Autoignition of varied cetane number fuels at low temperatures

The reactivity of six kerosene based control fuels, specifically formulated for cetane number variation, are investigated by measuring ignition delay time in a heated rapid compression machine. Cetane numbers vary from 30 to 55 (increment of 5) while holding other properties relatively constant by adjusting chemical group composition. Main cetane variation was controlled through the distribution of normal alkanes and isoalkanes, which was fine-tuned using additives. Other fuel properties such as density, viscosity, H/C ratio, etc. were balanced using cyclic compounds and aromatics. Fuels were tested in the RCM at compressed pressures of P_c=?10 and 20?bar, equivalence ratios of ??=?0.25, 0.5 and 1.0, in the low to intermediate temperature range (620?K?≤?T_c?≤?730?K). Relations between cetane number and ignition delay time have been evaluated at multiple test conditions, and further analysis on multistage ignition has been conducted. Ignition delay times of fuels with higher cetane numbers are shorter at these temperatures for most conditions. First stage ignition delay time measurements have been observed to be relatively insensitive to P_c, ?, and fuel type, while deviations in overall ignition delay times are mainly attributed to second stage ignition delay time, impacted by variations in the first stage temperature. Control fuels of this type offer an opportunity to be used in practical experiments to determine the impact of cetane number on combustion dynamics.     

An improved method for the analysis of volatile polyfluorinated alkyl substances in environmental air samples

This article describes the optimisation and validation of an analytical method for the determination of volatile polyfluorinated alkyl substances (PFAS) in environmental air samples. Airborne fluorinated telomer alcohols (FTOHs) as well as fluorinated sulfonamides and sulfonamidoethanols (FOSAs/FOSEs) were enriched on glass-fibre filters (GFFs), polyurethane foams (PUFs) and XAD-2 resin by means of high-volume air samplers. Sensitive and selective determination was performed using gas chromatography/chemical ionisation–mass spectrometry (GC/CI–MS). Five mass-labelled internal standard (IS) compounds were applied to ensure the accuracy of the analytical results. No major blank problems were encountered. Recovery experiments were performed, showing losses of the most volatile compounds during extraction and extract concentration as well as strong signal enhancement for FOSEs due to matrix effects. Breakthrough experiments revealed losses of the most volatile FTOHs during sampling, while FOSAs/FOSEs were quantitatively retained. Both analyte losses and matrix effects could be remediated by application of adequate mass-labelled IS. Method quantification limits (MQLs) of the optimised method ranged from 0.2 to 2.5 pg/m³ for individual target compounds. As part of the method validation, an interlaboratory comparison of instrumental quantification methods was conducted. The applicability of the method was demonstrated by means of environmental air samples from an urban and a rural location in Northern Germany. Figure High-volume air sampling of volatile polyfluorinated alkyl substances using glass fibre filters and PUF/XAD-2 cartridges at a background monitoring site (Waldhof, Germany)     

Some conjectures on S n -derived nuclear permutational(or NMR) spin encodings

On existence of limiting ‐module decompositional sets for weak ‐branching at high n; on Voronoi polyhedral dual as geometric analogues to Cayley’s SU2 embedding theorem; and on SU dual group with retention of self‐associacy over subduced irrep set, as being the sufficient further condition to ensure the determinacy of SU embeddings. In the context of structures arising from nuclear permutation (NP) or NMR dual‐group spin algebras, the first conjecture sets out the high‐index n, and thus weak‐branching limit (WBL), aspects of module decompositions as giving rise to a set of numerical values for the associated Kostka coefficients which are invariant to further incrementation in the index; the existence of such combinatorial limit properties, implicit in sst tableaux enumerations, has not been addressed in the mathematics literature to date. Conjectures 2 and 3 are concerned with the questions of geometric and sufficient algebraic realisations of the determinacy of natural finite group embeddings in specific SU permutation groups. In conjecture 2, the Voronoi dual‐structures to the regular polyhedra for NP/NMR automorphic SU2 embedded spin symmetries hold the key to physical insight. Specifically, they provide a novel combinatorial geometric view of Cayley’s theorem; the mid‐face intersecting ‐axes of the initial NMR automorphic solids become (vertex) body‐diagonal axes of the specific‐dual Voronoi polyhedra, where a distinctness condition from the spin‐sites gives raise to a geometric statement of Cayley’s theorem. Conjecture 3 is concerned with SU embeddings for which the simple Cayley criterion alone is an insufficient condition to guarantee determinacy. The self‐associacy property and its retention over the subduced irrep‐subset(s) (i.e., comparable to studies of system‐invariants via Yamanouchi–Gel’fand subduction chains) is now seen as indicative of retention of determinacy for such SU group embeddings through the above sufficiency condition. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerically satisfactory solutions of hypergeometric recursions

Each family of Gauss hypergeometric functions

for fixed (not all equal to zero) satisfies a second order linear difference equation of the form

Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different values) can be transformed into each other. In this way, only with four basic difference equations can all other cases be obtained. For each of these recurrences, we give pairs of numerically satisfactory solutions in the regions in the complex plane where , and being the roots of the characteristic equation.

     

Surface characterisation of laser irradiated SiC ceramics by AES and XPS

Samples of sintered silicon carbide (SSiC) were irradiated with a KrF excimer laser (λ = 248 nm) at energy densities of 10, 15 and 25 J/cm² in He atmosphere. The composition of the near surface region was investigated by Auger electron spectroscopy (AES) and photoelectron spectroscopy (XPS) after lapping, laser irradiation and tribological treatment, respectively. By laser irradiation a surface layer is formed which contains about 30% oxygen. The existence of different bonding states of Si, C and O was established by factor analysis of the AES depth profiles and by XPS. By laser irradiation SiC is decomposed and a siliconoxycarbide with the average composition SiC_3.5O_1.5 is formed. Beneath the oxidised surface layer the nominal elemental composition SiC is found but the sample represents a mixture of Si, graphite and siliconoxycarbide with a small amount of SiC only. Obviously, the decomposition zone exceeds in a depth > 300 nm.     

Uniform Approximations of Bernoulli and Euler Polynomials in Terms of Hyperbolic Functions

Bernoulli and Euler polynomials are considered for large values of the order. Convergent expansions are obtained for B _n ( nz +1/2) and E _n ( nz +1/2) in powers of n ⁻¹, and coefficients are rational functions of z and hyperbolic functions of argument 1/(2 z ). These expansions are uniformly valid for | z ± i /2π|>1/2π and | z ± i /π|1/π, respectively. For a real argument, the accuracy of these approximations is restricted to the monotonic region. The range of validity of the uniformity parameter z is enlarged, respectively, to regions of the form | z ± i /2( m +1)π|>1/2( m +1)π and | z ± i /(2 m +1)π|>1/(2 m +1)π, m =1,2,3,…, by adding certain combinations of incomplete gamma functions to these uniform expansions. In addition, the convergence of these improved expansions is stronger, and for a real argument, the accuracy of these improved approximations is also better in the oscillatory region.     

Uniform asymptotic expansion for a class of polynomials biorthogonal on the unit circle

An asymptotic expansion including error bounds is given for polynomials {P _n, Q_n} that are biorthogonal on the unit circle with respect to the weight function (1?e^iθ)^α+β(1?e^?iθ)^α?β. The asymptotic parameter isn; the expansion is uniform with respect toz in compact subsets ofC{0}. The pointz=1 is an interesting point, where the asymptotic behavior of the polynomials strongly changes. The approximants in the expansions are confluent hyper-geometric functions. The polynomials are special cases of the Gauss hyper-geometric functions. In fact, with the results of the paper it follows how (in a uniform way) the confluent hypergeometric function is obtained as the limit of the hypergeometric function₂ F ₁(a, b; c; z/b), asb→±∞,z≠b, withz=0 as “transition” point in the uniform expansion.