Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

The influence of substrate kinetics on the microbial community structure in granular anaerobic biomass

The development of a strong, active granular sludge bed is necessary for optimal operation of upflow anaerobic sludge blanket reactors. The microbial and mechanical structure of the granules may have a strong influence on desirable properties such as growth rate, settling velocity and shear strength. Theories have been proposed for granule microbial structure based on the relative kinetics of substrate degradation, but contradict some observations from both modelling and microscopic studies. In this paper, the structures of four granule types were examined from full-scale UASB reactors, treating wastewater from a cannery, a slaughterhouse, and two breweries. Microbial structure was determined using fluorescence in situ hybridisation probing with 16S rRNA-directed oligonucleotide probes, and superficial structure and microbial density (volume occupied by cells and microbial debris) assessed using scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The granules were also modelled using a distributed parameter biofilm model, with a previously published biochemical model structure, biofilm modelling approach, and model parameters. The model results reflected the trophic structures observed, indicating that the structures were possibly determined by kinetics. Of particular interest were results from simulations of the protein grown granules, which were predicted to have slow growth rates, low microbial density, and no trophic layers, the last two of which were reflected by microscopic observations. The primary cause of this structure, as assessed by modelling, was the particulate nature of the wastewater, and the slow rate of particulate hydrolysis, rather than the presence of proteins in the wastewater. Because solids hydrolysis was rate limiting, soluble substrate concentrations were very low (below Monod half saturation concentration), which caused low growth rates. (C) 2003 Elsevier Ltd. All rights reserved.

Disposition kinetics of propranolol isomers in the perfused rat liver

The aim of this study was to define the determinants of the linear hepatic disposition kinetics of propranolol optical isomers using a perfused rat liver. Monensin was used to abolish the lysosomal proton gradient to allow an estimation of propranolol ion trapping by hepatic acidic vesicles. In vitro studies were used for independent estimates of microsomal binding and intrinsic clearance. Hepatic extraction and mean transit time were determined from outflow-concentration profiles using a nonparametric method. Kinetic parameters were derived from a physiologically based pharmacokinetic model. Modeling showed an approximate 34-fold decrease in ion trapping following monensin treatment. The observed model-derived ion trapping was similar to estimated theoretical values. No differences in ion-trapping values was found between R(+)- and S(-)- propranolol. Hepatic propranolol extraction was sensitive to changes in liver perfusate flow, permeability-surface area product, and intrinsic clearance. Ion trapping, microsomal and nonspecific binding, and distribution of unbound propranolol accounted for 47.4, 47.1, and 5.5% of the sequestration of propranolol in the liver, respectively. It is concluded that the physiologically more active S(-)- propranolol differs from the R(+)- isomer in higher permeability-surface area product, intrinsic clearance, and intracellular binding site values.

Kinetics of reduction of lead smelting slags with solid carbon

Research techniques and a methodology have been developed that enable the reduction kinetics of molten lead smelting slags with solid carbon to be studied. The rates of reduction of PbO-FeO-Fe2O3-CaO-SiO2 slags with carbon have been measured for a range of slag compositions for PbO concentrations between 3 and 100 weight percent, and temperatures between 1423 and 1573 K. The reduction rates were determined for both graphite and coke. Within the range of process conditions examined, it has been shown that the reaction rates are almost independent of carbon reactivity, SiO2/CaO and SiO2/Fe ratio in the range of compositions investigated and are not influenced by the presence of sulphur in the slag.The apparent first order rate constants for oxygen removal increase with increasing PbO concentration and oxygen activity in the slag. The data indicate that the rate limiting reaction step for the reduction of lead slags with solid carbon is the chemical reaction at the gas/slag interface.

Phosphate uptake and growth kinetics of Trichodesmium (Cyanobacteria) isolates from the North Atlantic Ocean and the Great Barrier Reef, Australia

We compared inorganic phosphate (P-i) uptake and growth kinetics of two cultures of the diazotrophic cyanobacterium Trichodesmium isolated from the North Atlantic Ocean (IMS101) and from the Great Barrier Reef, Australia (GBRTRLI101). Phosphate-limited cultures had up to six times higher maximum P-i uptake rates than P-replete cultures in both strains. For strain GBRTRLI101, cell-specific P-i uptake rates were nearly twice as high, due to larger cell size, but P-specific maximum uptake rates were similar for both isolates. Half saturation constants were 0.4 and 0.6 muM for P-i uptake and 0.1 and 0.2 muM for growth in IMS101 and GBRTRLI101, respectively. Phosphate uptake in both strains was correlated to growth rates rather than to light or temperature. The cellular phosphorus quota for both strains increased with increasing P-i up to 1.0 muM. The C:P ratios were 340-390 and N:P ratios were 40-45 for both strains under severely P-limited growth conditions, similar to reported values for natural populations from the tropical Atlantic and Pacific Oceans. The C:P and N:P ratios were near Redfield values in medium with >1.0 muM P-i. The North Atlantic strain IMS101 is better adapted to growing on P-i at low concentrations than is GBRTRLI101 from the more P-i-enriched Great Barrier Reef. However, neither strain can achieve appreciable growth at the very low (nanomolar) P-i concentrations found in most oligotrophic regimes. Phosphate could be an important source of phosphorus for Trichodesmium on the Great Barrier Reef, but populations growing in the oligotrophic open ocean must rely primarily on dissolved organic phosphorus sources.

Control of hypersonic turbulent skin friction by boundary-layer combustion of hydrogen

Shvab-Zeldovich coupling of flow variables has been used to extend Van Driest's theory of turbulent boundary-layer skin friction to include injection and combustion of hydrogen in the boundary layer. The resulting theory is used to make predictions of skin friction and heat transfer that are found to be consistent with experimental and numerical results. Using the theory to extrapolate to larger downstream distances at the same experimental conditions, it is found that the reduction in skin-friction drag with hydrogen mixing and combustion is three times that with mixing alone. In application to flow on a flat plate at mainstream velocities of 2, 4, and 6 knits, and Reynolds numbers from 3 X 10(6) to 1 x 10(8), injection and combustion of hydrogen yielded values of skin-friction drag that were less than one-half of the no-injection skin-friction drag, together with a net reduction in heat transfer when the combustion heat release in air was less than the stagnation enthalpy. The mass efficiency of hydrogen injection, as measured by effective specific impulse values, was approximately 2000 s.

Matching conditional moments in PDF modelling of nonpremixed combustion

The rate of generation of fluctuations with respect to the scalar values conditioned on the mixture fraction, which significantly affects turbulent nonpremixed combustion processes, is examined. Simulation of the rate in a major mixing model is investigated and the derived equations can assist in selecting the model parameters so that the level of conditional fluctuations is better reproduced by the models. A more general formulation of the multiple mapping conditioning (MMC) model that distinguishes the reference and conditioning variables is suggested. This formulation can be viewed as a methodology of enforcing certain desired conditional properties onto conventional mixing models. Examples of constructing consistent MMC models with dissipation and velocity conditioning as well as of combining MMC with large eddy simulations (LES) are also provided. (c) 2005 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Kinetics of reduction of FeO from slag by graphite and coal chars

The rates of reduction of FeO from iron-saturated FeO-CaO-Al2O3-SiO2 slags by graphite, coke, bituminous coal and anthracitic coal chars at temperatures in the range 1 673-1873 K have been measured using a sessile drop technique. The extents of reaction were determined using EPMA analysis of quenched samples, and on line gas analysis using a quadrupole mass spectrometer. The reaction rates have been shown to be dependent critically on carbon type. For the reaction geometry used in this investigation the reduction rates of graphite and coke are observed to be faster than with coal chars. This unexpected finding is shown to be associated with differences in the dominant chemical and mass transfer mechanisms occurring at the reaction interface. High reaction rates are observed to occur with the formation of liquid Fe-C alloy product and the associated gasification of carbon from the alloy. The rates of reduction by coal chars are determined principally by the chemical reaction at the carbon/gas interface and slag phase mass transfer.

Mg-based nanocomposites with high capacity and fast kinetics for hydrogen storage

Magnesium and its alloys have shown a great potential in effective hydrogen storage due to their advantages of high volumetric/ gravimetric hydrogen storage capacity and low cost. However, the use of these materials in fuel cells for automotive applications at the present time is limited by high hydrogenation temperature and sluggish sorption kinetics. This paper presents the recent results of design and development of magnesium-based nanocomposites demonstrating the catalytic effects of carbon nanotubes and transition metals on hydrogen adsorption in these materials. The results are promising for the application of magnesium materials for hydrogen storage, with significantly reduced absorption temperatures and enhanced ab/desorption kinetics. High level Density Functional Theory calculations support the analysis of the hydrogenation mechanisms by revealing the detailed atomic and molecular interactions that underpin the catalytic roles of incorporated carbon and titanium, providing clear guidance for further design and development of such materials with better hydrogen storage properties.

Phase separation, porous structure, and cure kinetics in aliphatic epoxy resin containing hyperbranched polyester

Thermosetting blends of an aliphatic epoxy resin and a hydroxyl-functionalized hyperbranched polymer (HBP), aliphatic hyperbranched polyester Boltorn H40, were prepared using 4,4'-diaminodiphenylmethane (DDM) as the curing agent. The phase behavior and morphology of the DDM-cured epoxy/HBP blends with HBP content up to 40 wt% were investigated by differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM). The cured epoxy/HBP blends are immiscible and exhibit two separate glass transitions, as revealed by DMA. The SEM observation showed that there exist two phases in the cured blends, which is an epoxy-rich phase and an HBP-rich phase, which is responsible for the two separate glass transitions. The phase morphology was observed to be dependent on the blend composition. For the blends with HBP content up to 10 wt%, discrete HBP domains are dispersed in the continuous cured epoxy matrix, whereas the cured blend with 40 wt% HBP exhibits a combined morphology of connected globules and bicominuous phase structure. Porous epoxy thermosets with continuous open structures on the order of 100-300 nm were formed after the HBP-rich phase was extracted with solvent from the cured blend with 40 wt% HBP. The DSC study showed that the curing rate is not obviously affected in the epoxy/HBP blends with HBP content up to 40 wt %. The activation energy values obtained are not remarkably changed in the blends; the addition of HBP to epoxy resin thus does not change the mechanism of cure reaction of epoxy resin with DDM. (c) 2006 Wiley Periodicals, Inc.

Mechanism and kinetics of dithiobenzoate-mediated RAFT polymerization. I. The current situation

Investigations into the kinetics and mechanism of dithiobenzoate-mediated Reversible Addition-Fragmentation Chain Transfer (RAFT) polymerizations, which exhibit nonideal kinetic behavior, such as induction periods and rate retardation, are comprehensively reviewed. The appreciable uncertainty in the rate coefficients associated with the RAFT equilibrium is discussed and methods for obtaining RAFT-specific rate coefficients are detailed. In addition, mechanistic studies are presented, which target the elucidation of the fundamental cause of rate retarding effects. The experimental and theoretical data existing in the literature are critically evaluated and apparent discrepancies between the results of different studies into the kinetics of RAFT polymerizations are discussed. Finally, recommendations for further work are given. (c) 2006 Wiley Periodicals, Inc.