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).

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.

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.

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.

Adaptive model for foreground extraction in adverse lighting conditions

Background elimination models are widely used in motion tracking systems. Our aim is to develop a system that performs reliably under adverse lighting conditions. In particular, this includes indoor scenes lit partly or entirely by diffuse natural light. We present a modified "median value" model in which the detection threshold adapts to global changes in illumination. The responses of several models are compared, demonstrating the effectiveness of the new model.

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.

DDoS attack detection at local area networks using information theoretical metrics

DDoS attacks are one of the major threats to Internet services. Sophisticated hackers are mimicking the features of legitimate network events, such as flash crowds, to fly under the radar. This poses great challenges to detect DDoS attacks. In this paper, we propose an attack feature independent DDoS flooding attack detection method at local area networks. We employ flow entropy on local area network routers to supervise the network traffic and raise potential DDoS flooding attack alarms when the flow entropy drops significantly in a short period of time. Furthermore, information distance is employed to differentiate DDoS attacks from flash crowds. In general, the attack traffic of one DDoS flooding attack session is generated by many bots from one botnet, and all of these bots are executing the same attack program. As a result, the similarity among attack traffic should higher than that among flash crowds, which are generated by many random users. Mathematical models have been established for the proposed detection strategies. Analysis based on the models indicates that the proposed methods can raise the alarm for potential DDoS flooding attacks and can differentiate DDoS flooding attacks from flash crowds with conditions. The extensive experiments and simulations confirmed the effectiveness of our proposed detection strategies.

The effective radius and resistance to slippage

This work reveals that parallel gripper flat-jaw configuration affects grasping effectiveness. An important finding is the fact that object grasp reliability is influenced significantly by gripper's ability to develop high resistance to object rotation in the gripper. The concept of effective torque radius, which increases resistance to object rotation in the gripper, is presented here and can be extrapolated to other grasping devices and grasping strategies to improve their reliability and make them more effective. Grippers with full-jaw contact surface and those with discrete contact areas have been investigated using simple experimental setups. Essential mathematical models needed for analytical investigation, based on simple mechanics for full-jaw contact surfaces and discrete-jaw contact surfaces, are presented. These may be useful for gripper jaw design purposes.

Robust optimal motion cueing algorithm based on the linear quadratic regulator method and a genetic algorithm

The aim of this paper is to design and develop an optimal motion cueing algorithm (MCA) based on the genetic algorithm (GA) that can generate high-fidelity motions within the motion simulator's physical limitations. Both, angular velocity and linear acceleration are adopted as the inputs to the MCA for producing the higher order optimal washout filter. The linear quadratic regulator (LQR) method is used to constrain the human perception error between the real and simulated driving tasks. To develop the optimal MCA, the latest mathematical models of the vestibular system and simulator motion are taken into account. A reference frame with the center of rotation at the driver's head to eliminate false motion cues caused by rotation of the simulator to the translational motion of the driver's head as well as to reduce the workspace displacement is employed. To improve the developed LQR-based optimal MCA, a new strategy based on optimal control theory and the GA is devised. The objective is to reproduce a signal that can follow closely the reference signal and avoid false motion cues by adjusting the parameters from the obtained LQR-based optimal washout filter. This is achieved by taking a series of factors into account, which include the vestibular sensation error between the real and simulated cases, the main dynamic limitations, the human threshold limiter in tilt coordination, the cross correlation coefficient, and the human sensation error fluctuation. It is worth pointing out that other related investigations in the literature normally do not consider the effects of these factors. The proposed optimized MCA based on the GA is implemented using the MATLAB/Simulink software. The results show the effectiveness of the proposed GA-based method in enhancing human sensation, maximizing the reference shape tracking, and reducing the workspace usage.

Boron carbide reinforced aluminium matrix composite : physical, mechanical characterization and mathematical modelling

This paper investigates the manufacturing of aluminium-boron carbide composites using the stir casting method. Mechanical and physical properties tests to obtain hardness, ultimate tensile strength (UTS) and density are performed after solidification of specimens. The results show that hardness and tensile strength of aluminium based composite are higher than monolithic metal. Increasing the volume fraction of B4C, enhances the tensile strength and hardness of the composite; however over-loading of B4C caused particle agglomeration, rejection from molten metal and migration to slag. This phenomenon decreases the tensile strength and hardness of the aluminium based composite samples cast at 800 °C. For Al-15 vol% B4C samples, the ultimate tensile strength and Vickers hardness of the samples that were cast at 1000 °C, are the highest among all composites. To predict the mechanical properties of aluminium matrix composites, two key prediction modelling methods including Neural Network learned by Levenberg-Marquardt Algorithm (NN-LMA) and Thin Plate Spline (TPS) models are constructed based on experimental data. Although the results revealed that both mathematical models of mechanical properties of Al-B4C are reliable with a high level of accuracy, the TPS models predict the hardness and tensile strength values with less error compared to NN-LMA models.