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.     

Small angle neutron scattering from oxygen precipitates in silicon

The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×10¹⁷ O_i/cm³ and 13×10¹⁷ O_i/cm³ have been heated at 750° C for 96 h. SiO₂ precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.2 Å^–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å^–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×10¹⁷ O_i/cm³ oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×10¹⁷ O_i/cm³. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam.     

Geometric quantization of topological gauge theories

We show that Abelian gauge theories in 2+1 space-time dimensions with the introduction of a topological Chern-Simons term can be quantized with the use of the symplectic formalism. The consistency of our results are verified by the agreement with the ones from the Dirac case.     

Localising gravity in composite monopole brane worlds without bulk cosmological constant

We study a 7-dimensional brane world scenario with a Ricci-flat 3-brane residing in the core of a composite monopole defect, i.e., a defect composed of a 't Hooft–Polyakov and a global monopole. Admitting a direct interaction between the two bosonic sectors of the theory, we analyse the structure of the space–time in the limits of small, respectively large direct interaction coupling constant. For large direct interaction, the global monopole disappears from the system and leaves behind a negative cosmological constant in the bulk such that gravity-localising solutions are possible without a priori introduction of a bulk cosmological constant.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Shape transition from InAs quantum dash to quantum dot on InP(3 1 1)A

We report on the shape transition from InAs quantum dashes to quantum dots (QDs) on lattice-matched GaInAsP on InP(3 1 1)A substrates. InAs quantum dashes develop during chemical-beam epitaxy of 3.2 monolayers InAs, which transform into round InAs QDs by introducing a growth interruption without arsenic flux after InAs deposition. The shape transition is solely attributed to surface properties, i.e., increase of the surface energy and symmetry under arsenic deficient conditions. The round QD shape is maintained during subsequent GaInAsP overgrowth because the reversed shape transition from dot to dash is kinetically hindered by the decreased ad-atom diffusion under arsenic flux.     

Diblock copolymers based on allyl methacrylate: Synthesis,characterization, and chemical modification

Different diblock copolymers constituted by one segment of a monomer supporting a reactive functional group, like allyl methacrylate (AMA), were synthesized by atom transfer radical polymerization (ATRP). Bromo‐terminated polymers, like polystyrene (PS), poly(methyl methacrylate) (PMMA), and poly(butyl acrylate) (PBA) were employed as macroinitiators to form the other blocks. Copolymerizations were carried out using copper chloride with N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) as the catalyst system in benzonitrile solution at 70 °C. At the early stage, the ATRP copolymerizations yielded well‐defined linear block copolymers. However, with the polymerization progress a change in the macromolecular architecture takes place due to the secondary reactions caused by the allylic groups, passing to a branched and/or star‐shaped structure until finally yielding gel at monomer conversion around 40% or higher. The block copolymers were characterized by means of size exclusion chromatography (SEC), ¹H NMR spectroscopy, and differential scanning calorimetry (DSC). In addition, one of these copolymers, specifically P(BA‐b‐AMA), was satisfactorily modified through osmylation reaction to obtain the subsequent amphiphilic diblock copolymer of P(BA‐b‐DHPMA), where DHPMA is 2,3‐dihydroxypropyl methacrylate; demonstrating the feasibility of side‐chain modification of the functional obtained copolymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3538–3549, 2007