Poisson's equation for queues driven by a Markovian marked point process

LetV _t be the virtual waiting time at timet in a queue having marked point process input generated by a finite Markov process {J_t}, such that in addition to Markovmodulated Poisson arrivals there may also be arrivals at jump times of {J_t}. In this setting, Poisson's equation isA g=–f whereA is the infinitesimal generator of {(V_t, J_t)}. It is shown that the solutiong can be expressed asKf for some suitable kernelK, and the explicit form ofK is evaluated. The results are applied to compute limiting variance constants for (normalized) time averages of functionsf(V _t, J_t), in particularf(V _t,J_t)=V_t.     

Kristallisationskinetik von Polymeren

Zusammenfassung Es wird eine differential-thermoanalytische Hochdruckanlage beschrieben, mit der Untersuchungen in einem Druckgebiet von 1-6000 at angestellt werden können. Der Schmelzvorgang eines Hexamethylensuccinat-Polyesters läßt sich sowohl isobar bei konstanten Aufheizgeschwindigkeiten als auch isotherm nach einer neuen DTPA-Methode mit konstanter Druckminderungsrate verfolgen. Die Zunahme der Schmelztemperatur mit dem Druck ist zu dTinm/dp =0,016 °C at^–1 bestimmt worden. Die isotherm gemessenen Kristallisationsgeschwindigkeiten und Keimzahlen nehmen stark mit dem Druck zu. Bezogen auf gleichbleibende thermodynamische Triebkraft der Kristallisation, also bei konstanter reduzierter Unterkühlung T/T_m nimmt die Kristallisationsgeschwindigkeit und Keimzahl leicht ab. Das ist auf die erschwerte Beweglichkeit der Makromoleküle und auch auf die Zunahme der Freien Oberflächenenergie der Faltenfläche _e bei der Kristallisation unter erhöhtem Druck und die damit verbundene Bildung von Kristallen mit größerer Faltenhöhe oder gestreckten Ketten zurückzuführen.

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Summary A differential-thermal-calorimetric method is described which permits measurements in the pressure range of 1 to 6000 at. The melting process of a hexa-methylenesuccinate-polyester is investigated by a constant heating or pressure-decreasing method. The change of the melting point with pressure is 0.016 °C at^–1. The isothermal crystallization and formation of nuclei increases with the pressure, but decreases if carried out at constant thermodynamic driving force approximated by a reduced supercooling T/T_m. This is caused by a decrease of the diffusion rate with increasing pressure and by an increase of the surface free energy of the fold surface. The latter leads to the tendency of the crystallizing polymer system to form extended chain crystals in order to reduce the formation of fold surfaces.

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X. Mitt.:K. Ueberreiter und W. Felber, Kolloid-Z. u. Z. Polymere242, 1173 (1970).

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Herrn Prof. Dr.R. Hosemann zum 60. Geburtstag gewidmet.

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Wir danken Frl.Koblitz für die Messungen der Molekulargewichte.     

Efficient simulation of finite horizon problems in queueing and insurance risk

Let ψ(u,t) be the probability that the workload in an initially empty M/G/1 queue exceeds u at time t<∞, or, equivalently, the ruin probability in the classical Crámer-Lundberg model. Assuming service times/claim sizes to be subexponential, various Monte Carlo estimators for ψ(u,t) are suggested. A key idea behind the estimators is conditional Monte Carlo. Variance estimates are derived in the regularly varying case, the efficiencies are compared numerically and also the estimators are shown to have bounded relative error in some main cases. In part, also extensions to general Lévy processes are treated.     

Photopolymerization of methacrylate monomers using polyhedral silsesquioxanes bearing side-chain amines as photoinitiator

Organotriethoxysilanes (APS-PGE2) were synthesized by reacting 1 mol of 3-(aminopropyl)triethoxysilane with 2 mol of 1,2-epoxy-3-phenoxypropane (PGE). Polyhedral oligomeric silsesquioxanes functionalized with bulky amino groups (ASSQO) were prepared by hydrolytic condensation of APS-PGE2 catalyzed by formic acid. Methacrylate resins were activated for visible light polymerization by the addition of 1 wt.% CQ in combination with the synthesized ASSQO at loadings between 0 and 30 wt.%. The progress of monomer conversion versus irradiation time showed that the CQ/ASSQO pair is an efficient photoinitiator system because a fast reaction and high conversion result from 60 s irradiation at 600 mW/cm². The lack of methacrylate groups in the ASSQO, able to polymerize with the methacrylate resin, results in the absence of chemical bond between the ASSQO cages and the matrix. Debonding of ASSQO cages from the polymer give rise to nanovoids; which allows the methacrylate matrix to yield and deform plastically. Consequently, the final effect is a decrease in the flexural modulus and compressive strength with increasing amounts of ASSQO. The present study highlights the surface effect on the overall properties in nanostructured materials.     

A Kinetic Model for the Reactions of Co and H2 to CH4 and C2H2 in a Flow Microwave Discharge Reactor

A kinetic model was developed to describe the reactions of CO and H2 to CH4 and C2H2in a microwave plasma. The experimental system consisted of a 24 mm I.D. tubular quartz reactor which passed through a microwave cavity. A variable-incident power waveguide system could supply up to 800 watts of incident microwave power to the cavity. The reactant gas mixture of H2 and CO flowed through the reactor, where a plasma was maintained under pressures of 20 - 100 mm Hg. The reactor effluent was analyzed by IR spectroscopy for CH4 and C2H2. Conversions of up to 5.3% CO to C2H2 and 7.2% CO to CH4 were observed. A 26-reaction kinetic model was developed and fitted to the experimental data. The plasma reactor was modeled in two zones: a discharge zone where electron-impact dissociations produce H, C, and O, and a downstream recombination zone where the atomic species from the discharge recombine. The discharge zone was modeled as a well-mixed reactor, and the recombination zone was modeled as a plug-flow reactor. The model was able to explain the asymptotic shape of the observed conversion versus residence time data; the effect is due to a kinetic limitation. This also explains why the conversions obtained in the plasma cannot be predicted by thermodynamic equilibrium.     

Kristallisation unter hohem Druck Der Einfluß verschiedener Kristallisations- und Temperbedingungen auf die Festigkeit eines Polyesters

Zusammenfassung In einem Autoklaven wurden Prüfstäbe aus Poly-Hexamethylen (Mw = 12.700) im Temperaturbereich von 50°–100°C unter hohem Druck (6.000 at) kristallisiert. Die Biegefestigkeit der spröden Stäbe nimmt mit steigendem Kristallisationsdruck zu.Untersuchungen der Kristallisationsgeschwindigkeit in einem Hochdruck-Differentialkalorimeter zeigen, daß die durch primäre und sekundäre Keimbildung geprägte sphärolithische Überstruktur für die Festigkeit bestimmend ist.Ein Bruch verläuft vorwiegend entlang der Dendritgrenzen radial zum Kern hin, ein Weg, den auch ein Lösungsmittel wählt. Eine langsame Kristallisation bei geringer Unterkühlung vermehrt die Schwachstellen in der interdendritischen Phase. Bei großer Unterkühlung und bei hohem Druck steigt mit der Keimzahl auch die Festigkeit.Untersuchungen der Lösungsmitteldiffusion im Sphärolithen bestätigen einen festeren Aufbau des Kerngebiets. Beim Tempern tritt durch Nachkristallisation eine Ausheilung der interdendritischen Schwachstellen ein.

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Summary Test rods of poly-hexamethylene (Mw = 12,700) have been crystallized under high pressure (up to 6,000 atm) within a temperature range of 50°–100°C in an autoclave. The bending strength of the brittle rods increases with increasing crystallization pressure. The spherulitic structure obtained by primary and secondary nucleation determines the strength as investigations of the crystallization rate in a high pressure-differential-calorimeter prove.A rupture runs radial to the nucleus, parallel to the borders of dendrites constituting a spherulite, a path also chosen by a penetrating solvent.Slow crystallization at small supercooling increases the extension of weak spots in the interdendritic phase. Strength increases with the number of nuclei at high supercooling and pressure.Investigations of the diffusion of a solvent into the spherulites prove a rigid, resistant structure of the nuclei.Annealing causes a decrease of the number of weak spots in the interdendritic phase by recrystallization.

     

Transient Properties of Many-Server Queues and Related QBDs

The time τ(n) of first passage from queue length x to queue length n>x in a many-server queue with both the arrival process and service intensities governed by a finite Markov process is considered. The mean and the Laplace transform are computed as solutions of systems of linear equations coming out by optional stopping of a martingale obtained as a stochastic integral of the exponential Wald martingale for Markov additive processes. Compared to existing techniques for QBD's, the approach has the advantage of being far more efficient for large n.