Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

Reproducibility of a laboratory-based 40-km cycle time-trial on a stationary wind-trainer in highly trained cyclists

The purpose of the present study was to examine the reproducibility of laboratory-based 40-km cycle time-trial performance on a stationary wind-trainer. Each week, for three consecutive weeks, and on different days, forty-three highly trained male cyclists ((x) over bar +/- SD; age = 25 +/- 6 y; mass = 75 +/- 7 kg; peak oxygen uptake [(V) over dot O-2 peak] = 64.8 +/- 5.2 ml x kg(-1) x min(-1)) performed: 1) a (V) over dot O-2 peak test, and 2) a 40-km time-trial on their own racing bicycle mounted to a stationary wind-trainer (Cateye - Cyclosimulator). Data from all tests were compared using a one-way analysis of variance. Performance on the second and third 40-km time-trials were highly related (r = 0.96; p < 0.001), not significantly different (57:21 +/- 2:57 vs. 57:12 +/- 3:14 min:s), and displayed a low coefficient of variation (CV) = 0.9 +/- 0.7%. Although the first 40-km time-trial (58:43 +/- 3:17min:s) was not significantly different from the second and third tests (p = 0.06), inclusion of the first test in the assessment of reliability increased within-subject CV to 3.0 +/- 2.9%. 40-km time-trial speed (km x h(-1)) was significantly (p < 0.001) related to peak power output (W; r = 0.75), (V) over dot O-2 peak (1 x min(-1); r = 0.53), and the second ventilatory turnpoint (1 x min(-1); r = 0.68) measured during the progressive exercise tests. These data demonstrate that the assessment of 40-km cycle time-trial performance in well-trained endurance cyclists on a stationary wind-trainer is reproducible, provided the athletes perform a familiarization trial.

Model-based analysis of anaerobic acetate uptake by a mixed culture of polyphosphate-accumulating and glycogen-accumulating organisms

An increasing number of studies shows that the glycogen-accumulating organisms (GAOs) can survive and may indeed proliferate under the alternating anaerobic/aerobic conditions found in EBPR systems, thus forming a strong competitor of the polyphosphate-accumulating organisms (PAOs). Understanding their behaviors in a mixed PAO and GAO culture under various operational conditions is essential for developing operating strategies that disadvantage the growth of this group of unwanted organisms. A model-based data analysis method is developed in this paper for the study of the anaerobic PAO and GAO activities in a mixed PAO and GAO culture. The method primarily makes use of the hydrogen ion production rate and the carbon dioxide transfer rate resulting from the acetate uptake processes by PAOs and GAOs, measured with a recently developed titration and off-gas analysis (TOGA) sensor. The method is demonstrated using the data from a laboratory-scale sequencing batch reactor (SBR) operated under alternating anaerobic and aerobic conditions. The data analysis using the proposed method strongly indicates a coexistence of PAOs and GAOs in the system, which was independently confirmed by fluorescent in situ hybridization (FISH) measurement. The model-based analysis also allowed the identification of the respective acetate uptake rates by PAOs and GAOs, along with a number of kinetic and stoichiometric parameters involved in the PAO and GAO models. The excellent fit between the model predictions and the experimental data not involved in parameter identification shows that the parameter values found are reliable and accurate. It also demonstrates that the current anaerobic PAO and GAO models are able to accurately characterize the PAO/GAO mixed culture obtained in this study. This is of major importance as no pure culture of either PAOs or GAOs has been reported to date, and hence the current PAO and GAO models were developed for the interpretation of experimental results of mixed cultures. The proposed method is readily applicable for detailed investigations of the competition between PAOs and GAOs in enriched cultures. However, the fermentation of organic substrates carried out by ordinary heterotrophs needs to be accounted for when the method is applied to the study of PAO and GAO competition in full-scale sludges. (C) 2003 Wiley Periodicals, Inc.

An approach to verifying and debugging simulation models governed by ordinary differential equations: Part 1. Methodology for residual generation

For dynamic simulations to be credible, verification of the computer code must be an integral part of the modelling process. This two-part paper describes a novel approach to verification through program testing and debugging. In Part 1, a methodology is presented for detecting and isolating coding errors using back-to-back testing. Residuals are generated by comparing the output of two independent implementations, in response to identical inputs. The key feature of the methodology is that a specially modified observer is created using one of the implementations, so as to impose an error-dependent structure on these residuals. Each error can be associated with a fixed and known subspace, permitting errors to be isolated to specific equations in the code. It is shown that the geometric properties extend to multiple errors in either one of the two implementations. Copyright (C) 2003 John Wiley Sons, Ltd.

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.