Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

Block copolymer nanoparticles of controlled sizes via ring‐opening metathesis polymerization

This article describes the formation and characterization of self‐assembled nanoparticles of controlled sizes based on amphiphilic block copolymers synthesized by ring‐opening metathesis polymerization. We synthesized a novel hydrophobic derivative of norbornene; this monomer could be polymerized using Grubbs' catalyst [Cl₂Ru(CHPh)(PCy₃)₂] forming polymers of controlled molecular weight. We synthesized amphiphilic block copolymers of controlled composition and showed that they assemble into nanoparticles of controlled size. The nanoparticles were characterized using dynamic light scattering and transmission electron microscopy. Tuning the composition of the block copolymer enables the tuning of the diameters of the nanoparticles in the 30‐ to 80‐nm range. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3352–3359, 2004     

Large melting point depression of 2–3‐nm length‐scale nanocrystals formed by the self‐assembly of an associative polymer: Telechelic,pyrene‐labeled poly(dimethylsiloxane)

Large melting point depressions for organic nanocrystals, in comparison with those of the bulk, were observed in an associative polymer: telechelic, pyrene‐labeled poly(dimethylsiloxane) (Py‐PDMS‐Py). Nanocrystals formed within nanoaggregates of pyrenyl units that were immiscible in poly(dimethylsiloxane). For 5 and 7 kg/mol Py‐PDMS‐Py, physical gels resulted, with melting points exceeding 40 °C and with small‐angle X‐ray scattering peaks indicating that the crystals were nanoconfined, were 2–3 nm long, and contained roughly 18–30 pyrenyl dye end units. In contrast, 30 kg/mol Py‐PDMS‐PY was not a gel and exhibited no scattering peak at room temperature; however, after 12 h of annealing at ?5 °C, multiple melting peaks were present at 5–30 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3470–3475, 2004     

Diffraction grating in noncrosslinked polymers

The diffraction efficiency and morphology of the transmission modes of holographic polymer dispersed liquid crystals were studied with respect to the molecular structure of poly(urethane acrylate) (PUA), the film (polymer/liquid crystal) and resin (oligomer/monomer) compositions, and the cell thickness. PUA, based on N‐vinylpyrrolidone and ethyl hexyl acrylate, with low‐molecular‐weight poly(propylene glycol) at a low oligomer content, showed high diffraction efficiency. The results were interpreted in terms of the monomer reactivity and polymer elasticity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 613–620, 2004     

Desorption behavior of a surfactant in a linear low‐density polyethylene blend at elevated temperatures

The desorption behavior of a surfactant in a linear low‐density polyethylene (LLDPE) blend at elevated temperatures of 50, 70, and 80 °C was studied with Fourier transform infrared spectroscopy. The composition of the LLDPE blend was 70:30 LLDPE/low‐density polyethylene. Three different specimens (II, III, and IV) were prepared with various compositions of a small molecular penetrant, sorbitan palmitate (SPAN‐40), and a migration controller, poly(ethylene acrylic acid) (EAA), in the LLDPE blend. The calculated diffusion coefficient (D) of SPAN‐40 in specimens II, III, and IV, between 50 and 80 °C, varied from 1.74 × 10^?11 to 6.79 × 10^?11 cm²/s, from 1.10 × 10^?11 to 5.75 × 10^?11 cm²/s, and from 0.58 × 10^?11 to 4.75 × 10^?11 cm²/s, respectively. In addition, the calculated activation energies (E_D) of specimens II, III, and IV, from the plotting of ln D versus 1/T between 50 and 80 °C, were 42.9, 52.7, and 65.6 kJ/mol, respectively. These values were different from those obtained between 25 and 50 °C and were believed to have been influenced by the interference of Tinuvin (a UV stabilizer) at elevated temperatures higher than 50 °C. Although the desorption rate of SPAN‐40 increased with the temperature and decreased with the EAA content, the observed spectral behavior did not depend on the temperature and time. For all specimens stored over 50 °C, the peak at 1739 cm^?1 decreased in a few days and subsequently increased with a peak shift toward 1730 cm^?1. This arose from the carbonyl stretching vibration of Tinuvin, possibly because of oxidation or degradation at elevated temperatures. In addition, the incorporation of EAA into the LLDPE blend suppressed the desorption rate of SPAN‐40 and retarded the appearance of the 1730 cm^?1 peak. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1114–1126, 2004     

Synthesis and gas barrier characterization of poly(ethylene isophthalate)

Poly(ethylene isophthalate) (PEI) was synthesized for this research with essentially a condensation polymerization of isophthalic acid and ethylene glycol catalyzed by zinc acetate and antimony trioxide. Several samples were obtained, and their characteristics were observed and compared with poly(ethylene terephthalate) (PET). The synthesized PEI samples were chemically identified by ¹H NMR. Thermal analysis with differential scanning calorimetry (DSC) yielded results that indicate the samples were primarily amorphous, with a glass‐transition temperature of 55–60 °C. Molecular weights of these PEI samples were also obtained through intrinsic viscosity measurements (Mark–Houwink equation). Molecular weights varied with conditions of the polymerization, and the highest molecular weight achieved was 21,000 g/mol. Finally, the diffusion coefficient, solubility, and permeability of CO₂ gas in PEI were measured and found to be substantially lower than in PET, as anticipated from their isomeric chemical structures. This is because in PET the phenyl rings are substituted in the para (1,4) positions, which allows for their facile flipping, effectively permitting gases to pass through. However, the meta‐substituted phenyl rings in PEI do not permit such ring flipping, and thus PEI may be more suitable for barrier applications. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4247–4254, 2004     

Pressure and temperature dependence of the gas‐transport properties of dense poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] membranes

The gas‐transport properties of poly[2,6‐toluene‐2,2‐bis(3,4‐dicarboxylphenyl)hexafluoropropane diimide] (6FDA‐2,6‐DAT) have been investigated. The sorption behavior of dense 6FDA‐2,6‐DAT membranes is well described by the dual‐mode sorption model and has certain relationships with the critical temperatures of the penetrants. The solubility coefficient decreases with an increase in either the pressure or temperature. The temperature dependence of the diffusivity coefficient increases with an increase in the penetrant size, as the order of the activation energy for the diffusion jump is CH₄ > N₂ > O₂ > CO₂. Also, the average diffusion coefficient increases with increasing pressure for all the gases tested. As a combined contribution from sorption and diffusion, permeability decreases with increases in the pressure and the kinetic diameter of the penetrant molecules. Even up to 32.7 atm, no plasticization phenomenon can be observed on flat dense 6FDA‐2,6‐DAT membranes from their permeability–pressure curves. However, just as for other gases, the absolute value of the heat of sorption of CO₂ decreases with increasing pressure at a low‐pressure range, but the trend changes when the feed pressure is greater than 10 atm. This implies that CO₂‐induced plasticization may occur and reduce the positive enthalpy required to create a site into which a penetrant can be sorbed. Therefore, a better diagnosis of the inherent threshold pressure for the plasticization of a glassy polymer membrane may involve examining the absolute value of the heat of sorption as a function of pressure and identifying the turning point at which the gradient of the absolute value of the heat of sorption against pressure turns from a negative value to a positive one. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 354–364, 2004     

Dynamic Strategic Pricing and Speed of Diffusion

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.     

Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.     

Modelling of an underground waste disposal site by upscaling

In this paper, we study the global behaviour of an underground waste disposal in order to have an accurate upscaled model suitable for the computations involved in safety assessment processes. We start from a detailed model describing the transport of pollutant leaking from a high number of units. Using the method of homogenization, going to the limit, we obtain first a macroscopic model where the sources are now appearing globally. Then we compute a first‐order matched asymptotic expansion and we give the error estimates for this approximation. Copyright © 2004 John Wiley & Sons, Ltd.