A formal representation of assumptions in process modelling

In this work, we present a systematic approach to the representation of modelling assumptions. Modelling assumptions form the fundamental basis for the mathematical description of a process system. These assumptions can be translated into either additional mathematical relationships or constraints between model variables, equations, balance volumes or parameters. In order to analyse the effect of modelling assumptions in a formal, rigorous way, a syntax of modelling assumptions has been defined. The smallest indivisible syntactical element, the so called assumption atom has been identified as a triplet. With this syntax a modelling assumption can be described as an elementary assumption, i.e. an assumption consisting of only an assumption atom or a composite assumption consisting of a conjunction of elementary assumptions. The above syntax of modelling assumptions enables us to represent modelling assumptions as transformations acting on the set of model equations. The notion of syntactical correctness and semantical consistency of sets of modelling assumptions is defined and necessary conditions for checking them are given. These transformations can be used in several ways and their implications can be analysed by formal methods. The modelling assumptions define model hierarchies. That is, a series of model families each belonging to a particular equivalence class. These model equivalence classes can be related to primal assumptions regarding the definition of mass, energy and momentum balance volumes and to secondary and tiertinary assumptions regarding the presence or absence and the form of mechanisms within the system. Within equivalence classes, there are many model members, these being related to algebraic model transformations for the particular model. We show how these model hierarchies are driven by the underlying assumption structure and indicate some implications on system dynamics and complexity issues. (C) 2001 Elsevier Science Ltd. All rights reserved.

Coupling 3D visualisation to qualitative assessment of built environment designs

Geographical information systems (GIS) coupled to 3D visualisation technology is an emerging tool for urban planning and landscape design applications. The utility of 3D GIS for realistically visualising the built environment and proposed development scenarios is much advocated in the literature. Planners assess the merits of proposed changes using visual impact assessment (VIA). We have used Arcview GIS and visualisation software: called PolyTRIM from the University of Toronto, Centre for Landscape Research (CLR) to create a 3D scene for the entrance to a University campus. The paper investigates the thesis that to facilitate VIA in planning and design requires not only visualisation, but also a structured evaluation technique (Delphi) to arbitrate the decision-making process. (C) 2001 Elsevier Science B.V. All rights reserved.

Design, modelling and analysis of a six component force balance for hypervelocity wind tunnel testing

A combination of modelling and analysis techniques was used to design a six component force balance. The balance was designed specifically for the measurement of impulsive aerodynamic forces and moments characteristic of hypervelocity shock tunnel testing using the stress wave force measurement technique. Aerodynamic modelling was used to estimate the magnitude and distribution of forces and finite element modelling to determine the mechanical response of proposed balance designs. Simulation of balance performance was based on aerodynamic loads and mechanical responses using convolution techniques. Deconvolution was then used to assess balance performance and to guide further design modifications leading to the final balance design. (C) 2001 Elsevier Science Ltd. All rights reserved.

Three-dimensional orthotropic viscoelastic finite element model of a human ligament

Ligaments undergo finite strain displaying hyperelastic behaviour as the initially tangled fibrils present straighten out, combined with viscoelastic behaviour (strain rate sensitivity). In the present study the anterior cruciate ligament of the human knee joint is modelled in three dimensions to gain an understanding of the stress distribution over the ligament due to motion imposed on the ends, determined from experimental studies. A three dimensional, finite strain material model of ligaments has recently been proposed by Pioletti in Ref. [2]. It is attractive as it separates out elastic stress from that due to the present strain rate and that due to the past history of deformation. However, it treats the ligament as isotropic and incompressible. While the second assumption is reasonable, the first is clearly untrue. In the present study an alternative model of the elastic behaviour due to Bonet and Burton (Ref. [4]) is generalized. Bonet and Burton consider finite strain with constant modulii for the fibres and for the matrix of a transversely isotropic composite. In the present work, the fibre modulus is first made to increase exponentially from zero with an invariant that provides a measure of the stretch in the fibre direction. At 12% strain in the fibre direction, a new reference state is then adopted, after which the material modulus is made constant, as in Bonet and Burton's model. The strain rate dependence can be added, either using Pioletti's isotropic approximation, or by making the effect depend on the strain rate in the fibre direction only. A solid model of a ligament is constructed, based on experimentally measured sections, and the deformation predicted using explicit integration in time. This approach simplifies the coding of the material model, but has a limitation due to the detrimental effect on stability of integration of the substantial damping implied by the nonlinear dependence of stress on strain rate. At present, an artificially high density is being used to provide stability, while the dynamics are being removed from the solution using artificial viscosity. The result is a quasi-static solution incorporating the effect of strain rate. Alternate approaches to material modelling and integration are discussed, that may result in a better model.

Modelling cement grinding circuits

Modelling and simulation studies were carried out at 26 cement clinker grinding circuits including tube mills, air separators and high pressure grinding rolls in 8 plants. The results reported earlier have shown that tube mills can be modelled as several mills in series, and the internal partition in tube mills can be modelled as a screen which must retain coarse particles in the first compartment but not impede the flow of drying air. In this work the modelling has been extended to show that the Tromp curve which describes separator (classifier) performance can be modelled in terms of d(50)(corr), by-pass, the fish hook, and the sharpness of the curve. Also the high pressure grinding rolls model developed at the Julius Kruttschnitt Mineral Research Centre gives satisfactory predictions using a breakage function derived from impact and compressed bed tests. Simulation studies of a full plant incorporating a tube mill, HPGR and separators showed that the models could successfully predict the performance of the another mill working under different conditions. The simulation capability can therefore be used for process optimization and design. (C) 2001 Elsevier Science Ltd. All rights reserved.

Step size control for efficient discrete element simulation

The step size determines the accuracy of a discrete element simulation. The position and velocity updating calculation uses a pre-calculated table and hence the control of step size can not use the integration formulas for step size control. A step size control scheme for use with the table driven velocity and position calculation uses the difference between the calculation result from one big step and that from two small steps. This variable time step size method chooses the suitable time step size for each particle at each step automatically according to the conditions. Simulation using fixed time step method is compared with that of using variable time step method. The difference in computation time for the same accuracy using a variable step size (compared to the fixed step) depends on the particular problem. For a simple test case the times are roughly similar. However, the variable step size gives the required accuracy on the first run. A fixed step size may require several runs to check the simulation accuracy or a conservative step size that results in longer run times. (C) 2001 Elsevier Science Ltd. All rights reserved.

Quantum slow motion

We investigate the center-of-mass motion of cold atoms in a standing amplitude modulated laser field. We use a simple model to explain the momentum distribution of the atoms after any distinct number of modulation cycles. The atoms starting near a classical phase-space resonance move slower than we would expect classically. We explain this by showing that for a wave packet on the classical resonances we can replace the complicated dynamics in the quantum Liouville equation in phase space by its classical dynamics with a modified potential.

Probabilistic modelling of CO2 corrosion laboratory data using neural networks

The present paper addresses two major concerns that were identified when developing neural network based prediction models and which can limit their wider applicability in the industry. The first problem is that it appears neural network models are not readily available to a corrosion engineer. Therefore the first part of this paper describes a neural network model of CO2 corrosion which was created using a standard commercial software package and simple modelling strategies. It was found that such a model was able to capture practically all of the trends noticed in the experimental data with acceptable accuracy. This exercise has proven that a corrosion engineer could readily develop a neural network model such as the one described below for any problem at hand, given that sufficient experimental data exist. This applies even in the cases when the understanding of the underlying processes is poor. The second problem arises from cases when all the required inputs for a model are not known or can be estimated with a limited degree of accuracy. It seems advantageous to have models that can take as input a range rather than a single value. One such model, based on the so-called Monte Carlo approach, is presented. A number of comparisons are shown which have illustrated how a corrosion engineer might use this approach to rapidly test the sensitivity of a model to the uncertainities associated with the input parameters. (C) 2001 Elsevier Science Ltd. All rights reserved.

Molecular motion in nanocomposites of poly(ethylene oxide) and montmorillonite

Motion of chains of poly(ethylene oxide) within the interlayer spacing of 2:1 phyllosilicate/montmorillonite was studied with H-1 and C-13 NMR spectroscopy. Measurements of the H-1 NMR line widths and relaxation times across a large temperature range were used to determine the effect of bulk thermal transitions on polymer chain motion within the nanocomposites. The results were consistent with previous reports of low apparent activation energies of motion. Details of the frequency and geometry of motion were obtained from a comparison of the C-13 cross-polarity/magic-angle spinning spectra and relaxation times of the nanocomposite with those of the pure polymer. (C) 2001 John Wiley & Sons, Inc.

The modelling of froth zone recovery in batch and continuously operated laboratory flotation cells

This paper proposes an integrated methodology for modelling froth zone performance in batch and continuously operated laboratory flotation cells. The methodology is based on a semi-empirical approach which relates the overall flotation rate constant to the froth depth (FD) in the flotation cell; from this relationship, a froth zone recovery (R,) can be extracted. Froth zone recovery, in turn, may be related to the froth retention time (FRT), defined as the ratio of froth volume to the volumetric flow rate of concentrate from the cell. An expansion of this relationship to account for particles recovered both by true flotation and entrainment provides a simple model that may be used to predict the froth performance in continuous tests from the results of laboratory batch experiments. Crown Copyright (C) 2002 Published by Elsevier Science B.V. All rights reserved.