Homogeneous Schemes Research Articles

Partial catalytic oxidation of methane to synthesis gas over rhodium: in situ Raman experiments and detailed simulations

The partial catalytic oxidation of methane to synthesis gas over Rh/ZrO 2 was investigated experimentally and numerically at fuel-to-air equivalence ratios of 2.5 and 4.0 and pressures of 4 and 6 bar. Experiments were performed in an optically accessible, laboratory-scale, channel-flow catalytic reactor and involved in situ one-dimensional Raman measurements of major species (CH 4, O 2, H 2O, CO 2, H 2, CO, and N 2) concentrations across the reactor boundary layer. The numerical model included a two-dimensional elliptic code with elementary homogeneous (gaseous) and heterogeneous (catalytic) chemical reaction schemes. Homogeneous ignition experiments and numerical predictions have validated the employed gas-phase reaction mechanism and have further delineated the reactor extent over which the contribution of the homogeneous reaction pathway was negligible. Over the reactor extent where oxygen was still available, the employed heterogeneous reaction scheme provided good agreement with the measured species concentrations, overpredicting only to a small degree the partial over the total oxidation route. In the oxygen-depleted zones of the reactor, however, the heterogeneous scheme overpredicted to a greater degree the impact of steam reforming and water gas shift reactions, resulting in higher computed hydrogen yields at the reactor exit. Additional experiments and predictions were carried out in a sub-scale gas-turbine honeycomb reactor, at operating conditions leading to oxygen breakthrough. The predictions again favored the partial over the total oxidation route. A modified heterogeneous scheme was proposed that provided very good agreement with measurements in the honeycomb reactor and in the oxygen-rich zones of the laboratory-scale reactor. The hydrogen produced during partial oxidation was partly re-adsorbed on the catalyst leading to superadiabatic surface temperatures, thus exemplifying the importance of proper thermal management in commercial reactors.

Homogeneous ignition of CH 4/air and H 2O and CO 2-diluted CH 4/O 2 mixtures over Pt; an experimental and numerical investigation at pressures up to 16 bar

The homogeneous ignition of CH 4/air, CH 4/O 2/H 2O/N 2, and CH 4/O 2/CO 2/N 2 mixtures over platinum was investigated experimentally and numerically at pressures 4 bar ⩽ p ⩽ 16 bar, temperatures 1120 K ⩽ T ⩽ 1420 K, and fuel-to-oxygen equivalence ratios 0.30 ⩽ ϕ ⩽ 0.40. Experiments have been performed in an optically accessible catalytic channel-flow reactor and included planar laser induced fluorescence (LIF) of the OH radical for the determination of homogeneous (gas-phase) ignition and one-dimensional Raman measurements of major species concentrations across the reactor boundary layer for the assessment of the heterogeneous (catalytic) processes preceding homogeneous ignition. Numerical predictions were carried out with a 2D elliptic CFD code that included elementary heterogeneous and homogeneous chemical reaction schemes and detailed transport. The employed heterogeneous reaction scheme accurately captured the catalytic methane conversion upstream of the gaseous combustion zone. Two well-known gas-phase reaction mechanisms were tested for their capacity to reproduce measured homogeneous ignition characteristics. There were substantial differences in the performance of the two schemes, which were ascribed to their ability to correctly capture the p– T– ϕ parameter range of the self-inhibited ignition behavior of methane. Comparisons between measured and predicted homogeneous ignition distances have led to the validation of a gaseous reaction scheme at 6 bar ⩽ p ⩽ 16 bar, a pressure range of particular interest to gas-turbine catalytically stabilized combustion (CST) applications. The presence of heterogeneously produced water chemically promoted the onset of homogeneous ignition. Experiments and predictions with CH 4/O 2/H 2O/N 2 mixtures containing 57% per volume H 2O have shown that the validated gaseous scheme was able to capture the chemical impact of water in the induction zone. Experiments with CO 2 addition (30% per volume) were in good agreement with the numerical simulations and have indicated that CO 2 had only a minor chemical impact on homogeneous ignition.

Knowledge discovery by probabilistic clustering of distributed databases

Clustering of distributed databases facilitates knowledge discovery through learning of new concepts that characterise common features and differences between datasets. Hence, general patterns can be learned rather than restricting learning to specific databases from which rules may not be generalisable. We cluster databases that hold aggregate count data on categorical attributes that have been classified according to homogeneous or heterogeneous classification schemes. Clustering of datasets is carried out via the probability distributions that describe their respective aggregates. The homogeneous case is straightforward. For heterogeneous data we investigate a number of clustering strategies, of which the most efficient avoid the need to compute a dynamic shared ontology to homogenise the classification schemes prior to clustering.

Trends and perspectives: Architectures for integrating legacy information systems with modern bar code technology

The homogeneous ignition of CH4/air, CH4/O2/H2O/N2, and CH4/O2/CO2/N2 mixtures over platinum was investigated experimentally and numerically at pressures 4 bar ⩽ p ⩽ 16 bar, temperatures 1120 K ⩽ T ⩽ 1420 K, and fuel-to-oxygen equivalence ratios 0.30 ⩽ φ ⩽ 0.40. Experiments have been performed in an optically accessible catalytic channel-flow reactor and included planar laser induced fluorescence (LIF) of the OH radical for the determination of homogeneous (gas-phase) ignition and one-dimensional Raman measurements of major species concentrations across the reactor boundary layer for the assessment of the heterogeneous (catalytic) processes preceding homogeneous ignition. Numerical predictions were carried out with a 2D elliptic CFD code that included elementary heterogeneous and homogeneous chemical reaction schemes and detailed transport. The employed heterogeneous reaction scheme accurately captured the catalytic methane conversion upstream of the gaseous combustion zone. Two well-known gas-phase reaction mechanisms were tested for their capacity to reproduce measured homogeneous ignition characteristics. There were substantial differences in the performance of the two schemes, which were ascribed to their ability to correctly capture the p–T–φ parameter range of the self-inhibited ignition behavior of methane. Comparisons between measured and predicted homogeneous ignition distances have led to the validation of a gaseous reaction scheme at 6 bar ⩽ p ⩽ 16 bar, a pressure range of particular interest to gas-turbine catalytically stabilized combustion (CST) applications. The presence of heterogeneously produced water chemically promoted the onset of homogeneous ignition. Experiments and predictions with CH4/O2/H2O/N2 mixtures containing 57% per volume H2O have shown that the validated gaseous scheme was able to capture the chemical impact of water in the induction zone. Experiments with CO2 addition (30% per volume) were in good agreement with the numerical simulations and have indicated that CO2 had only a minor chemical impact on homogeneous ignition.

High-pressure catalytic combustion of methane over platinum: In situ experiments and detailed numerical predictions

The catalytic combustion of fuel-lean methane/air premixtures over platinum was investigated experimentally and numerically in the pressure range 4 to 16 bar. Experiments were performed in an optically accessible, laminar channel-flow catalytic reactor. In situ, spatially resolved Raman measurements of major species and temperature over the reactor boundary layer were used to assess the heterogeneous (catalytic) reactivity and planar laser-induced fluorescence (LIF) of the OH radical confirmed the absence of homogeneous (gas-phase) ignition. Numerical predictions were carried out with a two-dimensional elliptic code that included elementary heterogeneous and homogeneous chemical reaction schemes. Comparisons between measurements and numerical predictions have led to the assessment of the high-pressure validity of two different elementary heterogeneous chemical reaction schemes for the complete oxidation of methane over platinum. It was shown that the catalytic reactivity increased with increasing pressure and that crucial in the performance of the heterogeneous reaction schemes was the capture of the decrease in surface free-site availability with increasing pressure. Even in the absence of homogeneous ignition, the contribution of the gaseous reaction pathway to the conversion of methane could not be ignored at high pressures. The delineation of the regimes of significance for both heterogeneous and homogeneous pathways has exemplified the importance of the preignition gaseous chemistry in many practical high-pressure catalytic combustion systems. Sensitivity and reaction flux analyses were carried out on a validated elementary heterogeneous reaction scheme and led to the construction of reduced catalytic reaction schemes capable of reproducing accurately the catalytic methane conversion in the channel-flow configuration as well as in a surface perfectly stirred reactor (SPSR) and, when coupled to a homogeneous reaction scheme, the combined heterogeneous and homogeneous methane conversions. A global catalytic step could not reproduce the measured catalytic reactivity over the entire pressure range 4 to 16 bar.

Modified Three-point Difference Schemes of High-accuracy Order for Second Order Nonlinear Ordinary Differential Equations

AbstractThis work discusses issues on the design and analysis of three-point difference schemes for the nonlinear boundary-value problem. A new effective implementation of an exact three-point difference schemes on irregular grids in terms of homogeneous three-point difference schemes of a high-accuracy order is proposed.

Effects of finite rate heterogeneous kinetics on homogeneous ignition in catalytically stabilized channel flow combustion

The homogeneous (gas-phase) and heterogeneous (catalytic) ignition of fuel-lean premixtures is investigated analytically and numerically in two-dimensional laminar channel-flow configurations with uniform incoming properties and isothermal catalytic walls. First-order matched activation energy asymptotics are employed, along with a one-step catalytic reaction and a one-step large activation energy gaseous reaction. Parametric description of the chemically frozen state leads to a closed-form heterogeneous ignition criterion in terms of non-dimensional variables that are relevant to confined flows. Formulation of the weakly reactive state yields a closed-form homogeneous ignition criterion that includes explicitly the homogeneous and heterogeneous reactivities through the relevant gaseous and surface Damköhler numbers ( Da g and Da s , respectively). Both ignition criteria are valid over the range 0.002 ≤ x/( bRePr) ≤ 0.16, 1.5 ≤ T W / T IN ≤ 3, and 0.9 ≤ Le ≤ 2.0, where x is the streamwise distance, Re the incoming Reynolds number based on the channel half-height b, Pr the Prandtl number, T W / T IN the wall-to-inlet temperature ratio, and Le the Lewis number of the fuel. Numerical simulations have shown good agreement between the numerically and the analytically predicted homogeneous ignition distances. A reduction of the surface reactivity ( Da s ) promotes homogeneous ignition due to the associated increase of the near-wall fuel levels, and this effect is manifested in the homogeneous ignition criterion via a corresponding increase of the characteristic transverse diffusion time scale with decreasing Da s . It is shown that there exist infinite combinations of surface and gaseous reactivities yielding the same homogeneous ignition distance, suggesting caution in the interpretation of catalytically stabilized combustion (CST) experiments. Moreover, the homogeneous ignition distance is much more sensitive to the gaseous rather than to the surface reaction pathway, thus exemplifying the importance of validated homogeneous reaction schemes under CST-relevant conditions.

Theory of Difference Schemes

3R3. Theory of Difference Schemes. Pure and Applied Mathematics Series, Vol 240. - AA Samarskii (Fac of Comput Math and Cybernetics, Moscow MV Lomonosov State Univ, Moscow, Russia). Marcel Dekker, New York. 2001. 761 pp. ISBN 0-8247-0468-1. $225.00. Reviewed by VD Radulescu (Dept of Math, Univ of Craiova, 13, St AI Cuza, Craiova, 1100, Romania).The study of difference schemes is one of the central subjects in Numerical Analysis. Because of the variety and importance of their applications, in particular to Applied Mathematics, difference schemes caused developments in various areas of mathematics.This monograph is intended as an introduction to difference schemes at the advanced undergraduate and beginning graduate level. The author aimed at breaching the gap that too often exists between engineering and example-oriented textbooks on the one hand, and needlessly abstract mathematical formulations on the other. The book is divided into ten chapters, followed by a list of symbols and some concluding remarks. After several necessary prerequisites exposed in the first two chapters, the author develops in Chapters 3–5 concrete difference schemes for equations of elliptic, parabolic, and hyperbolic types. Chapter 3 focuses on homogeneous difference schemes for ordinary differential equations, by means of which the author solves the canonical problem of the theory of difference schemes in which a primary family of difference schemes is specified and schemes of a desired quality should be selected within the primary family. Chapter 4 is devoted to various difference approximations of second-order elliptic equations. The approximation technique for the Laplace operator and formulations of difference boundary conditions are described for regions of arbitrary shape. Chapter 5 provides the general theory of difference schemes in which it seems reasonable to eliminate constraints on the structure and implicit form of difference operators. Such a theory treats difference schemes as operator equations and operator-difference equations, which are analogs of difference schemes for time-dependent equations of mathematical physics.Chapter 6 includes a priori estimates expressing stability of two-layer and three-layer schemes in terms of the initial data and the right-hand side of the corresponding equations. This chapter also includes many good examples illustrating the practical use of general stability theory with regard to particular schemes to assist the users in subsequent implementations. The author’s strategy is that the stability is the most pressing problem in any algorithm, since it is a necessary rather than a sufficient condition for accuracy. The main purpose of the next three chapters is to show how the results of the general theory of difference schemes are aimed at starting principles for constructing difference schemes of a prescribed quality. The difference schemes for elliptic equations are viewed as operator equations of the first kind, while the difference schemes relating to analogs of nonstationary equations of mathematical physics are treated as difference equations with operator coefficients in an abstract space of any dimension. In the last chapter, several economical schemes and iterative methods for multidimensional problems in mathematical physics are developed. The book is well written and is strongly influenced by the well-known Russian school of Numerical Analysis. The point of view taken here, rigorous presentation without excessive formalism, is however nonstandard. In conclusion, Samarskii’s book Theory of Difference Schemes is original, interesting, and transmits a message in a clear and efficient way. On the whole, this monograph is an excellent contribution to the literature of numerical methods and computer algorithms for solving mathematical-physics problems. The book qualifies to be a reference work that certainly would be a valuable addition to libraries of universities and research laboratories pursuing research in Applied Mathematics.

An experimental and numerical investigation of homogeneous ignition in catalytically stabilized combustion of hydrogen/air mixtures over platinum

The gas-phase ignition of fuel-lean hydrogen/air mixtures over platinum was investigated experimentally and numerically in laminar channel-flow configurations. Experiments were performed at atmospheric pressure in an optically accessible catalytic channel combustor established by two Pt-coated parallel plates, 300 mm long (streamwise direction) and placed 7 mm apart (transverse direction). Planar laser induced fluorescence (PLIF) of the OH radical along the streamwise plane of symmetry was used to monitor the onset of homogeneous ignition, one-dimensional Raman measurements (across the 7-mm transverse direction) provided the boundary layer profiles of the major species and temperature, and thermocouples embedded beneath the catalyst yielded the surface temperature distribution. Computations were carried out using a two-dimensional elliptic fluid mechanical model that included multicomponent transport and elementary homogeneous (gas-phase) and heterogeneous (catalytic) chemical reaction schemes. Four homogeneous and three heterogeneous reaction schemes were tested in the model against measured homogeneous ignition characteristics. The differences between measured and predicted homogeneous ignition distances could be substantial (ranging from 8% to 66%, depending on the particular hetero/homogeneous schemes) and were ascribed primarily to the homogeneous reaction pathway. Sensitivity analysis indicated that the discrepancies induced by the gas-phase schemes originated either from the presence of heterogeneously-produced water due to its effectiveness as collision partner in the chain terminating reaction H + O2 + M = HO2 + M, or from an overall overprediction of the radical pool in the preignition zone. The heterogeneous schemes had significant differences in their surface coverage and radical fluxes, but these variations had practically no impact on homogeneous ignition. Sensitivity and reaction flux analyses have shown that this was attributed to the ability of all heterogeneous schemes to capture the measured mass-transport-limited fuel conversion and to the relative insensitivity of homogeneous ignition on the magnitude of the heterogeneous radical fluxes, provided that all radical adsorption reactions (OH, H, and O) were included in the heterogeneous schemes.

P-Cresol autoxidation using CoAPO-5 prepared by microwave heating of the precursor gel: comparison with homogeneous and biphasic reaction schemes using cobalt salt or complex catalysts

p-Cresol autoxidation to p-hydroxybenzaldehyde was performed at 60 °C and atmospheric pressure, using three methods: (1) quasi-heterogeneous reaction using CoAPO-5 catalyst; (2) homogeneous reaction using CoBr 2 salt; and (3) biphasic organic–aqueous interfacial reaction using cobalt complexes together with a surfactant. Cobalt was proven to be the most active/selective for the p-hydroxybenzaldehyde synthesis among the transition metal salts tested. Highly crystalline and uniform CoAPO-5 was prepared using microwave heating in 40 min from the precursor gels and characterized using XRD, SEM, and UV–VIS spectroscopy. p-Cresol conversion and selectivity to p-hydroxybenzaldehyde increase with the cobalt contents and improved as the Co/ p-cresol (mg/g) ratio increases to ca. 1.0. The oxygen selectivity was 82–85% for CoAPO-5, which is slightly higher than obtained with CoBr 2. The highly alkaline solution employed for the reaction, however, resulted in serious metal leaching. The biphasic reaction attempted for p-cresol autoxidation resulted in poor performance due to the limits in solvent selection. The performance of p-cresol autoxidation reaction was strongly governed by the solvent and followed the order methanol>ethanol>butanol, all miscible with water. Hardly any reaction took place in non-polar solvents such as chloroform or toluene, or in 2-ethyl-1-hexanol.

An experimental and numerical investigation of turbulent catalytically stabilized channel flow combustion of hydrogen/air mixtures over platinum

The turbulent catalytically stabilized combustion (CST) of fuel-lean hydrogen/air mixtures over platinum was investigated experimentally and numerically in channel-flow configurations. Experiments were performed in an optically accessible catalytic channel reactor, established by two Pt-coated ceramic plates 300 mm long and placed 7 mm apart, with incoming Reynolds numbers of 15,000 and 30,000. Planar laserinduced fluorescence of the OH radical was used to monitor the onset of homogeneous (gas-phase) ignition, one-dimensional (across the 7 mm transverse direction) Raman measurements of major species and temperature assessed the turbulent scalar transport, laser doppler velocimetry yielded the inlet velocity and turbulence, and thermocouples embedded beneath the catalyst provided the surface temperature distribution. Computations were carried out with a two-dimensional elliptic fluid mechanical code that included elementary heterogeneous and homogeneous chemical reaction schemes. Three different low-Reynolds number near-wall turbulence models were examined, in conjunction with a thermochemistry model that included a presumed-shape (Gaussian) probability density function approach for the gaseous reactions and a laminar-like closure for catalytic reactions. Comparisons between predictions and measurements have shown that key CST issues, such as catalytic fuel conversion and onset of homogeneous ignition, are strongly dependent on the particular turbulence model. Moreover, the discrepancies between predictions and measurements were ascribed to the capacity of the various turbulence models to capture the strong flow laminarization induced by the heat transfer from the hot catalytic surfaces. A turbulence model that yields good agreement with the measurements is presented as particularly suited for CST. Experiments and predictions have shown that a continuous increase of the turbulent transport led to incomplete combustion through the gaseous reaction zone with subsequent catalytic conversion of the leaked fuel and, finally, to extinction of the gaseous flame.

Homogeneous ignition in high-pressure combustion of methane/air over platinum: Comparison of measurements and detailed numerical predictions

The gas-phase ignition of fuel-lean methane/air premixtures over Pt was investigated experimentally and numerically in laminar channel-flow configurations at pressures of up to 10 bar. Experiments were performed in an optically accessible catalytic channel reactor established by two Pt-coated ceramic plates, 300 mm long (streamwise direction) and placed 7 mm apart (transverse direction). Planar laser-induced fluorescence (PLIF) of the OH radical along the streamwise plane of symmetry was used to monitor the onset of homogeneous (gas-phase) ignition, and thermocouples embedded beneath the catalyst provided the surface temperature distribution. Computations were carried out with a two-dimensional elliptic numerical code, which included the elementary heterogeneous (catalytic) reaction scheme for methane on Pt from Deutschmann and two different elementary homogeneous reaction schemes, Warnatz and GRI-3.0. Following homogeneous ignition, very stable V-shaped flames were established in the reactor. At pressures of up to 6 bar, the measured and predicted (Deutschmann/Warnatz schemes) flame sweep angles and OH levels were in good agreement with each other, while the homogeneous ignition distances were predicted within 10%. However, at pressures greater than or equal to 8 bar, a marked overprediction of the homogeneous ignition distances was evident (>25%). The Deutschmann/GRI-3.0 schemes yielded much shorter (≈55%–65%) homogeneous ignition distances at all pressures. Sensitivity analysis indicated that the latter discrepancies were ascribed to the homogeneous reaction pathway. GRI-3.0 yielded a much faster radical pool buildup than the scheme of Warnatz, clearly showing its inapplicability under catalytically stabilized combustion (CST) relevant conditions. The heterogeneous reactivity was enhanced with increasing pressure. Although the increase in pressure inhibited the adsorption of methane due to the resulting higher oxygen surface coverage, this effect was overtaken by the corresponding increase of the methane gas-phase concentration.

Catalytic combustion of methane/air mixtures over platinum: Homogeneous ignition distances in channel flow configurations

The homogeneous ignition of fuel-lean methane/air mixtures is investigated numerically in laminar plane channel configurations with platinum-coated isothermal walls and uniform incoming properties. Parametric studies are carried out to determine the dependence of the homogeneous ignition distance (χ ig ) on the fuel-to-air equivalence ratio (), the wall temperature ( T W ), the inlet temperature ( T IN ), the inlet velocity ( U IN ), and the channel wall separation (2 b ). Computations are performed with elliptic and parabolic two-dimensional numerical codes, both with elementary heterogeneous and homogeneous chemical reaction schemes. The applicability of the parabolic approach (boundary layer approximation) in assessing homogeneous ignition is investigated. The elliptic approach yields shorter x ig compared to those of the parabolic approach, but as U IN increases, their difference diminishes, and for U IN greater than a minimum value U m, IN , both computations give the same x ig . U m, IN depends strongly onand ranges from 8 m/s (=0.35) to 15.5 m/s (=0.55) at atmospheric pressure. An analytical homogeneous ignition criterion based on activation energy asymptotics, a one-step gaseous reaction and a mass-transport-limited surface reaction, is presented for catalytic channel configurations and adapted to lean methane/air combustion. The mass-transport-limited assumption is shown to be valid only at atmospheric pressure. A one-step gaseous reaction with a methane order of −0.33 and an activation energy of 243.4 kJ/mol yields, in conjunction with the analytical ignition criterion, homogeneous ignition distances at atmospheric pressure within 9.2% of those numerically predicted over a wide range of operating conditions (0.35≤≤0.55, 1380 K≤ T W ≤1600 K. 623 K≤ T IN ≤743 K and 1.5 mm≤ b ≤15 mm). The negative methane reaction order (methane self-inhibition) results in shorter x ig for the leaner mixtures. The apparent activation energy is higher than that of purely homogeneous combustion (≈200 kJ/mol) due to catalytic inhibition via radical adsorption.

Differentially Homogeneous Schemes

Let S be a Noetherian scheme and π: X→S be a flat morphism of finite type. Then π is said to be differentially homogeneous when X×SX is normally flat along the diagonal. Examples of these morphisms are smooth morphisms and finite field extensions. We study here different characterizations and properties of differentially homogeneous morphisms, and finally obtain the local structure of these morphisms.

Bioanalytical applications of polyion-sensitive electrodes

Recent developments in the design and bioanalytical applications of polyion-sensitive electrodes (PSEs) are reviewed. The general electrochemical principles governing the potentiometric response of such polymer membrane-based devices are summarized and new directions for the use of these novel sensors are detailed. These new directions include basic fundamental studies aimed at determining the thermodynamics of polyion extraction into ion exchanger-doped polymeric membranes, new methods to quantitate the anticoagulant drug heparin in whole blood via titrations with polycationic protamine, selective assays of protease activities (and inhibitors of such activities) using natural and synthetic polyionic peptides as substrates, and novel homogeneous immunoassay schemes based on potentiometric polyion detection.

Homogeneous reaction schemes with a great number of steady states

Homogeneous termolecular stage reaction schemes with a great number of internal (no zero coordinates) steady states have been investigated.

High-order compact schemes for second-order ordinary differential equations with singular coefficients

Homogeneous three-point finite-difference schemes of arbitrary order of accuracy for a second-order Dirichlet problem with generalized coefficients and generalized right-hand side are constructed and validated. Bibliography: 8 titles.

On parallelizing the EM algorithm for PET image reconstruction

The expectation maximization (EM) algorithm is one of the most suitable iterative methods for positron emission tomography (PET) image reconstruction; however, it requires a long computation time and an enormous amount of memory space. To overcome these problems, we present two classes of highly efficient parallelization schemes: homogeneous and inhomogeneous partitionings. The essential difference between these two classes is that the inhomogeneous partitioning schemes may partially overlap the communication with computation by deliberate exploitation of the inherent data access pattern with a multiple-ring communication pattern. In theory, the inhomogeneous partitioning schemes may outperform the homogeneous partitioning schemes. However, the latter require a simpler communication pattern. In an attempt to estimate the achievable performance and to analyze the performance degradation factors without actual implementation, we have derived efficiency prediction formulas for closely estimating the performance for the proposed parallelization schemes. We propose new integration and broadcasting algorithms for hypercube, ring, and n-D mesh topologies, which are more efficient than the conventional algorithms when the link setup time is relatively negligible. The concept of the proposed task and data partitioning schemes, the integration and broadcasting algorithms, and the efficiency estimation methods can be applied to many other problems that are rich in data parallelism, but without balanced exclusive partitioning. >

Direct potentiometric membrane electrode measurements of heparin binding to macromolecules

AbstractThe use of a newly developed heparin responsive polymeric membrane electrode for directly monitoring the binding of heparin to a variety of other biological macromolecules is examined. Potentiometric titrations of protamine, low‐density lipoprotein (LDL), polybrene, DNase enzyme, and polylysine with either porcine or beef lung heparin can be followed conveniently by the electrode at various solution pHs. Such titrations yield endpoints that are used to determine the stoichiometry for the interaction of the different heparins with these macromolecules. Based on prior heparin calibration curves, the titration data can be recast in Scatchard form to obtain binding constants for these solution‐phase heparin‐macromolecular reactions. The speed and simplicity of the proposed method make it an attractive alternative to classical solid‐phase binding methods or newer homogeneous fluorescent polarization schemes for studying the solution‐phase interaction of heparin with other macromolecules.

Chronopotentiometry with power-law perturbation functions at an expanding plane electrode with and without a preceding blank period for systems with a coupled first-order homogeneous chemical reaction

The systems formalism is used to obtain the interfacial concentration transients for power-law current input at an expanding plane electrode. The explicit results for the concentration transients obtained here pertain to arbitrary homogeneous reaction schemes coupled to the oxidant and reductant of a single charge-transfer step and the power-law form without and with a preceding blank period (for two types of power-law current profile, say, (i) I( t) = I 0( t− t 0) q for t ⩾ t 0, I( t) = 0 for t < t 0; and (ii) I( t) = I 0 t q for t ⩾ t 0, I( t) = 0 for t < t 0). Finally the potential transients are obtained using Padé approximants. The results of Galvez et al. (for E, CE, EC, aC) (J. Electroanal. Chem., 132 (1982) 15; 146 (1983) 221, 233, 243), Molina et al. (for E) (J. Electroanal. Chem., 227 (1987) 1 and Kies (for E) (J. Electroanal. Chem., 45 (1973) 71) are obtained as special cases.