Anisotropic convection model for the earth's mantle

The paper presents a theory for modeling flow in anisotropic, viscous rock. This theory has originally been developed for the simulation of large deformation processes including the folding and kinking of multi-layered visco-elastic rock (Muhlhaus et al. [1,2]). The orientation of slip planes in the context of crystallographic slip is determined by the normal vector - the director - of these surfaces. The model is applied to simulate anisotropic mantle convection. We compare the evolution of flow patterns, Nusselt number and director orientations for isotropic and anisotropic rheologies. In the simulations we utilize two different finite element methodologies: The Lagrangian Integration Point Method Moresi et al [8] and an Eulerian formulation, which we implemented into the finite element based pde solver Fastflo (www.cmis.csiro.au/Fastflo/). The reason for utilizing two different finite element codes was firstly to study the influence of an anisotropic power law rheology which currently is not implemented into the Lagrangian Integration point scheme [8] and secondly to study the numerical performance of Eulerian (Fastflo)- and Lagrangian integration schemes [8]. It turned out that whereas in the Lagrangian method the Nusselt number vs time plot reached only a quasi steady state where the Nusselt number oscillates around a steady state value the Eulerian scheme reaches exact steady states and produces a high degree of alignment (director orientation locally orthogonal to velocity vector almost everywhere in the computational domain). In the simulations emergent anisotropy was strongest in terms of modulus contrast in the up and down-welling plumes. Mechanisms for anisotropic material behavior in the mantle dynamics context are discussed by Christensen [3]. The dominant mineral phases in the mantle generally do not exhibit strong elastic anisotropy but they still may be oriented by the convective flow. Thus viscous anisotropy (the main focus of this paper) may or may not correlate with elastic or seismic anisotropy.

A 2D numerical model for simulating the physics of fault systems

Simulations provide a powerful means to help gain the understanding of crustal fault system physics required to progress towards the goal of earthquake forecasting. Cellular Automata are efficient enough to probe system dynamics but their simplifications render interpretations questionable. In contrast, sophisticated elasto-dynamic models yield more convincing results but are too computationally demanding to explore phase space. To help bridge this gap, we develop a simple 2D elastodynamic model of parallel fault systems. The model is discretised onto a triangular lattice and faults are specified as split nodes along horizontal rows in the lattice. A simple numerical approach is presented for calculating the forces at medium and split nodes such that general nonlinear frictional constitutive relations can be modeled along faults. Single and multi-fault simulation examples are presented using a nonlinear frictional relation that is slip and slip-rate dependent in order to illustrate the model.

Three-dimensional model for multi-component reactive transport with variable density groundwater flow

PHWAT is a new model that couples a geochemical reaction model (PHREEQC-2) with a density-dependent groundwater flow and solute transport model (SEAWAT) using the split-operator approach. PHWAT was developed to simulate multi-component reactive transport in variable density groundwater flow. Fluid density in PHWAT depends not on only the concentration of a single species as in SEAWAT, but also the concentrations of other dissolved chemicals that can be subject to reactive processes. Simulation results of PHWAT and PHREEQC-2 were compared in their predictions of effluent concentration from a column experiment. Both models produced identical results, showing that PHWAT has correctly coupled the sub-packages. PHWAT was then applied to the simulation of a tank experiment in which seawater intrusion was accompanied by cation exchange. The density dependence of the intrusion and the snow-plough effect in the breakthrough curves were reflected in the model simulations, which were in good agreement with the measured breakthrough data. Comparison simulations that, in turn, excluded density effects and reactions allowed us to quantify the marked effect of ignoring these processes. Next, we explored numerical issues involved in the practical application of PHWAT using the example of a dense plume flowing into a tank containing fresh water. It was shown that PHWAT could model physically unstable flow and that numerical instabilities were suppressed. Physical instability developed in the model in accordance with the increase of the modified Rayleigh number for density-dependent flow, in agreement with previous research. (c) 2004 Elsevier Ltd. All rights reserved.

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

Modelling of cold-formed purlin-sheeting systems .2. Simplified model

A number of theoretical and experimental investigations have been made into the nature of purlin-sheeting systems over the past 30 years. These systems commonly consist of cold-formed zed or channel section purlins, connected to corrugated sheeting. They have proven difficult to model due to the complexity of both the purlin deformation and the restraint provided to the purlin by the sheeting. Part 1 of this paper presented a non-linear elasto plastic finite element model which, by incorporating both the purlin and the sheeting in the analysis, allowed the interaction between the two components of the system to be modelled. This paper presents a simplified version of the first model which has considerably decreased requirements in terms of computer memory, running time and data preparation. The Simplified Model includes only the purlin but allows for the sheeting's shear and rotational restraints by modelling these effects as springs located at the purlin-sheeting connections. Two accompanying programs determine the stiffness of these springs numerically. As in the Full Model, the Simplified Model is able to account for the cross-sectional distortion of the purlin, the shear and rotational restraining effects of the sheeting, and failure of the purlin by local buckling or yielding. The model requires no experimental or empirical input and its validity is shown by its goon con elation with experimental results. (C) 1997 Elsevier Science Ltd.

An isolated perfused human placental lobule model for multiple indicator dilution studies

We describe a method for multiple indicator dilution studies in the isolated perfused human placental lobule developed to investigate the relationships between changes in pressure and flow and solute clearance. A peripheral lobule of a human placenta is perfused with a tissue culture-based medium and the perfusate oxygen tension, arterial and venous pressures, pH and perfusion temperature continuously monitored by a computerized system. Flow rates are readily changed. Bolus injections of vascular, extracellular and water space markers, and study compounds can be made into either maternal or fetal circulations, and precisely timed outflow fractions can be collected with computer-controlled fraction collectors, allowing simultaneous determination of concentration-time profiles of each marker. (C) 1997 Elsevier Science Inc.

Model for Differential Nursing Diagnosis of Alterations in Urinary Elimination Based on Fuzzy Logic

Nursing diagnoses associated with alterations of urinary elimination require different interventions, Nurses, who are not specialists, require support to diagnose and manage patients with disturbances of urine elimination. The aim of this study was to present a model based on fuzzy logic for differential diagnosis of alterations in urinary elimination, considering nursing diagnosis approved by the North American Nursing Diagnosis Association, 2001-2002. Fuzzy relations and the maximum-minimum composition approach were used to develop the system. The model performance was evaluated with 195 cases from the database of a previous study, resulting in 79.0% of total concordance and 19.5% of partial concordance, when compared with the panel of experts. Total discordance was observed in only three cases (1.5%). The agreement between model and experts was excellent (kappa = 0.98, P < .0001) or substantial (kappa = 0.69, P < .0001) when considering the overestimative accordance (accordance was considered when at least one diagnosis was equal) and the underestimative discordance (discordance was considered when at least one diagnosis was different), respectively. The model herein presented showed good performance and a simple theoretical structure, therefore demanding few computational resources.

Model based procedure for scale-up of wet overflow ball mills Part 1: Outline of the methodology

Bond's method for ball mill scale-up only gives the mill power draw for a given duty. This method is incompatible with computer modelling and simulation techniques. It might not be applicable for the design of fine grinding ball mills and ball mills preceded by autogenous and semi-autogenous grinding mills. Model-based ball mill scale-up methods have not been validated using a wide range of full-scale circuit data. Their accuracy is therefore questionable. Some of these methods also need expensive pilot testing. A new ball mill scale-up procedure is developed which does not have these limitations. This procedure uses data from two laboratory tests to determine the parameters of a ball mill model. A set of scale-up criteria then scales-up these parameters. The procedure uses the scaled-up parameters to simulate the steady state performance of full-scale mill circuits. At the end of the simulation, the scale-up procedure gives the size distribution, the volumetric flowrate and the mass flowrate of all the streams in the circuit, and the mill power draw.

Predicting coal ash slag flow characteristics (viscosity model for the Al2O3-CaO-'FeO'-SiO2 system)

A model has been developed which enables the viscosities of coal ash slags to be predicted as a function of composition and temperature under reducing conditions. The model describes both completely liquid and heterogeneous, i.e. partly crystallised, slags in the Al2O3-CaO-'FeO'-SiO2 system in equilibrium with metallic iron. The Urbain formalism has been modified to describe the viscosities of the liquid slag phase over the complete range of compositions and a wide range of temperatures. The computer package F * A * C * T was used to predict the proportions of solids and the compositions of the remaining liquid phases. The Roscoe equation has been used to describe the effect of presence of solid suspension (slurry effect) on the viscosity of partly crystallised slag systems. The model provides a good description of the experimental data of fully liquid, and liquid + solids mixtures, over the complete range of compositions and a wide range of temperatures. This model can now be used for viscosity predictions in industrial slag systems. Examples of the application of the new model to coal ash fluxing and blending are given in the paper. (C) 2001 Elsevier Science Ltd. All rights reserved.

A mixture model-based approach to the clustering of microarray expression data

Motivation: This paper introduces the software EMMIX-GENE that has been developed for the specific purpose of a model-based approach to the clustering of microarray expression data, in particular, of tissue samples on a very large number of genes. The latter is a nonstandard problem in parametric cluster analysis because the dimension of the feature space (the number of genes) is typically much greater than the number of tissues. A feasible approach is provided by first selecting a subset of the genes relevant for the clustering of the tissue samples by fitting mixtures of t distributions to rank the genes in order of increasing size of the likelihood ratio statistic for the test of one versus two components in the mixture model. The imposition of a threshold on the likelihood ratio statistic used in conjunction with a threshold on the size of a cluster allows the selection of a relevant set of genes. However, even this reduced set of genes will usually be too large for a normal mixture model to be fitted directly to the tissues, and so the use of mixtures of factor analyzers is exploited to reduce effectively the dimension of the feature space of genes. Results: The usefulness of the EMMIX-GENE approach for the clustering of tissue samples is demonstrated on two well-known data sets on colon and leukaemia tissues. For both data sets, relevant subsets of the genes are able to be selected that reveal interesting clusterings of the tissues that are either consistent with the external classification of the tissues or with background and biological knowledge of these sets.

Developing a meta model for the Bunge-Wand-Weber ontological constructs

At the core of the analysis task in the development process is information systems requirements modelling, Modelling of requirements has been occurring for many years and the techniques used have progressed from flowcharting through data flow diagrams and entity-relationship diagrams to object-oriented schemas today. Unfortunately, researchers have been able to give little theoretical guidance only to practitioners on which techniques to use and when. In an attempt to address this situation, Wand and Weber have developed a series of models based on the ontological theory of Mario Bunge-the Bunge-Wand-Weber (BWW) models. Two particular criticisms of the models have persisted however-the understandability of the constructs in the BWW models and the difficulty in applying the models to a modelling technique. This paper addresses these issues by presenting a meta model of the BWW constructs using a meta language that is familiar to many IS professionals, more specific than plain English text, but easier to understand than the set-theoretic language of the original BWW models. Such a meta model also facilitates the application of the BWW theory to other modelling techniques that have similar meta models defined. Moreover, this approach supports the identification of patterns of constructs that might be common across meta models for modelling techniques. Such findings are useful in extending and refining the BWW theory. (C) 2002 Elsevier Science Ltd. All rights reserved.