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Bergman, Ärlebäck Jonas. "Mathematical modelling in upper secondary mathematics education in Sweden." Doctoral thesis, Linköpings universitet, Tillämpad matematik, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54318.
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The aim of this thesis is to investigate and enhance our understanding of the notions of mathematical models and modelling at the Swedish upper secondary school level. Focus is on how mathematical models and modelling are viewed by the different actors in the school system, and what characterises the collaborative process of a didactician and a group of teachers engaged in designing and developing, implementing and evaluating teaching modules (so called modelling modules) exposing students to mathematical modelling in line with the present mathematics curriculum. The thesis consists of five papers and reports, along with a summary introduction, addressing both theoretical and empirical aspects of mathematical modelling. The thesis uses both qualitative and quantitative methods and draws partly on design-based research methodology and cultural-historical activity theory (CHAT). The results of the thesis are presented using the structure of the three curriculum levels of the intended, potentially implemented, and attained curriculum respectively. The results show that since 1965 and to the present day, gradually more and more explicit emphasis has been put on mathematical models and modelling in the syllabuses at this school level. However, no explicit definitions of these notions are provided but described only implicitly, opening up for a diversity of interpretations. From the collaborative work case study it is concluded that the participating teachers could not express a clear conception of the notions mathematical models or modelling, that the designing process often was restrained by constraints originating from the local school context, and that working with modelling highlights many systemic tensions in the established school practice. In addition, meta-results in form of suggestions of how to resolve different kinds of tensions in order to improve the study design are reported. In a questionnaire study with 381 participating students it is concluded that only one out of four students stated that they had heard about or used mathematical models or modelling in their education before, and the expressed overall attitudes towards working with mathematical modelling as represented in the test items were negative. Students’ modelling proficiency was positively affected by the students’ grade, last taken mathematics course, and if they thought the problems in the tests were easy or interesting. In addition empirical findings indicate that so-called realistic Fermi problems given to students working in groups inherently evoke modelling activities.
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Cinquin, Olivier. "Mathematical modelling of development." Thesis, University College London (University of London), 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.424702.
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Chalmers, Alexander David. "Mathematical Modelling of Atherosclerosis." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14986.
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In atherosclerosis, the arterial lining undergoes a specific sequence of inflammatory responses to an injury to the cells that line the blood vessel and to low density lipoprotein (LDL) particles from the blood stream that penetrate through this injury into the arterial wall. We model the events that take place inside the blood vessel wall that occur immediately after such an injury with a system of partial differential equations that involve the LDL particles, two proinflammatory cytokines, monocyte-derived macrophages and their lipid-filled counterparts, foam cells. The model includes the chemical and physical interactions with the endothelial cells that line the arterial wall. These interactions are formulated as boundary conditions. Through numerical simulations, we show that different LDL concentrations in the blood stream and different immune responses can qualitatively affect the development of a plaque. Numerical bifurcation analysis at the quasi-steady state through AUTO shows that there exists of a fold bifurcation when the flux of LDL into the plaque from the blood is high. An atherosclerotic plaque that develops within the intima, deforms the intima locally as macrophages and foam cells accumulate. We model the structure of the developing plaque by cell pressure and cell sorting models to account for the limited space within the intima. We do this by modelling cell movement in crowded tissue in a discrete space and extend this to a spatial domain where cells also moves due to cell pressure and chemotaxis. We model the mechanics of the physical interactions on the two bounding interfaces, (the lumen-intima boundary and the intima-media boundary) and of the tissue inside the domain and add advective terms to ensure that the mechanics of the cellular species is consistent with the underlying tissue deformation. Using a finite element solver, we produce numerical results in one dimension across the intima and in two dimensions as a cross section of an artery. With appropriate parameter values, this moving boundary problem produces results in agreement with the current theory on compensatory enlargement in atherosclerotic remodelling
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Nurtay, Anel. "Mathematical modelling of pathogen specialisation." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/667178.
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L’aparició de nous virus causants de malalties està estretament lligada a l’especialització de subpoblacions virals cap a nous tipus d’amfitrions. La modelització matemàtica proporciona un marc quantitatiu que pot ajudar amb la predicció de processos a llarg termini com pot ser l’especialització. A causa de la naturalesa complexa que presenten les interaccions intra i interespecífiques en els processos evolutius, cal aplicar eines matemàtiques complexes, com ara l’anàlisi de bifurcacions, al estudiar dinàmiques de població. Aquesta tesi desenvolupa una jerarquia de models de població per poder comprendre l’aparició i les dinàmiques d’especialització, i la seva dependència dels paràmetres del sistema. Utilitzant un model per a un virus de tipus salvatge i un virus mutat que competeixen pel mateix amfitrió, es determinen les condicions per a la supervivència únicament de la subpoblació mutant, juntament amb la seva coexistència amb el cep de tipus salvatge. Els diagrames d’estabilitat que representen regions de dinàmiques diferenciades es construeixen en termes de taxa d’infecció, virulència i taxa de mutació; els diagrames s’expliquen en base a les característiques biològiques de les subpoblacions. Per a paràmetres variables, s’observa i es descriu el fenomen d’intersecció i intercanvi d’estabilitat entre diferents solucions sistemàtiques i periòdiques en l’àmbit dels ceps de tipus salvatge i els ceps mutants en competència directa. En el cas de que diversos tipus d’amfitrions estiguin disponibles per a ser disputats per ceps especialitzats i generalistes existeixen regions de biestabilitat, i les probabilitats d’observar cada estat es calculen com funcions de les taxes d’infecció. S’ha trobat un rar atractor caòtic i s’ha analitzat amb l’ús d’exponents de Lyapunov. Això, combinat amb els diagrames d’estabilitat, mostra que la supervivència del cep generalista en un entorn estable és un fet improbable. A més, s’estudia el cas dels diversos ceps N>>1 que competeixen per diferents tipus de cèl·lules amfitriones. En aquest cas s’ha descobert una dependència no monotònica, contraria al que es preveia, del temps d’especialització sobre la mida inicial i la taxa de mutació, com a conseqüència de la realització d’un anàlisi de regressió sobre dades obtingudes numèricament. En general, aquest treball fa contribucions àmplies a la modelització matemàtica i anàlisi de la dinàmica dels patogens i els processos evolutius.La aparición de nuevos virus causantes de enfermedades está estrechamente ligada a la especialización de las subpoblaciones virales hacia nuevos tipos de anfitriones. La modelizaci ón matemática proporciona un marco cuantitativo que puede ayudar a la predicción de procesos a largo plazo como la especialización. Debido a la naturaleza compleja que presentan las interacciones intra e interespecíficas en los procesos evolutivos, aplicar herramientas matemáticas complejas, tales como el análisis de bifurcación, al estudiar dinámicas de población. Esta tesis desarrolla una jerarquía de modelos de población para poder comprender la aparición y las dinámicas de especialización, y su dependencia de los parámetros del sistema. Utilizando un modelo para un virus de tipo salvaje y un virus mutado que compiten por el mismo anfitrión, se determinan las condiciones para la supervivencia únicamente de la subpoblación mutante, junto con su coexistencia con la cepa de tipo salvaje. Los diagramas de estabilidad que representan regiones de dinámicas diferenciadas se construyen en términos de tasa de infección, virulencia y tasa de mutación; los diagramas se explican en base a las características biológicas de las subpoblaciones. Para parámetros variables, se observa y se describe el fenómeno de intersección e intercambio de estabilidad entre diferentes soluciones sistemáticas y periódicas en el ámbito de las cepas de tipo salvaje y las cepas mutantes en competencia directa. En el caso de que varios tipos de anfitriones estén disponibles para ser disputados por cepas especializadas y generalistas existen regiones de biestabilidad, y las probabilidades de observar cada estado se calculan como funciones de las tasas de infección. Se ha encontrado un raro atractor caótico y se ha analizado con el uso de exponentes de Lyapunov. Esto, combinado con los diagramas de estabilidad, muestra que la supervivencia de la cepa generalista en un entorno estable es un hecho improbable. Además, se estudia el caso de los varias cepas N>> 1 que compiten por diferentes tipos de células anfitrionas. En este caso se ha descubierto una dependencia no monotónica, contraria a lo que se preveía, del tiempo de especialización sobre el tamaño inicial y la tasa de mutación, como consecuencia de la realización de un análisis de regresión sobre datos obtenidos numéricamente. En general, este trabajo hace contribuciones amplias a la modelización matemática y el análisis de la dinámica de los patógenos y los procesos evolutivos.
The occurrence of new disease-causing viruses is tightly linked to the specialisation of viral sub-populations towards new host types. Mathematical modelling provides a quantitative framework that can aid with the prediction of long-term processes such as specialisation. Due to the complex nature of intra- and interspecific interactions present in evolutionary processes, elaborate mathematical tools such as bifurcation analysis must be employed while studying population dynamics. In this thesis, a hierarchy of population models is developed to understand the onset and dynamics of specialisation and their dependence on the parameters of the system. Using a model for a wild-type and mutant virus that compete for the same host, conditions for the survival of only the mutant subpopulation, along with its coexistence with the wild-type strain, are determined. Stability diagrams that depict regions of distinct dynamics are constructed in terms of infection rates, virulence and the mutation rate; the diagrams are explained in terms of the biological characteristics of the sub-populations. For varying parameters, the phenomenon of intersection and exchange of stability between different periodic solutions of the system is observed and described in the scope of the competing wild-type and mutant strains. In the case of several types of hosts being available for competing specialist and generalist strains, regions of bistability exist, and the probabilities of observing each state are calculated as functions of the infection rates. A strange chaotic attractor is discovered and analysed with the use of Lyapunov exponents. This, combined with the stability diagrams, shows that the survival of the generalist in a stable environment is an unlikely event. Furthermore, the case of N=1 different strains competing for different types of host cells is studied. For this case, a counterintuitive and non-monotonic dependence of the specialisation time on the burst size and mutation rate is discovered as a result of carrying out a regression analysis on numerically obtained data. Overall, this work makes broad contributions to mathematical modelling and analysis of pathogen dynamics and evolutionary processes.
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Tacon, Geoffrey Reginald Russell. "Mathematical modelling of liver kinetics /." [St. Lucia, Qld.], 2005. http://www.library.uq.edu.au/pdfserve.php?image=thesisabs/absthe19399.pdf.
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Du, Peng 1985. "Mathematical modelling of gastric electrophysiology." Thesis, University of Auckland, 2011. http://hdl.handle.net/2292/10234.
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This thesis investigates the electrophysiology of the stomach, using a joint experimental and mathematical modelling approach. Normal gastrointestinal (GI) motility is coordinated by multiple cooperating mechanisms, both intrinsic and extrinsic to the GI tract. A fundamental component of the GI motility is an omnipresent electrical activity termed slow waves, which are initiated and propagated by the interstitial cells of Cajal (ICCs) and smooth muscle cells (SMCs). The role of ICC and/or SMC pathophysiology in GI motility disorders is an area of on-going research. This thesis begins with an overview of the functions of the GI tract and slow wave electrophysiology. High-resolution electrode arrays were designed and manufactured using the printed-circuit-board (PCB) technology. The performance of the PCB electrodes were validated against the performance of epoxy-embedded electrodes in porcine subjects, in terms of amplitudes (0.17 vs 0.52 mV), velocity (15.9 vs 13.8 mms-1), and signal-to-noise ratio (9.7 vs 18.7 dB). The PCB electrodes were then used to record gastric slow waves from a number of human subjects. Automatic slow wave activation times identification and velocity calculation techniques were applied to analyse the recorded slow wave data. Analysis of the human data revealed that the gastric slow wave activity originates from a pacemaker region (average amplitude: 0.57 mV ; average velocity: 8.0 mms-1) in the stomach, and continues into the corpus (average amplitude: 0.25 mV ; average velocity: 3.0 mms-1), and then the antrum (average amplitude: 0.52 mV ; average velocity: 5.7 mms-1). The focus of this thesis then shifts to mathematical models of slow wave activity. An existing SMC model was adapted to investigate the effects of gastric electrical stimulation (GES) protocols, in conjunction with experimental recordings in rat antral SMCs. The simulations using the adapted SMC model showed that effective GES protocols could be adapted to include frequency-trains (40 Hz) of short pulse- width (3-6 ms); In a separate study, an existing ICC model was adapted to include a voltage-sensitive inositol 1,4,5-trisphosphate receptor model, which modelled entrainment of slow waves in a network of ICCs; Two coupling mechanisms were also proposed to link the slow waves in the ICC and SMC models. A continuum approach was used to model slow waves in tissue and whole-organ models. The monodomain equation was used to simulate slow wave propagation in a grid of SMCs coupled to a cell automata model, which was used to quantify the entrainment of normal slow wave activity and entrainment of slow waves by a 3.5 cpm GES protocol. The simulation results demonstrated the highest 'zone of entrainment' that could be achieved by the GES protocol was 78% of the modelled tissue area; Next, the bidomain equations were applied to simulate entrainment of slow waves in a wild-type (normal) and a degraded (serotonin receptor knockout) ICC networks obtained from mouse tissue. The ICC network models demonstrated that slow wave propagation was influenced by ICC loss. In addition, compared to the degraded ICC network, the normal ICC network model demonstrated a higher peak current density (1.94 vs 1.45 μAmm-2) as well as [Ca2+]i density (0.67 vs 0.41 mM mm-2), which could help to explain functional impairments that arise when ICC populations are depleted; The human recordings were used to create slow wave activation in a whole organ stomach model. The whole organ model was used as a platform to simulate gastric slow wave propagation, as well as to incorporate physiological characteristics that could not directly measured using the HR technique, such as the variation in the resting membrane potentials of gastric tissues. The final set of modelling studies employed the forward modelling technique to simulate the resultant body surface potential, i.e., electrogastrogram (EGG) of gastric slow waves. A virtual EGG analysis showed that the frequency of EGG matched the underlying slow waves (3 cpm) and the peak potential (-0.63 mV ) in the EGG signal could be correlated to the timing of the full antral activation. This thesis concludes with a discussion on the results and potential future research directions in this field.
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Memon, Sohail Ahmed. "Mathematical modelling of complex dynamics." Thesis, University of Central Lancashire, 2017. http://clok.uclan.ac.uk/20497/.
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Soft materials have a wide range of applications, which include the production of masks for nano–lithography, the separation of membranes with nano–pores, and the preparation of nano–size structures for electronic devices. Self–organization in soft matter is a primary mechanism for the formation of structure. Block copolymers are long chain molecules composed of several different polymer blocks covalently bonded into a single macromolecule, which belong to an important class of soft materials which can self–assemble into different nano–structures due to their natural ability to microphase separate. Experimental and theoretical studies of block copolymers are quite challenging and, without computer simulations, it is difficult and problematic to analyse modern experiments. The Cell Dynamics Simulation (CDS) technique is a fast and accurate computational technique, which has been used to investigate block copolymers. The stability has been analysed by making use of different discrete Laplacian operators using well–chosen time steps in CDS. This analysis offers stability conditions for phase–field, based on the Cahn–Hilliard Cook (CHC) equations of which CDS is the finite difference approximation. To overcome grid related artefacts (discretization errors) in the computational grid, the study has been done for employing an isotropic Laplacian operator in the CDS framework. Several 2D and 3D discrete Laplacians have been quantitatively compared for their isotropy. The novel 2D 9–point BV(D2Q9) isotropic stencil operators have been derived from the B.A.C. van Vlimmeren method and their isotropy measure has been determined optimally better than other exiting 2D 9–point discrete Laplacian operators. Overall, the stencils in 9–point family Laplacians in 2D and the 19–point stencil operators in 3D have been found to be optimal in terms of isotropy and time step stability. Considerable implementation of Laplacians with good isotropy has played an important role in achieving a proper structure factor in modelling methods of block copolymers. The novel models have been developed by implementing CDS via more stable implicit methods, including backward Euler, Crank–Nicolson (CN) and Alternating Direction Implicit (ADI) methods. The CN scheme were implemented for both one order and two order parameter systems in CDS and successful results were obtained compared to forward Euler method. Due to the implementation of implicit methods, the CDS has achieved second–order accuracy both in time and space and it has become stronger, robust and more stable technique for simulation of the phase–separation phenomena in soft materials.
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Abdullah, Zia. "Mathematical modelling of casting processes." Thesis, University of Ottawa (Canada), 1988. http://hdl.handle.net/10393/21048.
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MacDonald, Grant. "Mathematical modelling of semiconductor photocatalysis." Thesis, University of Strathclyde, 2016. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=27029.
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Semiconductor photocatalysis can be extremely effective in the complete mineralisation of hundreds of organic materials and has been utilised in various different commercial systems, for example, self-cleaning glass, purification of water, the purification of air, sterilisation/disinfection and detecting oxygen in food packaging. The aim of this thesis is to further the understanding of semiconductor photocatalysis using mathematical models. One of the main issues considered is the applicability of assuming that reaction intermediates remain in a steady-state throughout the majority of any reactions taking place. We show that this assumption is not always valid. First, we consider an intelligent ink that is used to test the effectiveness of self-cleaning glass. The system is modelled by a diffusion equation for the transport of dye molecules in the film coupled to an ordinary differential equation describing the photocatalytic reaction taking place at the glass surface. A finite difference method is introduced to solve the equations arising from the model. We are able to show that the proposed model can replicate experimental results well. The model also offers an explanation as to why the initial reaction rate is dependant on film thickness for several different reaction regimes considered. Second, we consider models motivated by systems where photocatalytic reactions take place throughout the domain as opposed to exclusively at domain boundaries. We present a numerical method to solve such systems, and based on informal experimental results, explain the reasons behind the initial reaction rate being dependent on the size of the domain. Third, we consider four previously published models based on the removal of organic pollutants using semiconductor photocatalysis. We introduce more general mathematical models and demonstrate that by doing so there are a wider rangeof systems that the models can be applied to. One model involves an expanding domain and we present a moving mesh finite difference method that is used to solve such systems. Fourth, we propose a moving mesh finite element method for coupled bulk-surface problems in two-dimensional time-dependant domains. These problems are motivated by a system where semiconductor photocatalysis is used to destroy organic dirt across a domain which is increasing in size. Finally, we show how to determine the colour of a substance based on its absorbance spectrum. By comparing predictions made from experimental data to published photographs we are able to demonstrate that we can accurately predict the colour of a substance.
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Kura, K. "Mathematical modelling of dominance hierarchies." Thesis, City, University of London, 2016. http://openaccess.city.ac.uk/15838/.
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In this research we analyse the formation of dominance hierarchies from different viewpoints and various models of dominance hierarchy formation have been proposed, one important class being winner--loser models and another being Swiss tournaments. We start by understanding the structure of hierarchies emerging under the influence of winner and loser effects and two situations are considered: (i) when each individual has the same, fixed (unchanged) aggression threshold, meaning that all of them use the same rule when deciding whether to fight or retreat, and (ii) when individuals select an aggression threshold comparing their own and their opponent's abilities, and fighting if and only if the situation is sufficiently favourable to themselves. For both situations, we investigate if we can achieve hierarchy linearity, and if so, when it is established. We are particularly interested in the question of how many fights are necessary to establish dominance hierarchy. To examine these questions we use existing and new statistical measures. Besides understanding the structure and the temporal dynamic of the hierarchy formation, we also analyse the effect of the information that each individual has about the strength of their opponents on linearity. For the second situation, where individuals choose different aggression threshold, we find the appropriate level of aggression and examine the conditions when an individual needs to be more aggressive and when not. Lastly, we develop a model which allows only the individuals with the same number of wins and losses to fight each other. We show that linear hierarchies are always established. A formula for the total number of fights is derived, and the effect of group size on the level of aggressiveness is analysed.
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Caunce, James Frederick Physical Environmental & Mathematical Sciences Australian Defence Force Academy UNSW. "Mathematical modelling of wool scouring." Awarded by:University of New South Wales - Australian Defence Force Academy. School of Physical, Environmental and Mathematical Sciences, 2007. http://handle.unsw.edu.au/1959.4/38650.
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Wool scouring is the first stage of wool processing, where unwanted contaminants are removed from freshly shorn wool. In most scouring machines wool is fed as a continuous mat through a series of water-filled scour and rinse bowls which are periodically drained. The purpose of this project is to mathematically model the scour bowl with the aim of improving efficiency. In this thesis four novel models of contaminant concentration within a scour bowl are developed. These are used to investigate the relationships between the operating parameters of the machine and the concentration of contamination within the scour bowl. The models use the advection-diffusion equation to simulate the settling and mixing of contamination. In the first model considered here, the scour bowl is simulated numerically using finite difference methods. Previous models of the scouring process only considered the average steady-state concentration of contamination within the entire scour bowl. This is the first wool scouring model to look at the bowl in two dimensions and to give time dependent results, hence allowing the effect of different drainage patterns to be studied. The second model looks at the important region at the top of the bowl - where the wool and water mix. The governing equations are solved analytically by averaging the concentration vertically assuming the wool layer is thin. Asymptotic analysis on this model reveals some of the fundamental behaviour of the system. The third model considers the same region by solving the governing equations through separation of variables. A fourth, fully two-dimensional, time dependent model was developed and solved using a finite element method. A model of the swelling of grease on the wool fibres is also considered since some grease can only be removed from the fibre once swollen. The swelling is modelled as a Stefan problem, a nonlinear diffusion equation with two moving boundaries, in cylindrical coordinates. Both approximate, analytical and a numerical solutions are found.
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Zhong, Guisong 1961. "Mathematical modelling of Osprey process." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=99554.
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Osprey process is a new kind of metal forming technology. In this process, a stream of liquid metal is atomized into a spray of molten droplets by a high velocity inert gas jet. The atomized droplets are accelerated towards a substrate of suitable shape and size. At the same time, they are rapidly cooled by the surrounding relatively cold gas and thereby partly solidified. After a certain flight distance, the droplets impinge on the cold substrate, and solidification continuous on the substrate. Near-net shaped products can be manufactured by this process.In this study, a simple mathematical model is established to describe the atomizing gas velocity profile and the velocity, thermal and solidification profiles of rapidly cooled metal droplets of different sizes during the in flight droplet-gas interaction. Given the relevant spray parameters, the model allows to predict quickly the transient droplet velocity, temperature, and solid fraction contents of individual droplets at various spray distances from the substrate. This model can be used to ascertain the suitability of the nozzle-substrate distance in Osprey process. The developed mathematical model has been used to predict thermal history and solidification behavior of atomized droplets of gamma-TiAl alloy. The model predicts undercooling, nucleation temperature, nucleation position and the extent of solidification of the in flight droplets of sizes ranging from 20 mum to 500 mum.
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Duursma, Gail Rene. "Mathematical modelling of fluidization phenomena." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305995.
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Qi, Qi. "Mathematical modelling of telomere dynamics." Thesis, University of Nottingham, 2011. http://eprints.nottingham.ac.uk/12258/.
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Telomeres are repetitive elements of DNA which are located at the ends of chromosomes. During cell division, telomeres on daughter chromomeres shorten until the telomere length falls below a critical level. This shortening restricts the number of cell divisions. In this thesis, we use mathematical modelling to study dynamics of telomere length in a cell in order to understand normal ageing (telomere shortening),Werner’s syndrome (a disease of accelerated ageing) and the immortality of cells caused by telomerase (telomere constant length maintenance). In the mathematical models we compared four possible mechanisms for telomere shortening. The simplest model assumes that a fixed amount of telomere is lost on each replication; the second supposes that telomere loss depends on telomere length; for the third case the amount of telomeres loss per division is fixed but the probability of dividing depends on telomere length; the fourth cases has both telomere loss and the probability of division dependent on telomere length. We start by developing Monte Carlo simulations of normal ageing using these four cases. Then we generalize the Monte Carlo simulations to consider Werner’s syndrome, where the extra telomeres are lost during replication accelerate the ageing process. In order to investigate how the distribution of telomere length varies with time, we derive, from the discrete model, continuum models for the four different cases. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. In addition to telomere loss, we also consider increases in telomere length caused by the enzyme telomerase, by appropriately extending the earlier Monte Carlo simulations and continuum models. Results from the Monte Carlo simulations and the deterministic models are shown to be in good agreement. We also show that the concentration of telomerase in cells can control their proliferative potential.
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Li, Beibei. "Mathematical modelling of aortic dissection." Thesis, University of Glasgow, 2013. http://theses.gla.ac.uk/3968/.
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An aortic dissection is a tear of the intima of the aortic wall that spreads into the media or between the media and adventitia. In addition to the original lumen for blood flow, the dissection creates a new flow channel, the `false' lumen that may cause the artery to narrow or even close over entirely. Aortic dissection is a medical emergency and can quickly lead to death. The mechanical property of the aorta has been described by the strain energy function given by Holzapfel et al. [2000]. The aorta is idealized as an elastic axisymmetric thickwalled tube with 3 layers. We focus on the dissection in media, which is considered as a composite reinforced by two families of fibres. We assume the dissection in the media is axisymmetric. The mathematical model for the dissection is presented. The 2D plane crack problem in linear elastic infinity plane and 2D strip, the axisymmetric crack problem in linear elastic compressible and incompressible tube, the axisymmetric crack problem in an incompressible axisymmetric aorta are applied to obtain solutions to three different problems. And the fluid flow inside the crack has been studied. The 2D plane crack problem in linear elastic infinity plane has been solved analytically. The 2D plane crack problem in linear elastic compressible and incompressible strip is modelled respectively and solved numerically. The models for axisymmetric crack problem in linear elastic compressible and incompressible tube are presented respectively. The numerical solutions for the crack problems are expressed, and the results are analyzed. The mathematical model of the incompressible aorta axisymmetric dissection is given, and the solutions are found numerically. The results change along with the different parameters in the strain energy function, which are analyzed and compared. The fluid flow inside the tear is assumed very thin which is expressed as the lubrication theory. We use the implicit method to model the Stokes equation numerically, and test the crack opening change along with time.
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Parsons, Mark. "Mathematical modelling of evolving networks." Thesis, University of Reading, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.590673.
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Network theory is a long standing, rapidly changing and highly motivated field. However, historically its results have been centred on static networks, leaving the area of evolving networks relatively less explored. In this thesis we draw from those existing results and extend them to the case of evolving networks to develop new analytical tools and representations. We do this through the introduction of an importance, or activity, metric for evolving networks, and the creation of a general framework for their models, allowing us to easily define, represent and classify them. We identify observable network properties and seek to predict the long term network structure of these modelled evolving networks. We find that networks can have a wide range of equilibria, even within the same model, from those devoid of network activity, to those exhibiting quasi-periodic network structure. These different equilibria within models are found to arise from chosen parameter values, highlighting the importance of their estimation. The properties upon which these models are based are often neglected for simplicity, however the application of our models to existing data proves their existence, and the significant variety of equilibria between network models shows us how important these properties are.
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Dyson, Rosemary. "Mathematical Modelling of Curtain Coating." Thesis, University of Oxford, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.489434.
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Harris, John Richard. "Mathematical modelling of mechanical alloying." Thesis, University of Nottingham, 2002. http://eprints.nottingham.ac.uk/10018/.
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This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignoring mixing phenomena. A methodology is developed that allows experimentally measured sieve-fractions to be converted into volumetric cluster size distributions. Model parameters describing the rate of aggregation and fragmentation are obtained by fitting the model's predicted average particle size data over time to that measured in experiments. Different size-dependent aggregation and fragmentation rates are tested in many milling scenarios and the most realistic size-dependence of rates is found. In the second part of the thesis, the best size-dependent rates are generalised and used with a two-component version of \Smol's system of equations. This model also includes binary mixing phenomena by considering clusters that have two types of component. The two-component models are applied to experimental situations using the methods developed for one-component models. Comparing these multi-component models to experimental measurements verifies the modelling method and gives reasonable agreement. An improved fragmentation rate is suggested to enhance the model's accuracy in the prediction of mixing rates.
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Cocks, David. "Mathematical modelling of dune formation." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442818.
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This study is concerned with the mathematical modelling of the formation and subsequent evolution of sand dunes, both beneath rivers (fluvial) and in deserts (Aeolian). Dunes are observed in the environment in many different shapes and sizes; we begin by discussing qualitatively how and why the different forms exist. The most important aspect of a successful model is the relationship between the bed shape and the shear stress that the flow exerts on the bed. We first discuss a simple model for this stress applied to fluvial dunes, which is able to predict dune-like structures, but does not predict the instability of a flat bed which we would hope to find. We therefore go on to look at improved models for the shear stress based on theories of turbulent flow and asymptotic methods, using assumptions of either a constant eddy viscosity or a mixing length model for turbulence. Using these forms for the shear stress, along with sediment transport laws, we obtain partial integrodifferential equations for the evolution of the bed, and we study these numerically using spectral methods. One important feature of dunes which is not taken into account by the above models is that of the slip face - a region of constant slope on the downwind side of the dune. When a slip face is present, there is a discontinuity in the slope of the bed, and hence it is clear that flow separation will occur. Previous studies have modelled separated flow by heuristically describing the boundary of the separated region with a cubic or quintic polynomial which joins smoothly to the bed at each end. We recreate this polynomial form for the wake profile and demonstrate a method for including it into an evolution system for dunes. The resulting solutions show an isolated steady-state dune which propagates downstream. From the asymptotic framework developed earlier with a mixing length model for turbulence, we are able, using techniques of complex analysis, to model the shape of the wake region from a purely theoretical basis, rather than the heuristic one used previously. We obtain a Riemann-Hilbert problem for the wake profile, which can be solved using well-known techniques. We then use this method to calculate numerically the wake profile corresponding to a number of dune profiles. Further, we are able to find an exact solution to the wake profile problem in the case of a sinusoidally shaped dune with a slip face. Having found a method to calculate the shear stress exerted on the dune from the bed profile in the case of separated flow, we then use this improved estimate of the shear stress in an evolution system as before. In order to do this efficiently, we consider an alternative method for calculating the wake profile based on the spectral method used for solving the evolution system. We find that this system permits solutions describing an isolated dune with a slip face which propagates downstream without changing shape. All of the models described above are implemented in two spatial dimensions; the wind is assumed to blow in one direction only, and the dunes are assumed to be uniform in a direction perpendicular to the wind flow. While this is adequate to explain the behaviour of transverse dunes, other dune shapes such as linear dunes, barchans, and star dunes are by nature three-dimensional, so in order to study the behaviour of such dunes, the extension of the models to three dimensions is essential. While most of the governing equations generalize easily, it is less obvious how to extend the model for separated flow, due to its reliance on complex variables. We implement some three-dimensional evolution models, and discuss the possibility of modelling three-dimensional flow separation.
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Ahmad, Mohammad Najeeb. "Mathematical modelling of fermentation systems." Thesis, Queen's University Belfast, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296797.
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Woodroffe, P. J. "Mathematical modelling of cell signalling." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.416886.
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Clark, John Malcolm. "Mathematical modelling of G.F.M. forging." Thesis, University of Sheffield, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.266125.
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Daae, Elisabeth Bull. "Mathematical modelling of biochemical pathways." Thesis, University College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327023.
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Gorrod, Martin John. "Mathematical modelling of Be stars." Thesis, University of Southampton, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385099.
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Rata, Scott. "Mathematical modelling of mitotic controls." Thesis, University of Oxford, 2018. https://ora.ox.ac.uk/objects/uuid:7bef862c-2025-4494-a2bb-4fe93584d92a.
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The mitotic cell cycle is fundamental to eukaryotic life. In mitosis, replicated chromosomes are segregated to form two new nuclei. This is essential to ensure the maintenance of chromosome number between parent and daughter cells. In higher eukaryotes, numerous cytological changes occur to facilitate the separation of the genetic material: the nuclear envelope breaks down, the mitotic spindle assembles, and the cell rounds-up. There is a well-conserved control network that regulates these processes to bring about the entry into mitosis, the separation of the genetic material, and the reversal of these processes during mitotic exit. To build a coherent model of these regulatory networks requires us to write the biochemical reactions in mathematical form. The work in this Thesis pertains to three fundamental switches: entry into mitosis, the metaphase-to-anaphase transition, and exit from mitosis. I present three studies from a systems-level perspective. The first investigates a novel bistable mechanism controlling mitotic entry/exit in vitro using purified proteins. Dephosphorylation of Greatwall kinase by the phosphatase PP2A-B55 creates a double negative feedback loop that gives a bistable system response with respect to cyclin-dependent kinase 1 (Cdk1) activity. The second looks at hysteresis between mitotic entry and mitotic exit in HeLa cells. Hysteresis persists when either of the regulatory loops of Cdk1 or its counter-acting phosphatase PP2A-B55 is removed, but is diminished when they are both removed. Finally, the regulation of separase in the metaphase-to-anaphase transition is analysed. Separase that is liberated from securin inhibition is isomerised by Pin1 into a conformation that can bind to cyclin B1. This binding peaks after separase has cleaved cohesin and initiated anaphase.
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Prieto, Curiel Rafael. "Mathematical modelling of social systems." Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10057708/.
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Mobility and migration patterns, the concentration of crime and opinion dynamics observed on the fear of crime are all examples of social systems in which complex patterns emerge that subsequently feed back into the overall system. This thesis describes new methods established to analyse such patterns which appear in social systems. The main application area is in the field of crime science, but the methods developed here have wider applications within other social systems, some of which are also explored in the thesis, such as migration or road accidents. Based on new assessments of data, by utilising novel techniques of analysis and visualisation, models are also developed to determine how the perception of security is affected by particular crimes. The new metrics and models developed here consider different types of situation. Firstly, for events which have low frequency and yet a high degree of concentration; secondly, the distribution of such events which allows them to be simulated under different conditions; and then finally, understanding the impact of different degrees of concentration. An individual's fear of crime is the result of a mixture of factors which go beyond merely the actual crime experienced by that person, such as fear shared by others, memory of past events and of previous perceptions, crime reported in the media and more. This thesis quantifies fear of crime in a way that may prove useful to identify factors which increase fear of crime besides crime itself, explain why fear of crime emerges in a population and suggests policies for controlling fear.
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Grandjean, Thomas R. B. "Mathematical modelling of transporter kinetics." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/61779/.
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Membrane transport proteins have recently been discovered to be ubiquitously expressed in the human body and of paramount importance in cellular uptake. Since all pharmaceutical compounds must pass through numerous cell membranes to travel and be absorbed by their target cells in order to achieve their desired therapeutic effects, transporters have attracted a lot of attention as a research field. As an emerging focus area, the precise mechanism of action of many of these transporters remains to be fully elucidated. In order to gain a detailed insight into these processes it is proposed to carry out mechanistic modelling of the pharmacokinetics of transporters. This thesis details the models developed to further our understanding of carrier mediated transport. The current knowledge on cellular uptake and efflux are discussed and mathematical models are developed for two prominent transporters. Structural identifiability and indistinguishability analyses are performed on all the models developed using a variety of methods to investigate the applicability of each method. Model fits gave very good agreement with in vitro data provided by AstraZeneca across a variety of experimental scenarios and different species. Mechanistic models for in vivo applications are also developed and found to characterise hepatic uptake in rat accurately. Recommendations for further work to fully validate the models developed so that they can perform robust, predictive simulations are proposed. The research in this thesis demonstrates that mechanistic modelling of complex biological processes allows for greater understanding of such systems.
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Shabala, Alexander. "Mathematical modelling of oncolytic virotherapy." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:cca2c9bc-cbd4-4651-9b59-8a4dea7245d1.
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This thesis is concerned with mathematical modelling of oncolytic virotherapy: the use of genetically modified viruses to selectively spread, replicate and destroy cancerous cells in solid tumours. Traditional spatially-dependent modelling approaches have previously assumed that virus spread is due to viral diffusion in solid tumours, and also neglect the time delay introduced by the lytic cycle for viral replication within host cells. A deterministic, age-structured reaction-diffusion model is developed for the spatially-dependent interactions of uninfected cells, infected cells and virus particles, with the spread of virus particles facilitated by infected cell motility and delay. Evidence of travelling wave behaviour is shown, and an asymptotic approximation for the wave speed is derived as a function of key parameters. Next, the same physical assumptions as in the continuum model are used to develop an equivalent discrete, probabilistic model for that is valid in the limit of low particle concentrations. This mesoscopic, compartment-based model is then validated against known test cases, and it is shown that the localised nature of infected cell bursts leads to inconsistencies between the discrete and continuum models. The qualitative behaviour of this stochastic model is then analysed for a range of key experimentally-controllable parameters. Two-dimensional simulations of in vivo and in vitro therapies are then analysed to determine the effects of virus burst size, length of lytic cycle, infected cell motility, and initial viral distribution on the wave speed, consistency of results and overall success of therapy. Finally, the experimental difficulty of measuring the effective motility of cells is addressed by considering effective medium approximations of diffusion through heterogeneous tumours. Considering an idealised tumour consisting of periodic obstacles in free space, a two-scale homogenisation technique is used to show the effects of obstacle shape on the effective diffusivity. A novel method for calculating the effective continuum behaviour of random walks on lattices is then developed for the limiting case where microscopic interactions are discrete.
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Fay, Gemma Louise. "Mathematical modelling of turbidity currents." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:62bb9382-1c50-47f3-8f59-66924cc31760.
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Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.
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Krupp, Armin Ulrich. "Mathematical modelling of membrane filtration." Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:ae6dd9e4-a862-4476-a8d9-35156848297f.
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In this thesis, we consider four different problems in membrane filtration, using a different mathematical approach in each instance. We account for the fluid-driven deformation of a filtercake using nonlinear poroelasticity in Chapter 2. By considering feeds with very high and very low particle concentrations, we introduce a quasi-static caking model that provides a suitable approximation to the full model for the physically realistic concentration regimes. We illustrate the agreements and differences between our model and the existing conventional cake-filtration law. In Chapter 3, we introduce a stochastic model for membrane filtration based on the quantised nature of the particles and show how it can be applied for feeds with different particle types and membranes with an interconnected pore structure. This allows us to understand the relation between the effects of clogging on the level of an individual pore and on the macroscopic level of the entire membrane. We conclude by explaining the transition between the discrete and continuous model based on the Fokker--Planck equation. In Chapter 4, we consider the inverse problem of determining the underlying filtration law from the spreading speed of a particle-laden gravity current. We first couple the theory of gravity currents with the stochastic model developed in Chapter~3 to determine a filtration law from a given set of experiments. We then generalise this idea for the porous medium equation, where we show that the position of the front follows a power law for the conventional filtration laws, which allows us to infer the clogging law in certain instances. We conclude the thesis by showing in Chapter 5 how we can combine experimental measurements for the clogging of a depth filter and simple fluid dynamics to accurately predict the pressure distribution in a multi-capsule depth filter during a filtration run.
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Evans, Matthew. "Mathematical modelling of calcium signalling." Thesis, University of East Anglia, 2017. https://ueaeprints.uea.ac.uk/63285/.
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Calcium (Ca2+) plays an integral role in a vast array of signalling pathways within both animals and plants. The study of these pathways has proven to be a fruitful avenue of research for experimental biologists and mathematical modellers. While the signalling processes have been well studied in animals, the same cannot be said of plants. This work takes a mathematical look at two important Ca2+ signalling pathways in plants, with a focus on how these signals are generated. Nuclear Ca2+ oscillations in legumes occur at a key step in the development of symbioses. The oscillations occur both inside the nucleus and in the perinuclear cytoplasm, and are temporally coordinated. We present and develop a model for simulating diffusion on the surface of the nucleus and relate the properties of this signalling to behaviour in the bulk. We show that diffusion of Ca2+ through the nuclear pore complexes provides a possible mechanism for this coordination and that this mechanism is robust to differences in Ca2+ diffusion rates in the two compartments or to different numbers of Ca2+ channels. Ca2+ has also been seen to propagate a wave travelling systemically through the root in response to salt stress. This wave is essential to the transcription of stress response genes in the leaves. We examine a range of di�erent models for propagation of the wave, demonstrating that a combined reactive oxygen species (ROS) and Ca2+ wave cooperatively propagate the signal. The presence of this accompanying ROS wave was confirmed in experiments by our collaborators. The present study highlights two very different Ca2+ signals and demonstrates the value of mathematical modelling for interpreting, understanding and furthering experimental investigations.
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Evans, Thomas W. "Mathematical modelling of phage dynamics." Thesis, University of Liverpool, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.511077.
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El-Khairi, Muna. "Mathematical modelling of tuberculosis infection." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/10747.
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Tuberculosis is one of the leading causes of death by infectious disease in the world today. However, the majority of individuals infected with Mycobacterium tuberculosis are able to contain bacterial growth and establish a latent infection. The aim of this thesis is to develop mathematical models to study the progression of disease in individuals infected with Mycobacterium tuberculosis. This work focuses on understanding bacterial and host defence mechanisms that govern the outcome of infection, and on identifying factors that affect the outcome of anti-tuberculosis chemotherapy. A detailed model of human tuberculosis infection in the lung and peripheral draining lymph node is developed that builds on models published in the literature. Analysis of this model suggests a differential role for innate and adaptive immune responses in determining the outcome of infection, and a possible role for an intracellular bacterial population in establishing a persistent infection. For certain parameter values this system has multiple steady states so the outcome of infection may also depend on initial conditions. This model is then modified to incorporate the effect of treatment with the antimycobacterial agent rifampicin. The model is used to investigate different treatment regimens and simulation results suggest that the length of tuberculosis therapy can be reduced by further optimizing the standard rifampicin dosing regimen. Simple predator-prey type models of infection are constructed to gain further insight into the mechanisms that control the establishment and maintenance of latency. These models support observations made from the full disease model regarding the roles of innate and adaptive immunity in fighting infection and the influence of an intracellular bacterial population that is protected from the innate immune system. The addition of a population of non-replicating or slow growing bacteria contributes to the establishment of latent infection and generally makes latency a more robust and stable state.
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Macdougall, Lindsey C. "Mathematical modelling of retinal metabolism." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/30615/.
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Age-related macular degeneration and diabetic retinopathy, in which the cells at the back of the eye degrade due to age and diabetes respectively, are prevalent causes of vision loss in adults. We formulate mathematical models of retinal metabolic regulation to investigate defects that may be responsible for pathology. Continuum PDE models are developed to test whether rod photoreceptors, light detecting cells in the eye, may regulate their energy demand by adapting their length under light and dark conditions. These models assume photoreceptor length depends on the availability of nutrients, such as oxygen, which diffuse and are consumed within the photoreceptor. Our results suggest that the length is limited by oxygen and phosphocreatine shuttle-derived ATP under dark and light conditions respectively. Parameter sensitivity analysis indicates that lowered mitochondrial efficiency due to ageing may be responsible for the damage to and death of photoreceptors that are characteristic of age-related macular degeneration. In the latter part of this thesis we shift our focus to the inner retina and examine how metabolite levels in the tissue surrounding the neurons (highly sensitive, excitable cells that transmit electrical signals) are regulated by glial cells. For instance, stimulated neurons activate their neighbours via the release of the neurotransmitter glutamate, while glial cells regulate neuronal activity via glutamate uptake. Diabetes produces large fluctuations in blood glucose levels, and eventually results in neuronal cell death, causing vision loss. We generate an ODE model for the exchange of key metabolites between neurons and surrounding cells. Using numerical and analytical techniques, we use the model to show that the fluctuations in blood glucose and metabolic changes associated with diabetes may result in abnormally high glutamate levels in the inner retina, which could lead to neuronal damage via excitotoxicity (unregulated neuronal stimulation).
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Domínguez, Hüttinger Elisa. "Mathematical modelling of epithelium homeostasis." Thesis, Imperial College London, 2014. http://hdl.handle.net/10044/1/47969.
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The body and organs of all animals are covered by epithelial tissues, such as the epidermis and the airway epithelium. Epithelial tissues play a key role in protecting the body from environmental aggressors. Failure to maintain a competent epithelium can lead to the onset of many diseases, including Atopic dermatitis (AD) and infection by Streptococcus pneumoniae. Treatment of AD is currently restricted to the relief of symptoms, mainly because the underlying mechanisms remain elusive. Antibiotic resistance threatens the effectiveness of the prevalent treatments for infection. Devising new and effective therapeutic strategies that halt the progression of these diseases requires an understanding of the different disease mechanisms that can cause loss of epithelial homeostasis in different patients. Intricate regulatory networks of several biochemical and cellular interactions maintain epithelium homeostasis in healthy individuals, but can also propagate different disturbances, resulting in a wide spectrum of possible disease phenotypes. In this thesis, we propose mathematical models of these regulatory networks to analyse the mechanisms that lead to the onset and progression of AD and pneumococcal infection from a systems-level perspective. Our mathematical model of AD reproduced, for the first time, the different stages of the disease that have been observed in the clinic. Moreover, we proposed different pathogenic mechanisms, triggered by different genetic and environmental risk factors that are known to predispose to AD. By assessing the effects of common treatments for AD, we suggested effective treatment strategies that can prevent the aggravation of the disease, in a patient-specific way. Our data-driven mathematical model of pneumococcal infection identified four qualitatively different mechanisms by which co-infection can drive the pathogenic process. They can be counteracted by distinctive treatment strategies that only partially involve antibiotics. Our work provides a theoretical framework for the integration and analysis of clinical and experimental data describing epithelial homeostasis.
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Brümmer, Anneke. "Mathematical modelling of DNA replication." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2010. http://dx.doi.org/10.18452/16212.
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Bevor sich eine Zelle teilt muss sie ihr gesamtes genetisches Material verdoppeln. Eukaryotische Genome werden von einer Vielzahl von Replikationsstartpunkten, den sogenannten Origins, aus repliziert, die über das gesamte Genome verteilt sind. In dieser Arbeit wird der zugrundeliegende molekulare Mechanismus quantitativ analysiert, der für die nahezu simultane Initiierung der Origins exakt ein Mal pro Zellzyklus verantwortlich ist. Basierend auf umfangreichen experimentellen Studien, wird zunächst ein molekulares regulatorisches Netzwerk rekonstruiert, welches das Binden von Molekülen an die Origins beschreibt, an denen sich schließlich komplette Replikationskomplexe (RKs) bilden. Die molekularen Reaktionen werden dann in ein Differentialgleichungssystem übersetzt. Um dieses mathematische Modell zu parametrisieren, werden gemessene Proteinkonzentrationen als Anfangswerte verwendet, während kinetische Parametersätze in einen Optimierungsverfahren erzeugt werden, in welchem die Dauer, in der sich eine Mindestanzahl von RKs gebildet hat, minimiert wird. Das Modell identifiziert einen Konflikt zwischen einer schnellen Initiierung der Origins und einer effizienten Verhinderung der DNA Rereplikation. Modellanalysen deuten darauf hin, dass eine zeitlich verzögerte Origininitiierung verursacht durch die multiple Phosphorylierung der Proteine Sic1 und Sld2 durch Cyclin-abhängige Kinasen, G1-Cdk bzw. S-Cdk, essentiell für die Lösung dieses Konfliktes ist. Insbesondere verschafft die Mehrfach-Phosphorylierung von Sld2 durch S-Cdk eine zeitliche Verzögerung, die robust gegenüber Veränderungen in der S-Cdk Aktivierungskinetik ist und außerdem eine nahezu simultane Aktivierung der Origins ermöglicht. Die berechnete Verteilung der Fertigstellungszeiten der RKs, oder die Verteilung der Originaktivierungszeiten, wird auch genutzt, um die Konsequenzen bestimmter Mutationen im Assemblierungsprozess auf das Kopieren des genetischen Materials in der S Phase des Zellzyklus zu simulieren.Before a cell divides it has to duplicate its entire genetic material. Eukaryotic genomes are replicated from multiple replication origins across the genome. This work is focused on the quantitative analysis of the underlying molecular mechanism that allows these origins to initiate DNA replication almost simultaneously and exactly once per cell cycle. Based on a vast amount of experimental findings, a molecular regulatory network is constructed that describes the assembly of the molecules at the replication origins that finally form complete replication complexes. Using mass–action kinetics, the molecular reactions are translated into a system of differential equations. To parameterize the mathematical model, the initial protein concentrations are taken from experimental data, while kinetic parameter sets are determined using an optimization approach, in particular a minimization of the duration, in which a minimum number of replication complexes has formed. The model identifies a conflict between the rapid initiation of replication origins and the efficient inhibition of DNA rereplication. Analyses of the model suggest that a time delay before the initiation of DNA replication provided by the multiple phosphorylations of the proteins Sic1 and Sld2 by cyclin-dependent kinases in G1 and S phase, G1-Cdk and S-Cdk, respectively, may be essential to solve this conflict. In particular, multisite phosphorylation of Sld2 by S-Cdk creates a time delay that is robust to changes in the S-Cdk activation kinetics and additionally allows the near-simultaneous activation of multiple replication origins. The calculated distribution of the assembly times of replication complexes, that is also the distribution of origin activation times, is then used to simulate the consequences of certain mutations in the assembly process on the copying of the genetic material in S phase of the cell cycle.
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Jones, Tiffany. "Mathematical modelling of cancer growth." Thesis, Curtin University, 2014. http://hdl.handle.net/20.500.11937/2546.
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In this thesis we use optimal parameter selection techniques to optimise parameters for mathematical models describing both non-cancerous and cancerous growths. We use computational methods to implement the optimal parameter selection models and discuss our results. We develop a novel model to describe melanoma growth using a set of ordinary differential equations. We incorporate into our model the mutated Braf protein which to our knowledge has not been included in a modelling sense until now.
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Dargaville, Steven. "Mathematical modelling of LiFePO4 cathodes." Thesis, Queensland University of Technology, 2013. https://eprints.qut.edu.au/60800/4/Steven_Dargaville_Thesis.pdf.
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LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases.
The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance.
The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints.
This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport.
Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.
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Olofsson, Thomas. "Mathematical modelling of jointed rock masses." Doctoral thesis, Luleå tekniska universitet, Byggkonstruktion och -produktion, 1985. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-26756.
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In this thesis, a theoretical model of the mechanical behaviour of jointed rock masses is developed. An equivalent material approach is used to formulate the constitutive equations, where the structural components, intact rock and joints are assigned continuous material properties. The elastic and inelastic properties of the joints are modelled by an elasto-viscoplastic formulation. The model can be used to study general stress and strain paths for both two- and three-dimensional structures based on constitutive equations, i.e. stress-strain relations or in finite element codes. The rock mass model using the equivalent material approach can be applied to hard rock masses with several sets of intersecting continuous joints. The theoretical model developed for a single joint can also be used for discrete formulation of joint elements in finite element codes, cf. chapter 3. The intact rock is treated as a linearly elastic material. The elastic behaviour of the joint is modelled with a constant stiffness matrix. The onset of plastic flow is initiated when the normal stress exceeds the normal compressive strength of the joint asperities or the tensile normal strength of the joint. the shear stress exceeds the cohesive strength and frictional resistance of the joint surface. The normal tensile strength and the cohesion of the joints are assumed to be constant material properties. The frictional parameters the dilation rate, and the shear asperity angle, and the compressive normal strength are functions of the the compressive normal strength are functions of the applied stress field and joint displacement. Simple relations based on Barton's constants joint roughness coefficient, JRC, joint compressive strength, JCS, and the residual friction angle, 0r, simple relations are fitted to these parameters. This implies that input data to the model can be extracted from the Rock Mechanics literature for a wide variety of joints. Results from laboratory shear box test and numerical calculations has been made for a number of different joints. Good agreement was obtained. It shows, that peak shear strength behaviour of joint in principal is a function of dilation rate. Further, the calculations indicated that the elastic off-diagonal behaviour of joints, reported in the rock mechanics literature, is related to the dilation angle at the asperities in contact. By means of finite element technique the model is applied to a circular opening in a jointed rock mass. It is concluded that the model offers several advantages over a discrete formulation.Godkänd; 1985; 20070502 (ysko)
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Fatouros, Dimitrios Michael. "Mathematical modelling for international tax planning." Thesis, Imperial College London, 1998. http://hdl.handle.net/10044/1/7954.
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Reddyhoff, Dennis. "Mathematical modelling of acetaminophen induced hepatotoxicity." Thesis, Loughborough University, 2016. https://dspace.lboro.ac.uk/2134/23008.
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Acetaminophen, known as paracetamol in the UK and Tylenol in the United States, is a widespread and commonly used painkiller all over the world. Taken in large enough doses, however, it can cause fatal liver damage. In the U.S., 56000 people are admitted to hospital each year due to acetaminophen overdose and its related effects, at great cost to healthcare services. In this thesis we present a number of different models of acetaminophen metabolism and toxicity. Previously, models of acetaminophen toxicity have been complex and due to this complexity, do not lend themselves well to more advanced mathematical analysis such as the perturbation analysis presented later in this thesis. We begin with a simple model of acetaminophen metabolism, studying a single liver cell and performing numerical and sensitivity analysis to further understand the most important mechanisms and pathways of the model. Through this we identify key parameters that affect the total toxicity in our model. We then proceed to perform singular perturbation analysis, studying the behaviour of the model over different timescales, finding a number of key timescales for the depletion and subsequent recovery of various cofactors as well as critical dose above which we see toxicity occurring. Later in the thesis, this model is used to model metabolism in a spheroid cell culture, examining the difference spatial effects have on metabolism across a 3D cell culture. We then present a more complex model, examining the difference the addition of an adaptive response to acetaminophen overdose from the Nrf2 signalling pathway, has on our results. We aim to reproduce an unexplained result in the experimental data of our colleagues, and so analyse the steady states of our model when subjected to an infused dose, rather than a bolus one. We identify another critical dose which leads to GSH depletion in the infused dose case and find that Nrf2 adaptation decreases toxicity and model sensitivity. This model is then used as part of a whole-body PBPK model, exploring the effects that the distribution of the drug across the bloodstream and different organs has. We explore the affects of that a delay in up-regulation from the Nrf2 pathway has on the model, and find that with rescaled parameters we can qualitatively reproduce the results of our collaborators. Finally, we present the results of in vitro work that we have undertaken, the aim of which was to find new parameters for the model in human hepatocytes, rather than from rodent models, and find a new value for a parameter in our model from human cell lines.
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Perkins, Gregory Martin Parry Materials Science & Engineering Faculty of Science UNSW. "Mathematical modelling of underground coal gasification." Awarded by:University of New South Wales. Materials Science and Engineering, 2005. http://handle.unsw.edu.au/1959.4/25518.
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Mathematical models were developed to understand cavity growth mechanisms, heat and mass transfer in combination with chemical reaction, and the factors which affect gas production from an underground coal gasifier. A model for coal gasification in a one-dimensional spatial domain was developed and validated through comparison with experimental measurements of the pyrolysis of large coal particles and cylindrical coal blocks. The effects of changes in operating conditions and coal properties on cavity growth were quantified. It was found that the operating conditions which have the greatest impact on cavity growth are: temperature, water influx, pressure and gas composition, while the coal properties which have the greatest impact are: the thermo-mechanical behaviour of the coal, the coal composition and the thickness of the ash layer. Comparison of the model results with estimates from field scale trials, indicate that the model predicts growth rates with magnitudes comparable to those observed. Model results with respect to the effect of ash content, water influx and pressure are in agreement with trends observed in field trials. A computational fluid dynamics model for simulating the combined transport phenomena and chemical reaction in an underground coal gasification cavity has been developed. Simulations of a two-dimensional axi-symmetric cavity partially filled with an inert ash bed have shown that when the oxidant is injected from the bottom of the cavity, the fluid flow in the void space is dominated by a single buoyancy force due to temperature gradients established by the combustion of volatiles produced from the gasification of carbon at the cavity walls. Simulations in which the oxidant was injected from the top of the cavity reveal a weak fluid circulation due to the absence of strong buoyancy forces, leading to poor gasification performance. A channel model of gas production from underground coal gasification was developed, which incorporates a zero-dimensional cavity growth model and mass transfer due to natural convection. A model sensitivity study is presented and model simulations elucidate the effects of operating conditions and coal properties on gas production.
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Depree, Nicholas Brian. "Mathematical modelling of an annealing furnace." Thesis, University of Auckland, 2010. http://hdl.handle.net/2292/5855.
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The metal coating line at New Zealand Steel relies on a large electric radiant furnace to heat steel strip before hot-dip galvanising in a continuous process. The temperature evolution of the strip inside the furnace is vital in ensuring the speci ed mechanical properties are achieved for a range of steel products. Ductile products require high temperatures su cient to cause recrystallisation of the steel microstructure, while stronger products must be heated without causing recrystallisation. Strip dimensions and desired properties are changed often and irregularly during operation, and these changes and associated furnace control actions cause changes in furnace and strip temperatures and rate of heat transfer over several di erent time scales. Accurate control of temperature is di cult because temperature measurement devices are strongly a ected by re ected radiation in the furnace cavity. The furnace is often operating during transient temperature conditions, as control actions take e ect very slowly compared to the the rate of change of operational targets. Understanding of the transient behaviour of this system of interrelated, nonlinear variables can be improved using modelling to calculate furnace and strip temperatures as a result of control actions in real time, which cannot otherwise be measured or predicted. It is shown that a three-dimensional model is capable of accurately calculating furnace temperatures changing over both time and location, requiring minimal simpli cation of the physical system, but is computationally expensive. Radiative heat exchange in the furnace cavity causes signi cantly increased temperature along the edges of the steel strip, which can cause reject product due to localised softening. It was found that furnace thermocouples are strongly a ected by re ected radiation, so that furnace wall temperatures be may signi cantly hotter than measured. A simpli ed, coupled temperature-metallurgical model was shown to accurately calcui late both furnace and strip temperatures and metallurgical changes, while the 3D model provides understanding of e ects not explicitly modelled in the simpli ed model. The simpli ed model is used for optimisation of furnace operational parameters, to improve plant throughput and energy e ciency while maintaining desired metallurgical properties, which is demonstrated by application to common products at NZ Steel.
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Petrakis, Leonidas. "The mathematical modelling of tumour growth." Thesis, Brunel University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427666.
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King, J. R. "Mathematical aspects of semiconductor process modelling." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375274.
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Anderson, Jacob T. "Mathematical modelling of lake level fluctuations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302759.
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Terrill, E. L. "Mathematical modelling of some spinning processes." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.280001.
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Hewitt, Ian. "Mathematical modelling of geophysical melt drainage." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509957.
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Fluid flows involving transport of a liquid phase in close proximity with its solid phase involve continuous transfer of mass and heat, which can influence the nature of the drainage that occurs. We consider mathematical models for two such situations; magma flow in the mantle and water flow beneath glaciers. In part I, we derive a model for porous flow within a partially molten column of mantle undergoing decompression melting. By ignoring composition effects, and by scaling the equations appropriately, approximate analytical solutions can be found for one-dimensional upwelling, which allow the region and extent of melting to be determined. We study the dynamics of open channels of melt flow in the same situation, and find that such channels would have low pressure compared to the surrounding porous flow, and therefore draw in melt from a region of the size of a compaction length. We suggest that such channels could form through the unstable effects of melting caused by heat transfer by the upwelling melt. We emphasise the similarity with channels of meltwater that are known to exist beneath ice. In part II we pose a generalised model for subglacial water flow, which is described as an effective porous medium, the pore space being determined from an evolution equation. This is used to investigate the flow into a channel, which is found to be drawn from a surrounding region whose size, we suggest, determines the spacing between major drainage channels beneath ice sheets. These are compared to the observed spacing of eskers. A critical condition on the discharge necessary to sustain a channel is found, which may provide a criteria to decide where and when channelised drainage occurs. Lastly, a simple drainage model is used to explain seasonal variations in the velocity of a valley glacier.
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Grills, Claire Melissa Emma. "Mathematical and statistical modelling of apoptosis." Thesis, Queen's University Belfast, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517342.
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Sandbach, Steven D. "Mathematical and laboratory modelling of ventilation." Thesis, University of Manchester, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.506639.
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