Polling systems in heavy traffic: Exhaustiveness of service policies

We study the expected delay in cyclic polling models with general ‘branching-type’ service disciplines. For this class of models, which contains models with exhaustive and gated service as special cases, we obtain closed-form expressions for the expected delay under standard heavy-traffic scalings. We identify a single parameter associated with the service discipline at each queue, which we call the ‘exhaustiveness’. We show that the scaled expected delay figures depend on the service policies at the queues only through the exhaustiveness of each of the service disciplines. This implies that the influence of different service disciplines, but with the same exhaustiveness, on the expected delays at the queues becomes the same when the system reaches saturation. This observation leads to a new classification of the service disciplines. In addition, we show monotonicity of the scaled expected delays with respect to the exhaustiveness of the service disciplines. This induces a complete ordering in terms of efficiency of the service disciplines. The results also lead to new rules for optimization of the system performance with respect to the service disciplines at the queues. Further, the exact asymptotic results suggest simple expected waiting-time approximations for polling models in heavy traffic. Numerical experiments show that the accuracy of the approximations is excellent for practical heavy-traffic scenarios. This revised version was published online in June 2006 with corrections to the Cover Date.     

Maximum-entropy data analysis

The reconstruction of physical quantities from (computer-) experimental data is very often hampered by the presence of noise, insufficient information and above all by the ill-posed nature of the underlying inversion problem. It will be demonstrated that the maximum entropy concepts is particularly suited for this type of data-analysis problems. It is based on Bayesian statistics and provides a consistent probabilistic theory to obtain unbiased results, independent of any model assumptions. This is particularly desirable if there is no additional information to justify these hypotheses. If, on the other hand, additional prior knowledge is available, it can be effectively incorporated into the computation, leading to more stringent confidence intervals.     

The pole expansion in normalized QED

We present a pole expansion for the propagators in the framework of normalized quantum electrodynamics and compare it with the more canonical results from S-matrix theory.     

Writhing instabilities of twisted rods: from infinite to finite length

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.     

Quantification problems in depth profiling of pwr steels using Ar+ ion sputtering and XPS analysis.

The oxide scales of AISI 304 formed in boric acid solutions at 300 degrees C and pH = 4.5 have been studied using X-ray photoelectron spectroscopy (XPS) depth profiling. The present focus is depth profile quantification both in depth and chemical composition on a molecular level. The roughness of the samples is studied by atomic force microscopy before and after sputtering, and the erosion rate is determined by measuring the crater depth with a surface profilometer and vertical scanning interferometry. The resulting roughness (20-30 nm), being an order of magnitude lower than the crater depth (0.2-0.5 microm), allows layer-by-layer profiling, although the ion-induced effects result in an uncertainty of the depth calibration of a factor of 2. The XPS spectrum deconvolution and data evaluation applying target factor analysis allows chemical speciation on a molecular level. The elemental distribution as a function of the sputtering time is obtained, and the formation of two layers is observed-one hydroxide (mainly iron-nickel based) on top and a second one deeper, mainly consisting of iron-chromium oxides.     

Chemical analysis and distribution investigation of trace elements in indium matrix by spark source mass spectrometry

Summary High-purity indium was analysed by spark source mass spectrometry, using electrical and photoplate detection. For the calibration of the differences in elemental sensitivity, a standard sample was prepared in which 10 impurities were determined by graphite furnace atomic absorption spectrometry. In this way accuracies of less than 40% were obtained for relatively homogeneous elements at ppm and sub-ppm level. About 40 elements could be determined with detection limits of 10 to 30 ppb. Two pattern recognition methods, principal component analysis and clustering analysis, were applied to obtain information on trace element distribution, which indicated that a number of elements were strongly spatially correlated in the analysed sample.

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Chemische Analyse und Verteilungsbestimmung von Spurenelementen in Indium-Matrix durch Funkenquellen-Massenspektrometrie

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On leave from: Department of Chemistry, Nanjing Normal University, Nanjing, People's Republic of China     

Isotone relations revisited

We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.