Density variation of different shaped food particulates in fluid bed drying : empirical models

Three particular geometrical shapes of parallelepiped, cylindrical and spheres were selected from potatoes (aspect ratio = 1:1, 2:1, 3:1), cut beans (length:diameter = 1:1, 2:1, 3:1) and peas respectively. The density variation of food particulates was studied in a batch fluidised bed dryer connected to a heat pump dehumidifier system. Apparent density and bulk density were evaluated with non-dimensional moisture at three different drying temperatures of 30, 40 and 50 o C. Relative humidity of hot air was kept at 15% in all drying temperatures. Several empirical relationships were developed for the determination of changes in densities with the moisture content. Simple mathematical models were obtained to relate apparent density and bulk density with moisture content.

Important omitted spatial variables in safety models: Understanding contributing crash causes at intersections

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causation—rests upon the pursuit of numerous lines of inquiry. The research community has focused on analytical methods development (negative binomial specifications, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might think of different lines of inquiry in terms of ‘low lying fruit’—areas of inquiry that might provide significant improvements in understanding crash causation. It is the contention of this research that omitted variable bias caused by the exclusion of important variables is an important line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant ability to better understand contributing factors to crashes. This study—believed to represent a unique contribution to the safety literature—develops and examines the role of a sizeable set of spatial variables in intersection crash occurrence. In addition to commonly considered traffic and geometric variables, examined spatial factors include local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools. The results indicate that inclusion of these factors results in significant improvement in model explanatory power, and the results also generally agree with expectation. The research illuminates the importance of spatial variables in safety research and also the negative consequences of their omissions.

Advanced mathematical modelling and experimental investigation of new torque arms for shaft-mounted drives

Shaft-mounted gearboxes are widely used in industry. The torque arm that holds the reactive torque on the housing of the gearbox, if properly positioned creates the reactive force that lifts the gearbox and unloads the bearings of the output shaft. The shortcoming of these torque arms is that if the gearbox is reversed the direction of the reactive force on the torque arm changes to opposite and added to the weight of the gearbox overloads the bearings shortening their operating life. In this paper, a new patented design of torque arms that develop a controlled lifting force and counteract the weight of the gearbox regardless of the direction of the output shaft rotation is described. Several mathematical models of the conventional and new torque arms were developed and verified experimentally on a specially built test rig that enables modelling of the radial compliance of the gearbox bearings and elastic elements of the torque arms. Comparison showed a good agreement between theoretical and experimental results.

Mathematical modelling of chronic wound healing

Chronicwounds fail to proceed through an orderly process to produce anatomic and functional integrity and are a significant socioeconomic problem. There is much debate about the best way to treat these wounds. In this thesis we review earlier mathematical models of angiogenesis and wound healing. Many of these models assume a chemotactic response of endothelial cells, the primary cell type involved in angiogenesis. Modelling this chemotactic response leads to a system of advection-dominated partial differential equations and we review numerical methods to solve these equations and argue that the finite volume method with flux limiting is best-suited to these problems. One treatment of chronic wounds that is shrouded with controversy is hyperbaric oxygen therapy (HBOT). There is currently no conclusive data showing that HBOT can assist chronic wound healing, but there has been some clinical success. In this thesis we use several mathematical models of wound healing to investigate the use of hyperbaric oxygen therapy to assist the healing process - a novel threespecies model and a more complex six-species model. The second model accounts formore of the biological phenomena but does not lend itself tomathematical analysis. Bothmodels are then used tomake predictions about the efficacy of hyperbaric oxygen therapy and the optimal treatment protocol. Based on our modelling, we are able to make several predictions including that intermittent HBOT will assist chronic wound healing while normobaric oxygen is ineffective in treating such wounds, treatment should continue until healing is complete and finding the right protocol for an individual patient is crucial if HBOT is to be effective. Analysis of the models allows us to derive constraints for the range of HBOT protocols that will stimulate healing, which enables us to predict which patients are more likely to have a positive response to HBOT and thus has the potential to assist in improving both the success rate and thus the cost-effectiveness of this therapy.

A framework for integrating disadvantaged analysis into transportation planning models

This research paper aims to develop a method to explore the travel behaviour differences between disadvantaged and non-disadvantaged populations. It also aims to develop a modelling approach or a framework to integrate disadvantage analysis into transportation planning models (TPMs). The methodology employed identifies significantly disadvantaged groups through a cluster analysis and the paper presents a disadvantage-integrated TPM. This model could be useful in determining areas with concentrated disadvantaged population and also developing and formulating relevant disadvantage sensitive policies. (a) For the covering entry of this conference, please see ITRD abstract no. E214666.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical VC dimension, empirical VC entropy, and margin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

Timing of births and endometrial cancer risk in Swedish women

While a protective long-term effect of parity on endometrial cancer risk is well established, the impact of timing of births is not fully understood. We examined the relationship between endometrial cancer risk and reproductive characteristics in a population-based cohort of 2,674,465 Swedish women, 20–72 years of age. During follow-up from 1973 through 2004, 7,386 endometrial cancers were observed. Compared to uniparous women, nulliparous women had a significantly elevated endometrial cancer risk (hazard ratio [HR] = 1.32, 95% confidence interval [CI], 1.22–1.42). Endometrial cancer risk decreased with increasing parity; compared to uniparous women, women with ≥4 births had a HR=0.66 (95% CI, 0.59–0.74); p-trend < 0.001. Among multiparous women, we observed no relationship of risk with age at first birth after adjustment for other reproductive factors. While we initially observed a decreased risk with later ages at last birth, this appeared to reflect a stronger relationship with time since last birth, with women with shorter times being at lowest risk. In models for multiparous women that included number of births, age at first and last birth, and time since last birth, age at last birth was not associated with endometrial cancer risk, while shorter time since last birth and increased parity were associated with statistically significantly reduced endometrial cancer risks. The HR was 3.95 (95%CI; 2.17–7.20; p-trend=<0.0001) for women with ≥25 years since a last birth compared to women having given birth within 4 years. Our findings support that clearance of initiated cells during delivery may be important in endometrial carcinogenesis. Keywords: endometrial carcinoma, parity, registry, reproductive factors

Numerical simulation of a fractional mathematical model for epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider numerical simulation of fractional model based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in advection and diffusion terms belong to the intervals (0; 1) or (1; 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of the Riemann-Liouville and Gr¨unwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Navigational Safety in Port Waters : Proactive Management of Collision Risk Using Traffic Conflicts

Traditionally navigational safety analyses rely on historical collision data which is often hampered because of low collision counts, insufficiency in explaining collision causation, and reactive approach to safety. A promising alternative approach that overcomes these problems is using navigational traffic conflicts or near-misses as an alternative to the collision data. This book discusses how traffic conflicts can effectively be used in modeling of port water collision risks. Techniques for measuring and predicting collision risks in fairways, intersections, and anchorages are discussed by utilizing advanced statistical models. Risk measurement models, which quantitatively measure collision risks in waterways, are discussed. To predict risks, a hierarchical statistical modeling technique is discussed which identifies the factors influencing the risks. The modeling techniques are illustrated for Singapore port data. Results showed that traffic conflicts are an ethically appealing alternative to collision data for fast, reliable and effective safety assessment, thus possessing great potential for managing collision risks in port waters.