A mathematical model of concentrate solids content for the wet drum magnetic separator

Low concentrate density from wet drum magnetic separators in dense medium circuits can cause operating difficulties due to inability to obtain the required circulating medium density and, indirectly, high medium solids losses. The literature is almost silent on the processes controlling concentrate density. However, the common name for the region through which concentrate is discharged-the squeeze pan gap-implies that some extrusion process is thought to be at work. There is no model of magnetics recovery in a wet drum magnetic separator, which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was done using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 turn diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in this work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. It is proposed, based both on the experimental observations of the present work and on observations reported in the literature, that the process controlling magnetic separator concentrate density is one of drainage. Such a process should be able to be defined by an initial moisture, a drainage rate and a drainage time, the latter being defined by the volumetric flowrate and the volume within the drainage zone. The magnetics can be characterised by an experimentally derived ultimate drainage moisture. A model based on these concepts and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to be a good fit to data over concentrate solids content values from 40% solids to 80% solids and for both magnetite and ferrosilicon feeds. (C) 2003 Elsevier Science B.V. All rights reserved.

A mathematical model of recovery of dense medium magnetics in the wet drum magnetic separator

Loss of magnetic medium solids from dense medium circuits is a substantial contributor to operating cost. Much of this loss is by way of wet drum magnetic separator effluent. A model of the separator would be useful for process design, optimisation and control. A review of the literature established that although various rules of thumb exist, largely based on empirical or anecdotal evidence, there is no model of magnetics recovery in a wet drum magnetic separator which includes as inputs all significant machine and operating variables. A series of trials, in both factorial experiments and in single variable experiments, was therefore carried out using a purpose built rig which featured a small industrial scale (700 mm lip length, 900 mm diameter) wet drum magnetic separator. A substantial data set of 191 trials was generated in the work. The results of the factorial experiments were used to identify the variables having a significant effect on magnetics recovery. Observations carried out as an adjunct to this work, as well as magnetic theory, suggests that the capture of magnetic particles in the wet drum magnetic separator is by a flocculation process. Such a process should be defined by a flocculation rate and a flocculation time; the latter being defined by the volumetric flowrate and the volume within the separation zone. A model based on this concept and containing adjustable parameters was developed. This model was then fitted to a randomly chosen 80% of the data, and validated by application to the remaining 20%. The model is shown to provide a satisfactory fit to the data over three orders of magnitude of magnetics loss. (C) 2003 Elsevier Science BY. All rights reserved.

Hemodynamic and ventilatory effects of manual respiratory physiotherapy techniques of chest clapping, vibration, and shaking in an animal model

Chest clapping, vibration, and shaking were studied in 10 physiotherapists who applied these techniques on an anesthetized animal model. Hemodynamic variables (such as heart rate, blood pressure, pulmonary artery pressure, and right atrial pressure) were measured during the application of these techniques to verify claims of adverse events. In addition, expired tidal volume and peak expiratory flow rate were measured to ascertain effects of these techniques. Physiotherapists in this study applied chest clapping at a rate of 6.2 +/- 0.9 Hz, vibration at 10.5 +/- 2.3 Hz, and shaking at 6.2 +/- 2.3 Hz. With the use of these rates, esophageal pressure swings of 8.8 +/- 5.0, 0.7 +/- 0.3, and 1.4 +/- 0.7 mmHg resulted from clapping, vibration, and shaking respectively. Variability in rates and forces generated by these techniques was 80% of variance in shaking force (P = 0.003). Application of these techniques by physiotherapists was found to have no significant effects on hemodynamic and most ventilatory variables in this study. From this study, we conclude that chest clapping, vibration, and shaking 1) can be consistently performed by physiotherapists; 2) are significantly related to physiotherapists' characteristics, particularly clinical experience; and 3) caused no significant hemodynamic effects.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

An EM-based Semi-Parametric Mixture Model Approach to the Regression Analysis of Competing-Risks Data

We consider a mixture model approach to the regression analysis of competing-risks data. Attention is focused on inference concerning the effects of factors on both the probability of occurrence and the hazard rate conditional on each of the failure types. These two quantities are specified in the mixture model using the logistic model and the proportional hazards model, respectively. We propose a semi-parametric mixture method to estimate the logistic and regression coefficients jointly, whereby the component-baseline hazard functions are completely unspecified. Estimation is based on maximum likelihood on the basis of the full likelihood, implemented via an expectation-conditional maximization (ECM) algorithm. Simulation studies are performed to compare the performance of the proposed semi-parametric method with a fully parametric mixture approach. The results show that when the component-baseline hazard is monotonic increasing, the semi-parametric and fully parametric mixture approaches are comparable for mildly and moderately censored samples. When the component-baseline hazard is not monotonic increasing, the semi-parametric method consistently provides less biased estimates than a fully parametric approach and is comparable in efficiency in the estimation of the parameters for all levels of censoring. The methods are illustrated using a real data set of prostate cancer patients treated with different dosages of the drug diethylstilbestrol. Copyright (C) 2003 John Wiley Sons, Ltd.

Comparison of DEM and experiment for a scale model SAG mill

Predictions of flow patterns in a 600-mm scale model SAG mill made using four classes of discrete element method (DEM) models are compared to experimental photographs. The accuracy of the various models is assessed using quantitative data on shoulder, toe and vortex center positions taken from ensembles of both experimental and simulation results. These detailed comparisons reveal the strengths and weaknesses of the various models for simulating mills and allow the effect of different modelling assumptions to be quantitatively evaluated. In particular, very close agreement is demonstrated between the full 3D model (including the end wall effects) and the experiments. It is also demonstrated that the traditional two-dimensional circular particle DEM model under-predicts the shoulder, toe and vortex center positions and the power draw by around 10 degrees. The effect of particle shape and the dimensionality of the model are also assessed, with particle shape predominantly affecting the shoulder position while the dimensionality of the model affects mainly the toe position. Crown Copyright (C) 2003 Published by Elsevier Science B.V. All rights reserved.

Model-based clustering in gene expression microarrays: An application to breast cancer data

In microarray studies, the application of clustering techniques is often used to derive meaningful insights into the data. In the past, hierarchical methods have been the primary clustering tool employed to perform this task. The hierarchical algorithms have been mainly applied heuristically to these cluster analysis problems. Further, a major limitation of these methods is their inability to determine the number of clusters. Thus there is a need for a model-based approach to these. clustering problems. To this end, McLachlan et al. [7] developed a mixture model-based algorithm (EMMIX-GENE) for the clustering of tissue samples. To further investigate the EMMIX-GENE procedure as a model-based -approach, we present a case study involving the application of EMMIX-GENE to the breast cancer data as studied recently in van 't Veer et al. [10]. Our analysis considers the problem of clustering the tissue samples on the basis of the genes which is a non-standard problem because the number of genes greatly exceed the number of tissue samples. We demonstrate how EMMIX-GENE can be useful in reducing the initial set of genes down to a more computationally manageable size. The results from this analysis also emphasise the difficulty associated with the task of separating two tissue groups on the basis of a particular subset of genes. These results also shed light on why supervised methods have such a high misallocation error rate for the breast cancer data.

A mechanistic model for carbon dioxide corrosion of mild steel in the presence of protective iron carbonate films - Part 3: Film growth model

A model of iron carbonate (FeCO3) film growth is proposed, which is an extension of the recent mechanistic model of carbon dioxide (CO2) corrosion by Nesic, et al. In the present model, the film growth occurs by precipitation of iron carbonate once saturation is exceeded. The kinetics of precipitation is dependent on temperature and local species concentrations that are calculated by solving the coupled species transport equations. Precipitation tends to build up a layer of FeCO3 on the surface of the steel and reduce the corrosion rate. On the other hand, the corrosion process induces voids under the precipitated film, thus increasing the porosity and leading to a higher corrosion rate. Depending on the environmental parameters such as temperature, pH, CO2 partial pressure, velocity, etc., the balance of the two processes can lead to a variety of outcomes. Very protective films and low corrosion rates are predicted at high pH, temperature, CO2 partial pressure, and Fe2+ ion concentration due to formation of dense protective films as expected. The model has been successfully calibrated against limited experimental data. Parametric testing of the model has been done to gain insight into the effect of various environmental parameters on iron carbonate film formation. The trends shown in the predictions agreed well with the general understanding of the CO2 corrosion process in the presence of iron carbonate films. The present model confirms that the concept of scaling tendency is a good tool for predicting the likelihood of protective iron carbonate film formation.

An energy-based model for swing hammer mills

An energy-based swing hammer mill model has been developed for coke oven feed preparation. it comprises a mechanistic power model to determine the dynamic internal recirculation and a perfect mixing mill model with a dual-classification function to mimic the operations of crusher and screen. The model parameters were calibrated using a pilot-scale swing hammer mill at various operating conditions. The effects of the underscreen configurations and the feed sizes on hammer mill operations were demonstrated through the fitted model parameters. Relationships between the model parameters and the machine configurations were established. The model was validated using the independent experimental data of single lithotype coal tests with the same BJD pilot-scale hammer mill and full operation audit data of an industrial hammer mill. The outcome of the energy-based swing hammer mill model is the capability to simulate the impact of changing blends of coal or mill configurations and operating conditions on product size distribution. Alternatively, the model can be used to select the machine settings required to achieve a desired product. (C) 2003 Elsevier Science B.V. All rights reserved.

A unified model of flames as gasdynamic discontinuities

Viewed on a hydrodynamic scale, flames in experiments are often thin so that they may be described as gasdynamic discontinuities separating the dense cold fresh mixture from the light hot burned products. The original model of a flame as a gasdynamic discontinuity was due to Darrieus and to Landau. In addition to the fluid dynamical equations, the model consists of a flame speed relation describing the evolution of the discontinuity surface, and jump conditions across the surface which relate the fluid variables on the two sides of the surface. The Darrieus-Landau model predicts, in contrast to observations, that a uniformly propagating planar flame is absolutely unstable and that the strength of the instability grows with increasing perturbation wavenumber so that there is no high-wavenumber cutoff of the instability. The model was modified by Markstein to exhibit a high-wavenumber cutoff if a phenomenological constant in the model has an appropriate sign. Both models are postulated, rather than derived from first principles, and both ignore the flame structure, which depends on chemical kinetics and transport processes within the flame. At present, there are two models which have been derived, rather than postulated, and which are valid in two non-overlapping regions of parameter space. Sivashinsky derived a generalization of the Darrieus-Landau model which is valid for Lewis numbers (ratio of thermal diffusivity to mass diffusivity of the deficient reaction component) bounded away from unity. Matalon & Matkowsky derived a model valid for Lewis numbers close to unity. Each model has its own advantages and disadvantages. Under appropriate conditions the Matalon-Matkowsky model exhibits a high-wavenumber cutoff of the Darrieus-Landau instability. However, since the Lewis numbers considered lie too close to unity, the Matalon-Matkowsky model does not capture the pulsating instability. The Sivashinsky model does capture the pulsating instability, but does not exhibit its high-wavenumber cutoff. In this paper, we derive a model consisting of a new flame speed relation and new jump conditions, which is valid for arbitrary Lewis numbers. It captures the pulsating instability and exhibits the high-wavenumber cutoff of all instabilities. The flame speed relation includes the effect of short wavelengths, not previously considered, which leads to stabilizing transverse surface diffusion terms.

A unit cell waveguide model of a reflectarray formed by microstrip patches and slots

An equivalent unit cell waveguide approach (WGA) is described to obtain reflection coefficient phase curves for designing a microstrip patch reflectarray supported by a ground plane with periodic apertures or slots. Based on the presented theory, a computer algorithm for determining the reflection coefficient of a plane wave normally incident on a multi-layer structure of patches and apertures is developed. The validity of the developed algorithm is verified by comparing the obtained results with those published in the literature and the ones generated by Agilent High Frequency Structure Simulator (HFSS). A good agreement in all the presented examples is obtained, proving that the developed theory and computer algorithm can be an effective tool for designing multi-layer microstrip reflectarrays with a periodically perforated ground plane. (C) 2003 Wiley Periodicals, Inc.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.