An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 2. Residuals analysis and a case study

In Part 1 of this paper a methodology for back-to-back testing of simulation software was described. Residuals with error-dependent geometric properties were generated. A set of potential coding errors was enumerated, along with a corresponding set of feature matrices, which describe the geometric properties imposed on the residuals by each of the errors. In this part of the paper, an algorithm is developed to isolate the coding errors present by analysing the residuals. A set of errors is isolated when the subspace spanned by their combined feature matrices corresponds to that of the residuals. Individual feature matrices are compared to the residuals and classified as 'definite', 'possible' or 'impossible'. The status of 'possible' errors is resolved using a dynamic subset testing algorithm. To demonstrate and validate the testing methodology presented in Part 1 and the isolation algorithm presented in Part 2, a case study is presented using a model for biological wastewater treatment. Both single and simultaneous errors that are deliberately introduced into the simulation code are correctly detected and isolated. Copyright (C) 2003 John Wiley Sons, Ltd.

Nitrifying microbial community analysis of nitrite accumulating biofilm reactor by fluorescence in situ hybridization

Biological nitrogen removal via nitrite pathway in wastewater treatment is very important especially in the cost of aeration and as an electron donor for denitrification. Wastewater nitrification and nitrite accumulations were carried out in a biofilm reactor. The biofilm reactor showed almost complete nitrification and most of the oxidized ammonium was present as nitrite at the ammonium load of 1.2 kg N/m3/d. Nitrite accumulation was achieved by the selective inhibition of nitrite oxidizers by free ammonia and oxygen limitation. Nitrite oxidation activity was recovered as soon as the inhibition factor was removed. Fluorescence in situ hybridization studies of the nitrite accumulating biofilm system have shown that genus Nitrosomonas which is specifically hybridized with probe NSM 156 was the dominant nitrifying bacteria while Nitrospira was less abundant than those of normal nitrification systems. Further FISH analysis showed that the combinations of Nitrosomonas and Nitrospira cells were identified as important populations of nitrifying bacteria in an autotrophic nitrifying biofilm system.

Induction in the timed interval calculus

The Timed Interval Calculus, a timed-trace formalism based on set theory, is introduced. It is extended with an induction law and a unit for concatenation, which facilitates the proof of properties over trace histories. The effectiveness of the extended Timed Interval Calculus is demonstrated via a benchmark case study, the mine pump. Specifically, a safety property relating to the operation of a mine shaft is proved, based on an implementation of the mine pump and assumptions about the environment of the mine. (C) 2002 Elsevier Science B.V. All rights reserved.

On the evaluation of some differential formulations for the pom-pom constitutive model

In recent years, progress has been made in modelling long chain branched polymers by the introduction of the so-called pompom model. Initially developed by McLeish and Larson (1998), the model has undergone several improvements or alterations, leading to the development of new formulations. Some of these formulations however suffer from certain mathematical defects. The purpose of the present paper is to review some of the formulations of the pom-pom constitutive model, and to investigate their possible mathematical defects. Next, an alternative formulation is proposed, which does not appear to exhibit mathematical defects, and we explore its modelling performance by comparing the predictions with experiments in non-trivial rheometric flows of an LDPE melt. The selected rheometric flows are the double step strain, as well as the large amplitude oscillatory shear experiments. For LAOS experiments, the comparison involves the use of Fourier-transform analysis.

Surface diffusion of strongly adsorbing vapors in activated carbon by a differential permeation method

Conventional methods to determine surface diffusion of adsorbed molecules are proven to be inadequate for strongly adsorbing vapors on activated carbon. Knudsen diffusion permeability (B-k) for strongly adsorbing vapors cannot be directly estimated from that of inert gases such as helium. In this paper three models are considered to elucidate the mechanism of surface diffusion in activated carbon. The transport mechanism in all three models is a combination of Knudsen diffusion, viscous flow and surface diffusion. The collision reflection factor f (which is the fraction of molecules undergoing collision to the solid surface over reflection from the surface) of the Knudsen diffusivity is assumed to be a function of loading. It was found to be 1.79 in the limit of zero loading, and decreases as loading increases. The surface diffusion permeability increases sharply at very low pressures and then starts to decrease after it has reached a maximum (B(mum)s) at a threshold pressure. The initial rapid increase in the total permeability is mainly attributed to surface diffusion. Interestingly the B(mum)s for all adsorbates appear at the same volumetric adsorbed phase concentration, suggesting that the volume of adsorbed molecules may play an important role in the surface diffusion mechanism in activated carbon. (C) 2003 Elsevier Ltd. All rights reserved.