Mathematical modelling

The development of a new process model of cement grinding in two-stage mills is discussed. The new model has been used to simulate cement grinding and predicting mill performance in open and closed circuit configuration. The new model considered the two-compartment mill as perfectly mixed slices in series. The breakage rate function uses the back calculation technique to determine offline using drop weight and abrasion tests.

Brain activity during automatic semantic priming revealed by event-related functional magnetic resonance imaging

Semantic priming occurs when a subject is faster in recognising a target word when it is preceded by a related word compared to an unrelated word. The effect is attributed to automatic or controlled processing mechanisms elicited by short or long interstimulus intervals (ISIs) between primes and targets. We employed event-related functional magnetic resonance imaging (fMRI) to investigate blood oxygen level dependent (BOLD) responses associated with automatic semantic priming using an experimental design identical to that used in standard behavioural priming tasks. Prime-target semantic strength was manipulated by using lexical ambiguity primes (e.g., bank) and target words related to dominant or subordinate meaning of the ambiguity. Subjects made speeded lexical decisions (word/nonword) on dominant related, subordinate related, and unrelated word pairs presented randomly with a short ISI. The major finding was a pattern of reduced activity in middle temporal and inferior prefrontal regions for dominant versus unrelated and subordinate versus unrelated comparisons, respectively. These findings are consistent with both a dual process model of semantic priming and recent repetition priming data that suggest that reductions in BOLD responses represent neural priming associated with automatic semantic activation and implicate the left middle temporal cortex and inferior prefrontal cortex in more automatic aspects of semantic processing.

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

SPAnDX: a process-based population dynamics model to explore management and climate change impacts on an invasive alien plant, Acacia nilotica

This paper describes a process-based metapopulation dynamics and phenology model of prickly acacia, Acacia nilotica, an invasive alien species in Australia. The model, SPAnDX, describes the interactions between riparian and upland sub-populations of A. nilotica within livestock paddocks, including the effects of extrinsic factors such as temperature, soil moisture availability and atmospheric concentrations of carbon dioxide. The model includes the effects of management events such as changing the livestock species or stocking rate, applying fire, and herbicide application. The predicted population behaviour of A. nilotica was sensitive to climate. Using 35 years daily weather datasets for five representative sites spanning the range of conditions that A. nilotica is found in Australia, the model predicted biomass levels that closely accord with expected values at each site. SPAnDX can be used as a decision-support tool in integrated weed management, and to explore the sensitivity of cultural management practices to climate change throughout the range of A. nilotica. The cohort-based DYMEX modelling package used to build and run SPAnDX provided several advantages over more traditional population modelling approaches (e.g. an appropriate specific formalism (discrete time, cohort-based, process-oriented), user-friendly graphical environment, extensible library of reusable components, and useful and flexible input/output support framework). (C) 2003 Published by Elsevier Science B.V.

Kinetic model for selective cultivation of microfungi in a microscreen process for food processing wastewater treatment and biomass production

The research was aimed at developing a technology to combine the production of useful microfungi with the treatment of wastewater from food processing. A recycle bioreactor equipped with a micro-screen was developed as a wastewater treatment system on a laboratory scale to contain a Rhizopus culture and maintain its dominance under non-aseptic conditions. Competitive growth of bacteria was observed, but this was minimised by manipulation of the solids retention time and the hydraulic retention time. Removal of about 90% of the waste organic material (as BOD) from the wastewater was achieved simultaneously. Since essentially all fungi are retained behind the 100 mum aperture screen, the solids retention time could be controlled by the rate of harvesting. The hydraulic retention time was employed to control the bacterial growth as the bacteria were washed through the screen at a short HRT. A steady state model was developed to determine these two parameters. This model predicts the effluent quality. Experimental work is still needed to determine the growth characteristics of the selected fungal species under optimum conditions (pH and temperature).

Fitness assessment of document model

Document classification is a supervised machine learning process, where predefined category labels are assigned to documents based on the hypothesis derived from training set of labelled documents. Documents cannot be directly interpreted by a computer system unless they have been modelled as a collection of computable features. Rogati and Yang [M. Rogati and Y. Yang, Resource selection for domain-specific cross-lingual IR, in SIGIR 2004: Proceedings of the 27th annual international conference on Research and Development in Information Retrieval, ACM Press, Sheffied: United Kingdom, pp. 154-161.] pointed out that the effectiveness of document classification system may vary in different domains. This implies that the quality of document model contributes to the effectiveness of document classification. Conventionally, model evaluation is accomplished by comparing the effectiveness scores of classifiers on model candidates. However, this kind of evaluation methods may encounter either under-fitting or over-fitting problems, because the effectiveness scores are restricted by the learning capacities of classifiers. We propose a model fitness evaluation method to determine whether a model is sufficient to distinguish positive and negative instances while still competent to provide satisfactory effectiveness with a small feature subset. Our experiments demonstrated how the fitness of models are assessed. The results of our work contribute to the researches of feature selection, dimensionality reduction and document classification.

A modified discrete random pore model allowing for different initial surface reactivity

We investigate here a modification of the discrete random pore model [Bhatia SK, Vartak BJ, Carbon 1996;34:1383], by including an additional rate constant which takes into account the different reactivity of the initial pore surface having attached functional groups and hydrogens, relative to the subsequently exposed surface. It is observed that the relative initial reactivity has a significant effect on the conversion and structural evolution, underscoring the importance of initial surface chemistry. The model is tested against experimental data on chemically controlled char oxidation and steam gasification at various temperatures. It is seen that the variations of the reaction rate and surface area with conversion are better represented by the present approach than earlier random pore models. The results clearly indicate the improvement of model predictions in the low conversion region, where the effect of the initially attached functional groups and hydrogens is more significant, particularly for char oxidation. It is also seen that, for the data examined, the initial surface chemistry is less important for steam gasification as compared to the oxidation reaction. Further development of the approach must also incorporate the dynamics of surface complexation, which is not considered here.