Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Applying linear time-varying constraints to econometric models: With an application to demand systems

When linear equality constraints are invariant through time they can be incorporated into estimation by restricted least squares. If, however, the constraints are time-varying, this standard methodology cannot be applied. In this paper we show how to incorporate linear time-varying constraints into the estimation of econometric models. The method involves the augmentation of the observation equation of a state-space model prior to estimation by the Kalman filter. Numerical optimisation routines are used for the estimation. A simple example drawn from demand analysis is used to illustrate the method and its application.

Measurements of neutral atom diffusion and electron-ion recombination by laser enhanced ionisation and planar laser induced fluorescence in an air-acetylene flame

The spatial and temporal evolution of a depleted atomic distribution created by laser enhanced ionisation (LEI) was employed to determine both a diffusion coefficient for sodium (Na) and an electron (e(-)) and sodium ion recombination rate coefficient in an analytical air-C2H2 flame. A depleted distribution of neutral sodium atoms was produced in a flame by ionising approximately 80% of the irradiated sodium atoms in a well defined region using a two step LEI excitation scheme. Following depletion by ionisation, planar laser induced fluorescence (PLIF) images of the depleted region recorded the diffusion and decay of the depleted Na distribution for different depletion-probe delays. From measurements of the diffused width of the distribution, an accurate diffusion coefficient D = (1.19 +/- 0.03) x 10(-3) m(2) s(-1) for Na was determined in teh burnt gases of the flame. Measurements of the integrated fluorescence intensity in the depleted region for different depletion-probe delays were related to an increase in atomic sodium concentration caused by electron-ion recombination. At high concentrations (greater than or equal to 50 mu g ml(-1)), where the electron and ion concentrations in the depleted region were assumed equal, a recombination rate coefficient of 4.2 x 10(-9) cm(3) s(-1) was calculated. (C) 1997 Elsevier Science B.V.

Nmr imaging of the diffusion of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate)

0Nuclear magnetic resonance (n.m.r.) imaging was used to study the ingress of water into poly(tetrahydrofurfuryl methacrylate-co-hydroxyethyl methacrylate). The study offers strong evidence that the diffusion is Fickian in nature. The diffusion coefficient, D, obtained by fitting the underlying diffusion profile, attainable from the images, according to the equation for Fickian diffusion, is 1.5 x 10(-11) m(2) s(-1), which is in good correlation with the value of 2.1 x 10(-11) m(2) s(-1), obtained from mass uptake measurements. Additionally, from the T-2-weighted images, Superimposed features observed in addition to the underlying Fickian diffusion profiles were shown to have a longer spin-spin relaxation time, T-2. This Suggests the presence of two types of water within the polymer matrix; a less mobile phase of absorbed water that is interacting strongly with the polymer matrix and a more mobile phase of absorbed water residing within the cracks observed in the environmental scanning electron micrograph. (C) 1997 Elsevier Science Ltd.

Percutaneous absorption of sunscreen agents from liquid paraffin: Self-association of octyl salicylate and effects on skin flux

This study provides an investigation of the availability of octyl salicylate (OS), a common sunscreen agent, from liquid paraffin and the effect of OS on skin permeability. A model membrane system to isolate the vehicle effect from membrane permeability has been developed. Partitioning of OS between liquid paraffin and aqueous receptor phases was conducted. Partition coefficients increased with increase in OS concentration. A range of OS concentrations in liquid paraffin was diffused across human epidermis and synthetic membranes into 4% bovine serum albumin in phosphate-buffered saline and 50% ethanol. Absorption profiles of OS obtained from silicone and low-density polyethylene (LDPE) membranes were similar to each other but higher than for the high-density polyethylene [HDPE (3 times)] membrane and human epidermis (15 times). The steady state fluxes and apparent permeability coefficients (K-p') obtained from the diffusion studies showed the same trends with all membranes, except for the HDPE membrane which showed greater increase in flux and K-p' at concentrations above 30%. IR spectra showed that several bands of OS were shifted with concentrations, and the molecular models further suggested that the main contribution to the self-association is from non-1,4 van der Waals interactions.

Models of alcohol use by young adults: An examination of various attitude-behavior theories

Objective: The aim of this study was to test the effectiveness of various attitude-behavior theories in explaining alcohol use among young adults. The theory of reasoned action (TRA), the theory of planned behavior and an extension of the TRA that incorporates past behavior were compared by the method of maximum-likelihood estimation, as implemented in LISREL for Windows 8.12. Method: Respondents consisted of 122 university students (82 female) who were questioned about their attitudes, subjective norms, perceived behavioral control, past behavior and intentions relating to drinking behavior. Students received course credit for their participation in the research. Results: Overall, the results suggest that the extension of the theory of reasoned action which incorporates past behavior provides the best fit to the data. For these young adults, their intentions to drink alcohol were predicted by their past behavior as well as their perceptions of what important others think they should do (subjective norm). Conclusions: The main conclusions drawn from the research concern the importance of focusing on normative influences and past behavior in explaining young adult alcohol use. Issues regarding the relative merit of various alternative models and the need for greater clarity in the measure of attitudes are also discussed.

Structure optimization combining soft-core interaction functions, the diffusion equation method, and molecular dynamics

Smoothing the potential energy surface for structure optimization is a general and commonly applied strategy. We propose a combination of soft-core potential energy functions and a variation of the diffusion equation method to smooth potential energy surfaces, which is applicable to complex systems such as protein structures; The performance of the method was demonstrated by comparison with simulated annealing using the refinement of the undecapeptide Cyclosporin A as a test case. Simulations were repeated many times using different initial conditions and structures since the methods are heuristic and results are only meaningful in a statistical sense.

Measuring macromolecular diffusion using heteronuclear multiple-quantum pulsed-field-gradient NMR

We have previously shown that H-1 pulsed-field-gradient (PFG) NMR spectroscopy provides a facile method for monitoring protein self-association and can be used, albeit with some caveats, to measure the apparent molecular mass of the diffusant [Dingley et al. (1995) J. Biomol. NMR, 6, 321-328]. In this paper we show that, for N-15-labelled proteins, selection of H-1-N-15 multiple-quantum (MQ) coherences in PFG diffusion experiments provides several advantages over monitoring H-1 single-quantum (SQ) magnetization. First, the use of a gradient-selected MQ filter provides a convenient means of suppressing resonances from both the solvent and unlabelled solutes. Second, H-1-N-15 zero-quantum coherence dephases more rapidly than H-1 SQ coherence under the influence of a PFG. This allows the diffusion coefficients of larger proteins to be measured more readily. Alternatively, the gradient length and/or the diffusion delay may be decreased, thereby reducing signal losses from relaxation. In order to extend the size of macromolecules to which these experiments can be applied, we have developed a new MQ PFG diffusion experiment in which the magnetization is stored as longitudinal two-spin order for most of the diffusion period, thus minimizing sensitivity losses due to transverse relaxation and J-coupling evolution.

Virtual plants - integrating architectural and physiological models

Recent advances in computer technology have made it possible to create virtual plants by simulating the details of structural development of individual plants. Software has been developed that processes plant models expressed in a special purpose mini-language based on the Lindenmayer system formalism. These models can be extended from their architectural basis to capture plant physiology by integrating them with crop models, which estimate biomass production as a consequence of environmental inputs. Through this process, virtual plants will gain the ability to react to broad environmental conditions, while crop models will gain a visualisation component. This integration requires the resolution of the fundamentally different time scales underlying the approaches. Architectural models are usually based on physiological time; each time step encompasses the same amount of development in the plant, without regard to the passage of real time. In contrast, physiological models are based in real time; the amount of development in a time step is dependent on environmental conditions during the period. This paper provides a background on the plant modelling language, then describes how widely-used concepts of thermal time can be implemented to resolve these time scale differences. The process is illustrated using a case study. (C) 1997 Elsevier Science Ltd.

A defense of backwards in time causation models in quantum mechanics

This paper offers a defense of backwards in time causation models in quantum mechanics. Particular attention is given to Cramer's transactional account, which is shown to have the threefold virtue of solving the Bell problem, explaining the complex conjugate aspect of the quantum mechanical formalism, and explaining various quantum mysteries such as Schrodinger's cat. The question is therefore asked, why has this model not received more attention from physicists and philosophers? One objection given by physicists in assessing Cramer's theory was that it is not testable. This paper seeks to answer this concern by utilizing an argument that backwards causation models entail a fork theory of causal direction. From the backwards causation model together with the fork theory one can deduce empirical predictions. Finally, the objection that this strategy is questionable because of its appeal to philosophy is deflected.