature reveals that a near-generic NACE-MS method for the fast profiling of alkaloids in forensically relevant plant samples has been developed.     

Gravitational Collapse and Ergodicity in Confined Gravitational Systems

The ergodic properties of many-body systems with repulsive-core interactions are the basis of classical statistical mechanics and are well established. This is not the case for systems of purely-attractive or gravitational particles. Here we consider two examples, (i) a family of one-dimensional systems with attractive power-law interactions, , and (ii) a system of N gravitating particles confined to a finite compact domain. For (i) we deduce from the numerically-computed Lyapunov spectra that chaos, measured by the maximum Lyapunov exponent or by the Kolmogorov–Sinai entropy, increases linearly for positive and negative deviations of ν from the case of a non-chaotic harmonic chain (ν = 2). For there is numerical evidence for two additional hitherto unknown phase-space constraints. For the theoretical interpretation of model (ii) we assume ergodicity and show that for a small-enough system the reduction of the allowed phase space due to any other conserved quantity, in addition to the total energy, renders the system asymptotically stable. Without this additional dynamical constraint the particle collapse would continue forever. These predictions are supported by computer simulations. PACS numbers: 05.45.Pq, Numerical simulation of chaotic systems, 05.20.−y, Classical statistical mechanics, 36.40.Qv, Stability and fragmentation of clusters, 95.10.Fh, Chaotic dynamics.