Deep bed filtration : mathematical models and observations

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. The O’Melia and Ali1 model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This article evaluates those models and their applicability under different operating conditions of filtration.

High rate filtration using buoyant medium : experiments and mathematical models

In this study, the high rate filtration system using buoyant medium of polypropylene or polystyrene was introduced with the study on its performance evaluation via: (i) specific surface coverage, (ii) ultimate specific deposit, (iii) blocking effect and (iv) particle detachment. The filter system was arranged in the downflow mode with an in-line flocculation. Experimental results obtained were analyzed using filtration models. This study showed that: (i) the specific surface coverage increased with the increase in the velocity; (ii) the ultimate specific deposit changed slightly at different filtration velocities and different flocculants; (iii) the blocking effect was significant in the transient stage removal of flocs; and (iv) the detachment model parameter was found to decrease with the increase in the adhesive force, Fad that acts on the flocs (above-micron size).

Managing realtime information flow between distributed discrete event simulation models

Investigates the creation of a method for the connection and communication of commercial off the shelf discrete-event simulation packages for simulation models of manufacturing systems. Through this research a method to connect different commercial off the shelf discrete-event simulation packages was successfully developed facilitating parallel development of models and the creation of extremely large models.

Modelling solute transport in structured soils: performance evaluation of the ADR and TRM models

The movement of chemicals through the soil to the groundwater or discharged to surface waters represents a degradation of these resources. In many cases, serious human and stock health implications are associated with this form of pollution. The chemicals of interest include nutrients, pesticides, salts, and industrial wastes. Recent studies have shown that current models and methods do not adequately describe the leaching of nutrients through soil, often underestimating the risk of groundwater contamination by surface-applied chemicals and overestimating the concentration of resident solutes. This inaccuracy results primarily from ignoring soil structure and nonequilibrium between soil constituents, water, and solutes. A multiple sample percolation system (MSPS), consisting of 25 individual collection wells, was constructed to study the effects of localized soil heterogeneities on the transport of nutrients (NO−3, Cl−, PO3−4) in the vadose zone of an agricultural soil predominantly dominated by clay. Very significant variations in drainage patterns across a small spatial scale were observed (one-way ANOVA, p < 0.001 indicating considerable heterogeneity in water flow patterns and nutrient leaching. Using data collected from the multiple sample percolation experiments, this paper compares the performance of two mathematical models for predicting solute transport, the advective-dispersion model with a reaction term (ADR), and a two-region preferential flow model (TRM) suitable for modelling nonequilibrium transport. These results have implications for modelling solute transport and predicting nutrient loading on a larger scale.

Mathematical modelling of the crankshaft pin grinding process

Novel mathematical models to predict crankshaft pin grinding forces, out-of-roundness and thermal damage were developed as part of this thesis. The models were validated at a local automotive manufacturer's plant. The outcomes of this research have resulted in reduced scrap and warranty costs, improved manufacturing process quality and reduced lead times.

Agent-based heuristics to solve NP-hard scheduling problems

A novel agent-driven heuristic approach was developed to control the operational scheduling for a local manufacturer. This approach outperformed the traditional kanban control mechanism under numerous simulated benchmarking tests. Using this approach, the individual machine loading was reduced by, on average, 28%, with the loading spread reduced by 85%

Dynamic interactions in models with Kaleckian lags

Provides a careful assessment of previous research on lags in economic models. Several interesting lines of research are opened up. Chief among them is the analysis of bubbles and their bursting in the financial components of economic models.

Designing adaptive artificial agents for an economic production and conflict model

Production and conflict models have been used over the past 30 years to represent the effects of unproductive resource allocation in economics. Their major applications are in modelling the assignment of property rights, rentseeking and defense economics. This paper describes the process of designing an agent used in a production and conflict model. Using the capabilities of an agent-based approach to economic modelling, we have enriched a simple decision-maker of the kind used in classic general equilibrium economic models, to build an adaptive and interactive agent which uses its own attributes, its neighbors’ parameters and information from its environment to make resource allocation decisions. Our model presents emergent and adaptive behaviors than cannot be captured using classic production and conflict agents. Some possible extensions for future applications are also recommended.

An agent-based approach to value theory and wealth distribution in economics

Any attempt to model an economy requires foundational assumptions about the relations between prices, values and the distribution of wealth. These assumptions exert a profound influence over the results of any model. Unfortunately, there are few areas in economics as vexed as the theory of value. I argue in this paper that the fundamental problem with past theories of value is that it is simply not possible to model the determination of value, the formation of prices and the distribution of income in a real economy with analytic mathematical models. All such attempts leave out crucial processes or make unrealistic assumptions which significantly affect the results. There have been two primary approaches to the theory of value. The first, associated with classical economists such as Ricardo and Marx were substance theories of value, which view value as a substance inherent in an object and which is conserved in exchange. For Marxists, the value of a commodity derives solely from the value of the labour power used to produce it - and therefore any profit is due to the exploitation of the workers. The labour theory of value has been discredited because of its assumption that labour was the only ‘factor’ that contributed to the creation of value, and because of its fundamentally circular argument. Neoclassical theorists argued that price was identical with value and was determined purely by the interaction of supply and demand. Value then, was completely subjective. Returns to labour (wages) and capital (profits) were determined solely by their marginal contribution to production, so that each factor received its just reward by definition. Problems with the neoclassical approach include assumptions concerning representative agents, perfect competition, perfect and costless information and contract enforcement, complete markets for credit and risk, aggregate production functions and infinite, smooth substitution between factors, distribution according to marginal products, firms always on the production possibility frontier and firms’ pricing decisions, ignoring money and credit, and perfectly rational agents with infinite computational capacity. Two critical areas include firstly, the underappreciated Sonnenschein-Mantel- Debreu results which showed that the foundational assumptions of the Walrasian general-equilibrium model imply arbitrary excess demand functions and therefore arbitrary equilibrium price sets. Secondly, in real economies, there is no equilibrium, only continuous change. Equilibrium is never reached because of constant changes in preferences and tastes; technological and organisational innovations; discoveries of new resources and new markets; inaccurate and evolving expectations of businesses, consumers, governments and speculators; changing demand for credit; the entry and exit of firms; the birth, learning, and death of citizens; changes in laws and government policies; imperfect information; generalized increasing returns to scale; random acts of impulse; weather and climate events; changes in disease patterns, and so on. The problem is not the use of mathematical modelling, but the kind of mathematical modelling used. Agent-based models (ABMs), objectoriented programming and greatly increased computer power however, are opening up a new frontier. Here a dynamic bargaining ABM is outlined as a basis for an alternative theory of value. A large but finite number of heterogeneous commodities and agents with differing degrees of market power are set in a spatial network. Returns to buyers and sellers are decided at each step in the value chain, and in each factor market, through the process of bargaining. Market power and its potential abuse against the poor and vulnerable are fundamental to how the bargaining dynamics play out. Ethics therefore lie at the very heart of economic analysis, the determination of prices and the distribution of wealth. The neoclassicals are right then that price is the enumeration of value at a particular time and place, but wrong to downplay the critical roles of bargaining, power and ethics in determining those same prices.

Mathematical modelling of deep bed filtration

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective-diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. O’Melia and Ali’s model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This paper evaluates those models and their applicability under different operating conditions of filtration.

Narrative structure analysis with education and training videos for e-learning

This paper deals with the problem ofstructuralizing education and training videos for high-level semantics extraction and nonlinear media presentation in e-learning applications. Drawing guidance from production knowledge in instructional media, we propose six main narrative structures employed in education and training videos for both motivation and demonstration during learning and practical training. We devise a powerful audiovisual feature set, accompanied by a hierarchical decision tree-based classification system to determine and discriminate between these structures. Based on a two-liered hierarchical model, we demonstrate that we can achieve an accuracy of 84.7% on a comprehensive set of education and training video data.

Mathematical modelling for Singapore primary classrooms : from a teacher’s lens

Limited Singapore research indicated a lack of exposure of modelling tasks at primary levels. Teacher reflection is used as a tool in design research cycles exploring the potentials of modelling tasks in a Singapore primary five classroom. Findings reveal that the teacher identified three potentials of a modelling task on children’s mathematisation process: the task provided a platform for children to (a) identify variables and form relationships between them, (b) relate school-based math learning to real-world experiences, and (c) justify their mathematical models. Implications on the promotion of modelling tasks at primary schools as well as teacher education are drawn.

Building awareness of mathematical modelling at teacher education: a case study in Indonesia

A growing interest to teach mathematics closely connected to its use in daily life has taken place in Indonesia for over a decade (Sembiring, Hadi, and Dolk 2008). This chapter  reports an exploratory case study of  the building of an awareness of mathematical modelling in teacher education in Indonesia. A modelling task, re-designing a parking lot (Ang 2009), was assigned to groups of pre-service secondary mathematics teachers. All groups undertook the stages of collecting data on a parking lot, identifying limitations in the current design of the parking lot, and proposing a new design based on their observations and analyses. The nature of the mathematical models elicited by pre-service teachers during various stages of completing the modelling task will be examined. Implications of this study suggest the need to encourage pre-service teachers to state the assumptions and real-world considerations and link them to the mathematical model in order to validate their models.