Series resonance circuit with ferroelectric capacitor

A series resonance circuit under sinuousoidal driving is investigated experimentally. The inductance consists of an air coil. The capacitance is made up of a ferroelectric material that introduces its nonlinear dielectric properties into the circuit. The dynamical system linear coil-nonlinear capacaitor shows an interesting behaviour. The phase portrait differs in general from the ellipse of the harmonic oscillator. For appropriate external conditions period doubling sequences, chaos and therein enclosed periodic windows might occur. Starting from a cubic nonlinearity of the dielectric properties a Duffing equation is proposed as a model for periodic behaviour of the series resonance circuit. Simulations of experimentally recorded phase portraits yield good agreement between experiment and model.     

Law of Sums of the Squares of Areas, Volumes and Hyper-Volumes of Regular Polytopes from Clifford Algebras

Inspired by the recent sums of the squares law obtained by [1] we derive the law of the sums of the squares of the areas, volumes and hyper-volumes associated with the faces, cells and hyper-cells of regular polytopes in diverse dimensions by using Clifford algebraic methods [5].     

Comparison of one-dimensional and comprehensive two-dimensional separations by gas chromatography

Comprehensive two-dimensional gas chromatography (GC x GC) can reveal information on the composition of a sample in a way that cannot be done by one-dimensional GC (1D-GC). GC x GC also offers much greater control of chromatographic selectivity based on molecular structure. However, in spite of more than 15 years of claims of the ability of GC x GC to resolve an overwhelmingly larger number of peaks than 1D-GC, and in spite of the theoretically proven potential of GC x GC to have an order of magnitude larger peak capacity than 1D-GC, the peak capacity of currently practiced GC x GC does not generally exceed the peak capacity attainable from 1D-GC with the same analysis time and the same minimal detectable concentration (MDC). The methodology for comparing the peak capacity of GC x GC to 1D-GC is described. The comparison of the performance of GC x GC to 1D-GC shows that the modulator is the key bottleneck limiting the performance of existing GC x GC. To realize the full potential of GC x GC, duration of injection from a modulator into the second-dimension column should be reduced by an order of magnitude or more. Use of powerful data analysis techniques such as peak deconvolution in both dimensions can further increase resolving power of GC x GC.     

Crystallographic nets and their quotient graphs

Crystallographic nets are defined. It is shown how these nets can be generated from finite graphs which are called the quotient graphs of the nets. The procedure yields the topology of the nets, their crystallographic point groups and their lattice types. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chemical vapour deposition polymerization of substituted [2.2]paracyclophanes

Chemical vapour deposition polymerisation of substituted [2.2]paracyclophanes is applied to the functionalised coating of stainless steel surfaces. Poly[o-trifluoroacetyl-p-xylylene-co-p-xylylene] ( 2a ), poly[o-hydroxymethyl-p-xylylene-co-p-xylylene] ( 2b ), poly[o-amino-p-xylylene-co-p-xylylene] ( 2c ) and poly(p-xylylene-2,3-dicarboxylic anhydride) ( 2d ) were deposited as thin layers.     

Optimizing capillary column backflush to improve cycle time and reduce column contamination

Interest in decreasing cycle times in capillary GC analyses has driven much of the instrumental developments of the last decade. Recent developments in GC instrumentation now make it reasonable to consider backflushing capillary columns on a routine basis. Significant reduction in analysis and total cycle times (typically 15–50% depending on the application) are readily achieved for analyses that currently require an extended temperature program and bakeout period to remove retained sample components and column contaminants. Setup and optimization of backflush conditions are relatively straight forward as long as some basic concepts are well understood. The parameters affecting capillary column backflushing are described. Examples are shown that help visualize what happens during backflush. The relationship between oven ramp rate and flow turns out to be an important variable that dictates minimum backflush times in temperature programmed CGC. Backflush times corresponding to 2–5 void volumes in the reversed direction are usually sufficient for backflushing, if performed after each temperature programmed run.