Memory effects in gas chromatographic detection with a microwave-induced plasma

Capillary gas chromatography coupled to microwave-inducedplasma detection furnishes sensitivity adequate for trace analysis when the signal is monitored at a carbon emission line. Work performed with one of these systems at high electronic gain for the carbon signal has revealed solvent band widths in excess of four minutes; these impeded quantification of peaks eluting after the solvent. This report discusses two phenomena which could be related to the unexpected intensity of this solvent response: photomultiplier tube saturation and carbon deposits in the quartz plasma discharge tube.     

Energy Conserving, Liouville, and Symplectic Integrators

In this paper, we construct an integrator that converves volume in phase space. We compare the results obtained using this method and a symplectic integrator. The results of our experiments do not reveal any superiority of the symplectic over strictly volume-preserving integrators. We also investigate the effect of numerically conserving energy in a numerical process by rescaling velocities to keep energy constant at every step. Our results for Henon-Heiles problem show that keeping energy constant in this way destroys ergodicity and forces the solution onto a periodic orbit.     

Projectivep-algebras

Presented by R. Freese.     

Canonical methods for Hamiltonian systems: numerical experiments

A Hamiltonian system possesses dynamics (e.g. preservation of volume in phase space and symplectic structure) that call for special numerical integrators, namely canonical methods. Recent research on this aspect have shown that canonical numerical integrators may be needed for Hamiltonian systems. In this paper, we focus on numerical experiments that compare canonical and non-canonical numerical integrators. Test problems are taken from different areas in physical sciences. These experiments help to buttress the claims that canonical numerical integrators give results that mimic the qualitative behavior of the original system and that canonical numerical integrators are suitable for long time integrations. Our experiments indicate that higher-order canonical methods allow for larger timestep than lower-order canonical methods.     

Topochemically Controlled Redox Reactions in the System In/Sn/Cl

The difference in reactivity of the two modifications of InCl in solid state reactions with SnCl₂ is discussed. It is explained on the basis of semi‐empirical and ab initio calculations giving the density of states diagrams of InCl and the energies of possible disproportionation reactions. Their general features are discussed on the basis of a simple bonding picture for open‐packed structures involving inert pair elements. A detailed analysis of the DOS distribution allows to pinpoint the observed redox instability to a specific structural feature of α‐InCl.     

Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations

The paper proves the existence of solutions to the magneto-hydrodynamics equations driven by random exterior forcing terms both in the velocity and in the magnetic field. The existence and uniqueness of an invariant measure is also obtained via coupling methods.     

Differentiation of species of the Baccharis genus by HPLC and chemometric methods.

Phytochemical investigation of the aerial parts of three Baccharis species (Asteraceae family) was performed using HPLC and chemometric methods, with the objective of distinguishing between three morphologically very similar species: Baccharis genistelloides Persoon var. trimera (Less.) DC, B. milleflora (Less.) DC and B. articulata (Lam.) Persoon. With the help of Principal Component Analysis (PCA) and variance weights, it was possible to characterize the chromatographic profiles of the alcoholic extracts of the three species. Application of Soft Independent Modeling of Class Analogy (SIMCA) and K-Nearest Neighbor (KNN) methods on a training set of 74 extracts resulted in models that correctly classified all eight samples in an independent test set.     

Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25