Spray drier simulation and air flow pattern studies

The literature pertaining to the key stages of spray drying has been reviewed in the context of the mathematical modelling of drier performance. A critical review is also presented of previous spray drying models. A new mathematical model has been developed for prediction of spray drier performance. This is applicable to slurries of rigid, porous crust-forming materials to predict trajectories and drying profiles for droplets with a distribution of sizes sprayed from a centrifugal pressure nozzle. The model has been validated by comparing model predictions to experimental data from a pilot-scale counter-current drier and from a full-scale co-current drier. For the latter, the computed product moisture content was within 2%, and the computed air exit temperature within 10oC of experimental data. Air flow patterns have been investigated in a 1.2m diameter transparent countercurrent spray tower by flow visualisation. Smoke was introduced into various zones within the tower to trace the direction, and gauge the intensity, of the air flow. By means of a set of variable-angle air inlet nozzles, a variety of air entry configurations was investigated. The existence of a core of high rotational and axial velocity channelling up the axis of the tower was confirmed. The stability of flow within the core was found to be strongly dependent upon the air entry arrangement. A probe was developed for the measurement of air temperature and humidity profiles. This was employed for studying evaporation of pure water drops in a 1.2m diameter pilot-scale counter-current drier. A rapid approach to the exit air properties was detected within a 1m distance from the air entry ports. Measured radial profiles were found to be virtually flat but, from the axial profiles, the existence of plug-flow, well-mixed-flow and some degree of air short-circuiting can be inferred. The model and conclusions should assist in the improved design and optimum operation of industrial spray driers.

Studies of solar radiation and its measurement

A mathematical model has been developed for predicting the spectral distribution of solar radiation incident on a horizontal surface. The solar spectrum in the wavelength range 0.29 to 4.0 micrometers has been divided in 144 intervals. Two variables in the model are the atmospheric water vapour content and atmospheric turbidity. After allowing for absorption and scattering in the atmosphere, the spectral intensity of direct and diffuse components of radiation are computed. When the predicted radiation levels are compared with the measured values for the total radiation and the values with glass filters RG715, RG630 and OG530, a close agreement (± 5%) has been achieved under clear sky conditions. A solar radiation measuring facility, close to the centre of Birmingham, has been set up utilising a microcomputer based data logging system. A suite of computer programs in the BASIC programming language has been developed and extensively tested for solar radiation data, logging, analysis and plotting. Two commonly used instruments, the Eppley PSP pyranometer and the Kipp and Zonen CM5 pyranometer, have been compared under different experimental conditions. Three models for computing the inclined plane irradiation, using total and diffuse radiation on a horizontal surface, have been tested for Birmingham. The anisotropic-alI-sky model, proposed by Klucher, provides a good agreement between the measured and the predicted radiation levels. Measurements of solar spectral distribution, using glass filters, are also reported for a number of inclines facing South.

The mathematical modelling of the environmental performance of buildings as an aid in the design process

This thesis is a theoretical study of the accuracy and usability of models that attempt to represent the environmental control system of buildings in order to improve environmental design. These models have evolved from crude representations of a building and its environment through to an accurate representation of the dynamic characteristics of the environmental stimuli on buildings. Each generation of models has had its own particular influence on built form. This thesis analyses the theory, structure and data of such models in terms of their accuracy of simulation and therefore their validity in influencing built form. The models are also analysed in terms of their compatability with the design process and hence their ability to aid designers. The conclusions are that such models are unlikely to improve environmental performance since: a the models can only be applied to a limited number of building types, b they can only be applied to a restricted number of the characteristics of a design, c they can only be employed after many major environmental decisions have been made, d the data used in models is inadequate and unrepresentative, e models do not account for occupant interaction in environmental control. It is argued that further improvements in the accuracy of simulation of environmental control will not significantly improve environmental design. This is based on the premise that strategic environmental decisions are made at the conceptual stages of design whereas models influence the detailed stages of design. It is hypothesised that if models are to improve environmental design it must be through the analysis of building typologies which provides a method of feedback between models and the conceptual stages of design. Field studies are presented to describe a method by which typologies can be analysed and a theoretical framework is described which provides a basis for further research into the implications of the morphology of buildings on environmental design.

Characterisation of electrospun polystyrene scaffolds for three-dimensional in vitro biological studies

The purpose of this study was to produce a well-characterised electrospun polystyrene scaffold which could be used routinely for three-dimensional (3D) cell culture experimentation. A linear relationship (p<0.01p<0.01) between three principal process variables (applied voltage, working distance and polymer concentration) and fibre diameter was reliably established enabling a mathematical model to be developed to standardise the electrospinning process. Surface chemistry and bulk architecture were manipulated to increase wetting and handling characteristics, respectively. X-ray photoelectron spectroscopy (XPS) confirmed the presence of oxygen-containing groups after argon plasma treatment, resulting in a similar surface chemistry to treated tissue culture plastic. The bulk architecture of the scaffolds was characterised by scanning electron microscopy (SEM) to assess the alignment of both random and aligned electrospun fibres, which were calculated to be 0.15 and 0.66, respectively. This compared to 0.51 for collagen fibres associated with native tissue. Tensile strength and strain of approximately of 0.15 MPa and 2.5%, respectively, allowed the scaffolds to be routinely handled for tissue culture purposes. The efficiency of attachment of smooth muscle cells to electrospun scaffolds was assessed using a modified 3-[4,5-dimethyl(thiazol-2yl)-3,5-diphery] tetrazolium bromide assay and cell morphology was assessed by phalloidin-FITC staining of F-actin. Argon plasma treatment of electrospun polystyrene scaffold resulted in significantly increased cell attachment (p<0.05p<0.05). The alignment factors of the actin filaments were 0.19 and 0.74 for the random and aligned scaffold respectively, compared to 0.51 for the native tissue. The data suggests that electrospinning of polystyrene generates 3D scaffolds which complement polystyrene used in 2D cell culture systems.

Differential effects of single -sex versus coed education on the mathematical reasoning ability, verbal reasoning ability, and self-concept of high school girls

This study explored the differential effects of single-sex versus coed education on the cognitive and affective development of young women in senior year of high school. The basic research question was: What are the differential effects of single-sex versus coed education on the development of mathematical reasoning ability, verbal reasoning ability, or self-concept of high school girls?^ This study was composed of two parts. In the first part, the SAT verbal and mathematical ability scores were recorded for those subjects in the two schools from which the sample populations were drawn. The second part of the study required the application of the Piers-Harris Children's Self-Concept Scale to subjects in each of the two sample populations. The sample schools were deliberately selected to minimize between group differences in the populations. One was an all girls school, the other coeducational.^ The research design employed in this study was the causal-comparative method, used to explore causal relationships between variables that already exist. Based on a comprehensive analysis of the data produced by this research, no significant difference was found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 verbal reasoning section. Nor was any significant difference found to exist between the mean scores of the senior girls in the single-sex school and the coed school on the SAT 1 mathematical reasoning section. Finally, no significant difference between the mean total scores of the senior girls in the single-sex school and the coed school on the Piers-Harris Children's Self-Concept Scale was found to exist.^ Contrary to what many other studies have found in the past about single-sex schools and their advantages for girls, this study found no support for such advantages in the cognitive areas of verbal and mathematical reasoning as measured by the SAT or in the affective area of self-concept as measured by the Piers-Harris Children's Self-Concept Scale. ^

Fundamental studies of the application of wheat for malting and brewing

Wheat (Triticum aestivum L.) has a long tradition as a raw material for the production of malt and beer. While breeding and cultivation efforts for barley have been highly successful in creating agronomically and brew- technical optimal specialty cultivars that have become well established as brewing barley varieties, the picture is completely different for brewing wheat. An increasing wheat beer demand results in a rising amount of raw material. Wheat has been - and still is – grown almost exclusively for the baking industry. It is this high demand that defines most of the wheat breeding objectives; and these objectives are generally not favourable in brewing industry. It is of major interest to screen wheat varieties for brewing processability and to give more focus to wheat as a brewing cereal. To obtain fast and reliable predications about the suitability of wheat cultivars a new mathematical method was developed in this work. The method allows a selection based on generally accepted quality characteristics. As selection criteria the parameters raw protein, soluble nitrogen, Kolbach index, extract and viscosity were chosen. During a triannual cultivation series, wheat varieties were evaluated on their suitability for brewing as well as stability to environmental conditions. To gain a fundamental understanding of the complex malting process, microstructural changes were evaluated and visualized by confocal laser scanning and scanning electron microscopy. Furthermore, changes observed in the micrographs were verified and endorsed by metabolic changes using established malt attributes. The degradation and formation of proteins during malting is essential for the final beer quality. To visualise fundamental protein changes taking place during malting, samples of each single process step were analysed and fractioned according their solubility. Protein fractions were analysed using a Lab-on-a-chip technique as well as OFFgel analysis. In general, a different protein distribution of wheat compared to barley or oat could be confirmed. During the malting process a degradation of proteins to small peptides and amino acids could be observed in all four Osborn fractions. Furthermore, in this study a protein profiling was performed to evaluate changes during the mashing process as well as the influence of grist composition. Differences in specific protein peaks and profile were detected for all samples during mashing. This study investigated the suitability of wheat for malting and brewing industry and closed the scientifical gap of amylolytic, cytolytic and proteolytic changes during malting and mashing.

Refractometry Studies of the Optical Properties of Polymer Films and the Development of Polymer Coated Refractive Index Sensors

Sensors for real-time monitoring of environmental contaminants are essential for protecting ecosystems and human health. Refractive index sensing is a non-selective technique that can be used to measure almost any analyte. Miniaturized refractive index sensors, such as silicon-on-insulator (SOI) microring resonators are one possible platform, but require coatings selective to the analytes of interest. A homemade prism refractometer is reported and used to characterize the interactions between polymer films and liquid or vapour-phase analytes. A camera was used to capture both Fresnel reflection and total internal reflection within the prism. For thin-films (d = 10 μm - 100 μm), interference fringes were also observed. Fourier analysis of the interferogram allowed for simultaneous extraction of the average refractive index and film thickness with accuracies of ∆n = 1-7 ×10-4 and ∆d < 3-5%. The refractive indices of 29 common organic solvents as well as aqueous solutions of sodium chloride, sucrose, ethylene glycol, glycerol, and dimethylsulfoxide were measured at λ = 1550 nm. These measurements will be useful for future calibrations of near-infrared refractive index sensors. A mathematical model is presented, where the concentration of analyte adsorbed in a film can be calculated from the refractive index and thickness changes during uptake. This model can be used with Fickian diffusion models to measure the diffusion coefficients through the bulk film and at the film-substrate interface. The diffusion of water and other organic solvents into SU-8 epoxy was explored using refractometry and the diffusion coefficient of water into SU-8 is presented. Exposure of soft baked SU-8 films to acetone, acetonitrile and methanol resulted in rapid delamination. The diffusion of volatile organic compound (VOC) vapours into polydimethylsiloxane and polydimethyl-co-polydiphenylsiloxane polymers was also studied using refractometry. Diffusion and partition coefficients are reported for several analytes. As a model system, polydimethyl-co-diphenylsiloxane films were coated onto SOI microring resonators. After the development of data acquisition software, coated devices were exposed to VOCs and the refractive index response was assessed. More studies with other polymers are required to test the viability of this platform for environmental sensing applications.

New methods for movement technique development in cross-country skiing using mathematical models and simulation

This Licentiate Thesis is devoted to the presentation and discussion of some new contributions in applied mathematics directed towards scientific computing in sports engineering. It considers inverse problems of biomechanical simulations with rigid body musculoskeletal systems especially in cross-country skiing. This is a contrast to the main research on cross-country skiing biomechanics, which is based mainly on experimental testing alone. The thesis consists of an introduction and five papers. The introduction motivates the context of the papers and puts them into a more general framework. Two papers (D and E) consider studies of real questions in cross-country skiing, which are modelled and simulated. The results give some interesting indications, concerning these challenging questions, which can be used as a basis for further research. However, the measurements are not accurate enough to give the final answers. Paper C is a simulation study which is more extensive than paper D and E, and is compared to electromyography measurements in the literature. Validation in biomechanical simulations is difficult and reducing mathematical errors is one way of reaching closer to more realistic results. Paper A examines well-posedness for forward dynamics with full muscle dynamics. Moreover, paper B is a technical report which describes the problem formulation and mathematical models and simulation from paper A in more detail. Our new modelling together with the simulations enable new possibilities. This is similar to simulations of applications in other engineering fields, and need in the same way be handled with care in order to achieve reliable results. The results in this thesis indicate that it can be very useful to use mathematical modelling and numerical simulations when describing cross-country skiing biomechanics. Hence, this thesis contributes to the possibility of beginning to use and develop such modelling and simulation techniques also in this context.

Moisture Desorption Studies on Polymer Hydrated and Vacuum Extruded Bentonite Clay Mat

Moisture desorption observations from two bentonite clay mats subjected to ten environmental zones with individually different combinations of laboratory-controlled constant temperatures (between 20 °C and 40 °C) and relative humidity (between 15% and 70%) are presented. These laboratory observations are compared with predictions from mathematical models, such as thin-layer drying equations and kinetic drying models proposed by Page, Wang and Singh, and Henderson and Pabis. The quality of fit of these models is assessed using standard error (SE) of estimate, relative percent of error, and coefficient of correlation. The Page model was found to better predict the drying kinetics of the bentonite clay mats for the simulated tropical climates. Critical study on the drying constant and moisture diffusion coefficient helps to assess the efficacy of a polymer to retain moisture and control desorption through water molecule bonding. This is further substantiated with the Guggenheim–Anderson–De Boer (GAB) desorption isotherm model which is presented.

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.

Mathematical pedagogical content knowledge in early childhood education: A study in initial teacher education in Portugal

The study aims to explore the specificity of mathematics Pedagogical Content Knowledge in Early Childhood Education Pedagogy. The pedagogy of ECE (Siraj-Blatchford, 2010) and the didactics of ECE (Pramling & Pramling-Samuelsson, 2011) suggest dimensions of knowledge that require strong content and PC knowledge of teachers. Recent studies about PCK of ECE teachers highlight similar specific dimensions: organization of educational environment and interactions with children (Lee, 2010, McCray, 2008, Rojas, 2008). The current framework for ECE Teacher Education in Portugal (since 2007) focuses both content knowledge and subject didactics. PCK has been labelled the 'great unknown' in ECE (Rojas, 2008) in traditions where the child's development is considered as the main knowledge base for ECE (Chen & McNamee, 2006, Cullen, 2005, Hedges & Cullen, 2005). We studied the perspectives of 27 initial teacher education students about knowledge for teaching and about ECE Pedagogy. We used one open-ended questionnaire and students' analysis of episodes focusing children's answers or discourse relevant for mathematics (about high numbers and square root). The questionnaire was anonymous and students’ permission to use the answers was obtained. In the questionnaire, interactions with children (62%) and organization of the educational environment (38%) are highlighted as the most important focus for the teacher. Students suggested tasks that were adult planned and oriented to further the situations presented in the episodes. Very few references to children's exploratory actions (Bonawitz et al., 2011) were made. The specificity of ECE (child initiated activities, e.g.) needs to be further developed in initial teacher education.

Modelling and studies of the spectral response of some optoelectronic components

Solar radiation takes in today's world, an increasing importance. Different devices are used to carry out spectral and integrated measurements of solar radiation. Thus the sensors can be divided into the fallow types: Calorimetric, Thermomechanical, Thermoelectric and Photoelectric. The first three categories are based on components converting the radiation to temperature (or heat) and then into electrical quantity. On the other hand, the photoelectric sensors are based on semiconductor or optoelectronic elements that when irradiated change their impedance or generate a measurable electric signal. The response function of the sensor element depends not only on the intensity of the radiation but also on its wavelengths. The radiation sensors most widely used fit in the first categories, but thanks to the reduction in manufacturing costs and to the increased integration of electronic systems, the use of the photoelectric-type sensors became more interesting. In this work we present a study of the behavior of different optoelectronic sensor elements. It is intended to verify the static response of the elements to the incident radiation. We study the optoelectronic elements using mathematical models that best fit their response as a function of wavelength. As an input to the model, the solar radiation values are generated with a radiative transfer model. We present a modeling of the spectral response sensors of other types in order to compare the behavior of optoelectronic elements with other sensors currently in use.