To see the other types of publications on this topic, follow the link: Mathematical modelling problems.
Dissertations / Theses on the topic 'Mathematical modelling problems'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Mathematical modelling problems.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Qiang, Feng. "Parallel problem generation for structured problems in mathematical programming." Thesis, University of Edinburgh, 2015. http://hdl.handle.net/1842/11688.
Full textAbstract:
The aim of this research is to investigate parallel problem generation for structured optimization problems. The result of this research has produced a novel parallel model generator tool, namely the Parallel Structured Model Generator (PSMG). PSMG adopts the model syntax from SML to attain backward compatibility for the models already written in SML [1]. Unlike the proof-of-concept implementation for SML in [2], PSMG does not depend on AMPL [3]. In this thesis, we firstly explain what a structured problem is using concrete real-world problems modelled in SML. Presenting those example models allows us to exhibit PSMG’s modelling syntax and techniques in detail. PSMG provides an easy to use framework for modelling large scale nested structured problems including multi-stage stochastic problems. PSMG can be used for modelling linear programming (LP), quadratic programming (QP), and nonlinear programming (NLP) problems. The second part of this thesis describes considerable thoughts on logical calling sequence and dependencies in parallel operation and algorithms in PSMG. We explain the design concept for PSMG’s solver interface. The interface follows a solver driven work assignment approach that allows the solver to decide how to distribute problem parts to processors in order to obtain better data locality and load balancing for solving problems in parallel. PSMG adopts a delayed constraint expansion design. This allows the memory allocation for computed entities to only happen on a process when it is necessary. The computed entities can be the set expansions of the indexing expressions associated with the variable, parameter and constraint declarations, or temporary values used for set and parameter constructions. We also illustrate algorithms that are important for delivering efficient implementation of PSMG, such as routines for partitioning constraints according to blocks and automatic differentiation algorithms for evaluating Jacobian and Hessian matrices and their corresponding sparsity partterns. Furthermore, PSMG implements a generic solver interface which can be linked with different structure exploiting optimization solvers such as decomposition or interior point based solvers. The work required for linking with PSMG’s solver interface is also discussed. Finally, we evaluate PSMG’s run-time performance and memory usage by generating structured problems with various sizes. The results from both serial and parallel executions are discussed. The benchmark results show that PSMG achieve good parallel efficiency on up to 96 processes. PSMG distributes memory usage among parallel processors which enables the generation of problems that are too large to be processed on a single node due to memory restriction.
2
Lamper, David. "Problems in mathematical finance : market modelling and derivative pricing." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270642.
Full text
3
Thornham, S. A. "The mathematical modelling of two problems in chemical engineering." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382778.
Full text
4
Pope, Martin Peter. "Mathematical modelling of unsteady problems in thin aerofoil theory." Thesis, University of Southampton, 1999. https://eprints.soton.ac.uk/192771/.
Full textAbstract:
The de-icing of aircraft wings by the injection of fluid through a slot in the leading edge of the wing is analysed. A review of current de-icing methods is presented and the semi-infinite slot-injection equation derived, which is a singular partial integro-differential equation. The Stefan condition is used to close the system. A discretisation of the equation is presented and the subsequent numerical results are analysed. The model is then revised to account for the retraction of the ice layer away from the slot. An asymptotic result for the thin ice layers is also presented. The problem of describing the motion of a thin, flexible membrane fixed at both ends (a 'sail') is then considered. The steady sail is analysed for the case of an inextensible sail and previous work on this topic is extended by using a discretisation of the singular integro-differential equation that is pertinent to the later analysis of the unsteady sail. An asymptotic expression for the eigenvalues of the system, defined as the values of the tension parameter for which the sail generates zero lift, is also presented. The problem is then extended to that of an extensible sail and numerical results are presented for both the sail with excess length and the membrane without slack. The case where the angle of incidence of the sail to the free stream is a prescribed function of time is then analysed. Previous work on this subject is extended to include the extensible sail and numerical results are presented. A linear stability analysis is then undertaken for both the extensible and elastic sails; the resulting quadratic eigenvalue problem is solved numerically and is in agreement with the numerical experiments. The trailing edge of the membrane is now permitted to move freely and thus the motion of a 'flag' is analysed. The inclusion of bending stiffness is found to be crucial to the stability properties of the flag. The steady equation of motion is numerically approximated for both a hinged flag and a flag that is clamped at the leading edge. The unsteady flag equation is then discretised and numerical results are presented. A linear stability analysis is performed, the conclusions of which are consistent with the numerical approximations of the unsteady flag equation.
5
Rout, Sweta. "The mathematical modelling and numerical solution of options pricing problems." Thesis, University of Greenwich, 2005. http://gala.gre.ac.uk/6285/.
Full textAbstract:
Accurate and efficient numerical solutions have been described for a selection of financial options pricing problems. The methods are based on finite difference discretisation coupled with optimal solvers of the resulting discrete systems. Regular Cartesian meshes have been combined with orthogonal co-ordinate transformations chosen for numerical accuracy rather than reduction of the differential operator to constant coefficient form. They allow detailed resolution in the regions of interest where accuracy is most desired, and grid coarsening where there is least interest. These transformations are shown to be effective in producing accurate solutions on modest computational grids. The spatial discretisation strategy is chosen to meet accuracy requirements as sell as to produce coefficient matrices with favourable sparsity and stability properties. In the case of single factor European options, a modified Crank-Nicolson, second order accurate finite difference scheme is presented, which uses adaptive upwind differences when the mesh Peclet conditions are violated. The resulting tridiagonal system of equations is solved using a direct solver. A careful study of grid refinement displays convergence towards the true solution and demonstrates a high level of accuracy can be obtained with this approach. Laplace inversion methods are also implemented as an alternative solution approach for the one-factor European option. Results are compared to those produced by the direct solver algorithm and are shown to be favourable. It is shown how Semi-Lagrange time-integration can solve the path-dependent Asian pricing problem, by integrating out the average price term and simplifying the finite difference equations into a parameterised Black-Scholes form. The implicit equations that result are unconditionally stable, second order accurate and can be solved using standard tridiagonal solvers. The Semi-Lagrange method is shown to be easily used in conjunction with co-ordinate transformations applied in both spatial directions. A variable time-stepping scheme is implemented in the algorithm. Early exercise is also easily incorporated, the resulting linear complementarity problem can be solved using a projection or penalty method (the penalty method is shown to be slightly more efficient). Second order accuracy has been confirmed for Asian options that must be held to maturity. A comparison with published results for continuous-average-rate put and call options, with and without early exercise, shows that the method achieves basis point accuracy and that Richardson extrapolation can also be applied.
6
Li, Xin Kai. "Mathematical modelling and numerical approximations for two-phase flow problems." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276843.
Full text
7
Alshanti, Waseem Ghazi. "Mathematical modelling and numerical simulations of various granular dynamical problems." Thesis, Curtin University, 2010. http://hdl.handle.net/20.500.11937/499.
Full textAbstract:
The absence of a general theory that describes the dynamical behaviour of the particulate materials makes the numerical simulations the most current powerful tool that can grasp many mechanical problems relevant to the granular materials. It provides a potential window and useful insight to answer massive questions related to the multi-state dynamical granular systems, including the prediction of internal particles behaviour within the particulate systems. In this thesis, based on a two-dimensional soft particle discrete element method (DEM), a numerical approach was developed to study three different granular dynamical problems, namely, the pulsation stress nature and the stress distribution on hopper wall during filling of granular solids into silos and discharging of granular solids from silos, the penetration of projectiles vertically into granular beds, and the stress distribution underneath granular piles. Moreover, an analytical approach based on the classical continuum mechanical theory was constructed to study the stress distributions at the base of a two-dimensional sand pile in search of the dip vertical stress directly beneath the apex of the sand pile.The granular material is assumed to be an assembly of visco-elastic discs and the motion of the particulate medium is governed by a set of nonlinear first order ordinary differential equations. This system is then solved numerically using the centred finite difference scheme. Based on the presented model, two-dimensional soft particle discrete element simulations have been developed and used to study different features of granular materials during filling and discharging processes in a silo system. The focus is on the stress pulsation mechanism developed on hopper wall and the influence of the wall and internal friction coefficients on the distribution of stresses on hopper wall throughout the static and dynamic processes of material filling and discharging from a silo.The vertical penetrations of projectiles into granular beds are simulated using a two-dimensional soft particle discrete element model to study the influence of various factors such as the impact velocity, lateral and vertical confinements, and the particle size on the projectile penetration distance. Moreover, we study the scaling of the projectile penetration distance with its impact velocity.Finally, to study the normal stress distributions along the base of a two dimensional granular pile, two different mathematical approaches are used for the investigation, including numerical simulations base on a two-dimensional soft particle discrete element model and analytical study based on the classical continuum theory. The influences of particle size and pile height on the normal force distributions beneath granular piles were investigated. Simulations results show the normal force distributions under granular pile that constructed from localised source exhibit a local minimum at the centre of the base under the pile vertex. For the continuum models, the linear elastic theory and plastic theory have been used. These continuum models include an elastic sand pile model and an elasto-plastic sand pile model with an inner plastic region and an outer elastic region. The elasto-plastic model exhibits the “M” shape stress distribution where the location of the local minimum of the vertical stress acting on a horizontal section of the sand pile is at centre.
8
Lund, I. D. "Hydrodynamics and mass transfer problems in wet spinning." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.370283.
Full text
9
Wilmott, S. "Mathematical modelling and analysis of some problems in parasitology and ecology." Thesis, University of Oxford, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382699.
Full text
10
DomiÌnguez-Ballesteros, MariÌa BeleÌn. "The modelling and analysis of mathematical programming problems : tools and applications." Thesis, Brunel University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.409843.
Full text
11
Timms, Robert. "Mathematical modelling and investigation of explosive pinch, friction and shear problems." Thesis, University of East Anglia, 2018. https://ueaeprints.uea.ac.uk/68331/.
Full textAbstract:
The mechanisms which lead to the accidental ignition of explosive materials in response to low energy stimuli are still not well understood. It is widely agreed that localised regions of increased temperature, so-called `hot spots', are responsible. Many mechanisms for hot spot generation have been suggested as a result of experimental studies, but the understanding of such processes remains incomplete. In this thesis, we use asymptotic and numerical techniques to investigate hot spot mechanisms, with a particular focus on those arising from impacts which pinch and shear explosives. First, a model which accounts for the effect of friction as an explosive material is pinched between two at plates is developed. An analytical solution is found by exploiting the small aspect ratio of the explosive sample. Numerical solution of the thermal part of the problem demonstrates that our model is able to predict important features observed in experiments, such as additional heating near to the plates. We then go on to study how the presence of a chemical reaction affects the development of shear bands as explosive materials are deformed. Through a boundary layer analysis, we are able to extract key non-dimensional parameters which control the development of shear bands in explosives, and discuss how this may inform the design of materials that are less susceptible to accidental ignitions due to mechanical insults. Finally, we investigate how molten layers of explosive, which can form between sliding surfaces during shear deformation, may act as a site for hot spot generation. In particular, we consider how the inhomogeneous nature of explosive materials affects the propagation of the melt front. Through a lubrication-type analysis, we demonstrate that the melt front is unstable to perturbations in the presence of a chemical reaction, and that material non-uniformities lead to localised heating within the molten layer.
12
Remias, Michael George. "Computational studies of some fuzzy mathematical problems." Thesis, Curtin University, 2012. http://hdl.handle.net/20.500.11937/1147.
Full textAbstract:
In modelling and optimizing real world systems and processes, one usually ends up with a linear or nonlinear programming problem, namely maximizing one or more objective functions subject to a set of constraint equations or inequalities. For many cases, the constraints do not need to be satisfied exactly, and the coefficients involved in the model are imprecise in nature and have to be described by fuzzy numbers to reflect the real world nature. The resulting mathematical programming problem is referred to as a fuzzy mathematical programming problem.Over the past decades, a great deal of work has been conducted to study fuzzy mathematical programming problems and a large volume of results have been obtained. However, many issues have not been resolved. This research is thus undertaken to study two types of fuzzy mathematical programming problems. The first type of problems is fuzzy linear programming in which the objective function contains fuzzy numbers. To solve this type of problems, we firstly introduce the concept of fuzzy max order and non-dominated optimal solution to fuzzy mathematical programming problems within the framework of fuzzy mathematics. Then, based on the new concept introduced, various theorems are developed, which involve converting the fuzzy linear programming problem to a four objective linear programming problem of non-fuzzy members. The theoretical results and methods developed are then validated and their applications for solving fuzzy linear problems are demonstrated through examples.The second type of problems which we tackle in this research is fuzzy linear programming in which the constraint equations or inequalities contain fuzzy numbers. For this work, we first introduce a new concept, the α-fuzzy max order. Based on this concept, the general framework of an α-fuzzy max order method is developed for solving fuzzy linear programming problems with fuzzy parameters in the constraints. For the special cases in which the constraints consist of inequalities containing fuzzy numbers with isosceles triangle or trapezoidal membership functions, we prove that the feasible solution space can be determined by the respective 3n or 4n non-fuzzy inequalities. For the general cases in which the constraints contain fuzzy numbers with any other form of membership functions, robust numerical algorithms have been developed for the determination of the feasible solution space and the optimal solution to the fuzzy linear programming problem in which the constraints contain fuzzy parameters. Further, by using the results for both the first and second types of problems, general algorithms have also been developed for the general fuzzy linear programming problems in which both the objective function and the constraint inequalities contain fuzzy numbers with any forms of membership functions. Some examples are then presented to validate the theoretical results and the algorithms developed, and to demonstrate their applications.
13
Moody, Shirley A. "Methods and tools for modelling linear and integer programming problems." Thesis, Brunel University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239161.
Full text
14
Taylor-King, Jake Patrick. "An interacting particle approach to problems in cancer : osteocyte network formation and histology analysis." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:030b64bd-0379-419e-91ab-7231c87a59b7.
Full textAbstract:
Two important factors in cancer progression are: metastatic ability, cancer spreading and disrupting healthy function of bodily processes; and heterogeneity, the variation in different cancers caused by genetics, the microenvironment, and stochasticity. In this thesis, we investigate two scenarios of interest using models and techniques inspired by interacting particle systems. First, we model osteocyte network formation. Within bone, dendritic osteocytes form a spatial network allowing communication between osteocytes and osteoblasts located on the bone surface. This communication network facilitates coordinated bone formation. In the presence of a cancer, osteocytes manifest with either over- or under-developed phenotypes. Preliminary studies measuring the number of osteocytes per unit area show that the number density of osteocytes changes between healthy and pathological bone. We develop a mathematical framework to describe spatial networks, and present a stochastic agent-based model for bone formation. Our approach allows us to probe both network structure and number density of osteocytes in bone. Analysis of our model is possible via mean-field equations. We consider variations of our model to predict how changing measurable biological parameters relating to osteoblast differentiation can allow for different morphologies. We use our model to hypothesise reasons for the limited efficacy of zoledronate therapy on metastatic breast cancer. Second, we model the diffusive microenvironment between cells to aid with pathology slide analysis. Intra-tumor phenotypic heterogeneity limits accuracy of clinical diagnostics and hampers the efficiency of anti-cancer therapies. Dealing with this cellular heterogeneity requires adequate understanding of its sources; phenotypes of tumour cells integrate hardwired (epi-)mutational differences with responses to microenvironmental cues. The latter come in the form of both direct physical interactions, and gradients of secreted signalling molecules. Here, we develop a partial differential equation based model that allows the separation of phenotypic responses to signalling gradients within tumour microenvironments from the combined influence of responses mediated by direct physical contact and hardwired (epi-)genetic differences. We apply our model for the analyses of breast cancer histological specimens. Our approach allows partial deconvolution of the complex inputs that shape phenotypic heterogeneity of tumour cells, and identifies cells that significantly impact gradients of signalling molecules.
15
Khorram, E. "Some developments in the machine interference problem : Investigation of models for machine maintenance problems involving inhomogeneous and regularly patrolled machines, with applications to the textile industry." Thesis, University of Bradford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234254.
Full text
16
Cobbold, Christina Anne. "Mathematical modelling of problems in human biology : dermal wound healing and atherosclerosis." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/471.
Full text
17
Dalwadi, Mohit. "Flow and nutrient transport problems in rotating bioreactor systems." Thesis, University of Oxford, 2014. https://ora.ox.ac.uk/objects/uuid:1d7298b7-cdf5-4240-a79c-b7b69f662c1a.
Full textAbstract:
Motivated by applications in tissue engineering, this thesis is concerned with the flow through and around a free-moving porous tissue construct (TC) within a high-aspect-ratio vessel (HARV) bioreactor. We formalise and extend various results for flow within a Hele-Shaw cell containing a porous obstacle. We also consider the impact of the flow on related nutrient transport problems. The HARV bioreactor is a cylinder with circular cross-section which rotates about its axis at a constant rate, and is filled with a nutrient-rich culture medium. The porous TC is modelled as a rigid porous cylinder with circular cross-section and is fully saturated with the fluid. We formulate the flow problem for a porous TC (governed by Darcy's equations) within a HARV bioreactor (governed by the Navier-Stokes equations). We couple the two regions via appropriate interfacial conditions which are derived by consideration of the intricate boundary-layer structure close to the TC surface. By exploiting various small parameters, we simplify the system of equations by performing an asymptotic analysis, and investigate the resulting system for the flow due to a prescribed TC motion. The motion of the TC is determined by analysis of the force and torque acting upon it, and the resulting equations of motion (which are coupled to the flow) are investigated. The short-time TC behaviour is periodic, but we are able to study the long-time drift from this periodic solution by considering the effect of inertia using a multiple-scale analysis. We find that, contrary to received wisdom, inertia affects TC drift on a similar timescale to tissue growth. Finally, we consider the advection of nutrient through the bioreactor and TC, and investigate the problem of nutrient advection-diffusion for a simplified model involving nutrient uptake.
18
Rajab, Rima Sheikh. "Some applications of continuous variable neighbourhood search metaheuristic (mathematical modelling)." Thesis, Brunel University, 2012. http://bura.brunel.ac.uk/handle/2438/6467.
Full textAbstract:
In the real world, many problems are continuous in nature. In some cases, finding the global solutions for these problems is di±cult. The reason is that the problem's objective function is non convex, nor concave and even not differentiable. Tackling these problems is often computationally too expensive. Although the development in computer technologies are increasing the speed of computations, this often is not adequate, particularly if the size of the problem's instance are large. Applying exact methods on some problems may necessitate their linearisation. Several new ideas using heuristic approaches have been considered particularly since they tackle the problems within reasonable computational time and give an approximate solution. In this thesis, the variable neighbourhood search (VNS) metaheuristic (the framework for building heuristic) has been considered. Two variants of variable neighbourhood search metaheuristic have been developed, continuous variable neighbourhood search and reformulation descent variable neighbourhood search. The GLOB-VNS software (Drazic et al., 2006) hybridises the Microsoft Visual Studio C++ solver with variable neighbourhood search metaheuristics. It has been used as a starting point for this research and then adapted and modified for problems studied in this thesis. In fact, two problems have been considered, censored quantile regression and the circle packing problem. The results of this approach for censored quantile regression outperforms other methods described in the literature, and the near-optimal solutions are obtained in short running computational time. In addition, the reformulation descent variable neighbourhood search variant in solving circle packing problems is developed and the computational results are provided.
19
Birchall, Alan. "Mathematical solutions to problems in radiological protection involving air sampling and biokinetic modelling." Thesis, University of Bristol, 1998. http://clok.uclan.ac.uk/19011/.
Full textAbstract:
Intakes of radionuclides are estimated with the personal air sampler (PAS) and by biological monitoring techniques: in the case of plutonium, there are problems with both methods. The statistical variation in activity collected when sampling radioactive aerosols with low number concentrations was investigated. By treating man as an ideal sampler, an analytical expression was developed for the probability distribution of intake following a single measurement on a PAS. The dependence on aerosol size, specific activity and density was investigated. The methods were extended to apply to routine monitoring procedures for plutonium. Simple algebraic approximations were developed to give the probability of exceeding estimated intakes and doses by given factors. The conditions were defined under which PAS monitoring meets the ICRP definition of adequacy. It was shown that the PAS is barely adequate for monitoring plutonium at ALl levels in typical workplaceconditions. Two algorithms were developed, enabling non-recycling and recycling compartmental models to be solved. Their accuracy and speed were investigated, and methods of dealing with partitioning, continuous intake, and radioactive progeny were discussed. Analytical, rather than numerical, methods were used. These are faster, and thus ideally suited for implementation on microcomputers. The algorithms enable non-specialists to solve quickly and easily any first order compartmental model, including all the ICRP metabolic models. Nonrecycling models with up to 50 compartments can be solved in seconds: recycling models take a little longer. A biokinetic model for plutonium in man following systemic uptake was developed. The proposed ICRP lung model (1989) was represented by a first order compartmental model. These two models were combined, and the recycling algorithm was used to calculate urinary and faecal excretion of plutonium following acute or chronic intake by inhalation. The results indicate much lower urinary excretion than predicted by ICRP Publication 54.
20
Liu, Shi-Qiang. "Modelling and solving train scheduling problems under capacity constraints." Thesis, Queensland University of Technology, 2008. https://eprints.qut.edu.au/37181/1/Shi-Qiang_Liu_Thesis.pdf.
Full textAbstract:
Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.
21
Debroux, Noémie. "Mathematical modelling of image processing problems : theoretical studies and applications to joint registration and segmentation." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR02/document.
Full textAbstract:
Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies<br>In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images
22
Dizha, Memory. "An analysis of mathematical modelling competencies of grade 11 learners in solving word problems involving quadratic equations." University of Western Cape, 2021. http://hdl.handle.net/11394/8317.
Full textAbstract:
Magister Educationis - MEd<br>This study analysed the modelling competencies of grade 11 learners and also explored the degree to which the learners’ competency in setting up a mathematical model inhibits the development of an acceptable solution for word problems.
The research data comprised 30 learners drawn from a secondary school in the Western Cape Province, South Africa. Data was collected via a task-based activity response sheet containing five word problems linked to either one of the following concepts: rectangle, two-digit number, average speed and petrol price. Learners’ responses were graded into four categories viz: correct, partially correct, incorrect and no response. Thereafter, the modelling competency framework was used to diagnose the modelling competencies of the sampled learners.
23
Rojas-Palma, Alejandro. "Study of some problems in modelling and optimization of bioprocesses." Thesis, Montpellier, 2016. http://www.theses.fr/2016MONTT292/document.
Full textAbstract:
L’objet de cette thèse est l’étude de certains problèmes liés à l’ingénierie des bioprocédés, en particulier l’analyse du comportement et de la culture optimale des microalgues et la connexion de plusieurs bioréacteurs. Trois problèmes sont proposés et analysés. Le première est basé sur une étude récente dans laquelle les auteurs modifient le modèle classique du Monod en incorporant l’incidence de la lumière sur la dynamique à travers le rôle de la croissance de la biomasse. L’idée est d’étudier un problème plus général de l’optimisation non linéaire qui considère maximisation de la biomasse moyenne de microalgues en fonction du temps, pour des intervalles de temps différents. La difficulté mathématique qui se pose est lié à la discontinuité des intervalles de temps qui rend la fonction à optimiser non différentiable. Ce manque de régularité comprend la formulation d’un problème d’optimisation non-lisse. Dans le deuxième problème, un modèle réduit du réservoir microalgues avec nitrification est analysé, en supposant que les microalgues peuvent se développer à partir de la consommation de nitrate et d’ammonium, de préférence par l’ammonium. La limitation de la lumière par l’auto-ombrage est également inclus dans le taux de croissance du microalgues comme inhibition non compétitive. En réduisant le système en utilisant la théorie des systèmes asymptotiquement autonomes, il peut être considéré comme une perturbation d’un système de deux espèces en compétition pour un substrat. Par conséquent, nous utilisons un résultat de systèmes perturbés non-évanescentes pour obtenir un théorème de stabilité pour la coexistence.Le dernier problème est lié aux systèmes compartimentés. Il est prouvé que pour une grande classe de systèmes entrées-sorties positifs de dimension finie, représentant transport et diffusion de soluté entre des compartiments mobiles et immobiles, il existe des représentations MINC (multiple interacting continua) et MRMT (multi-rate mass transfer) algébriquement équivalentes. En outre, des méthodes explicites sont donnés pour construire ces représentations équivalentes, où la contrôlabilité des systèmes joue un rôle important<br>The purpose of this thesis is to study some problems that arise from bioprocess engineering, in particular the behaviour analysis and optimal cultivation of microalgae and the connection of multiple bioreactors. The thesis consists of three problems. The first is based on a recent study in which the authors extend the classical Monod model incorporating light incidence on the dynamics through the role of biomass growth. The idea is to study a more general problem of nonlinear optimization which considers maximization average biomass of microalgae versus time, for different time intervals. The mathematical difficulty that arises is related to that discontinuity of the time intervals which causes non differentiability in some domain points. This lack of regularity involves the formulation of a non-smooth optimization problem. In the second problem, a reduced mathematical model of a microalgal pond with nitrification is analyzed, assuming that microalgae can grow either by ammonium consumption or by nitrate consuming, with preference for ammonium. Light limitation by self-shading is also included in the growth rate of microalgae as a noncompetitive inhibition.It is feasible to reduce the system using the theory of asymptotically autonomous systems and the limiting system obtained can be considered as a perturbation of a system of two species competing for a substrate. So, we use a result of non-vanishing perturbated systems to obtain a strong stability theorem for equilibrium coexistence. The last problem is related to compartmental systems. It is proved that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in mobile and immobile compartments, there exist MINC (multiple interacting continua) and MRMT (multirate mass transfer) algebraically equivalent representations. Moreover, we provide explicit methods to construct these representations, where controllability property is playing a crucial role
24
Vellender, Adam. "Mathematical modelling of crack problems in bi-material structures containing imperfect interfaces using the weight function technique." Thesis, Aberystwyth University, 2013. http://hdl.handle.net/2160/84f836a0-8654-4ebf-a956-c28509aad4a9.
Full textAbstract:
The main aim of this thesis is to generalise weight function techniques to tackle crack problems in bi-material linearly elastic and isotropic solids with imperfect interfaces. Our approach makes extensive use of weight functions which are special solutions to homogeneous boundary value problems that aid in the evaluation of constants in asymptotic expressions describing the behaviour of physical fields near crack tips. We use newly derived weight functions and respective techniques to tackle various aspects of a number of problems. The first major application is the use of the new weight functions to aid in the analysis of Bloch–Floquet waves; results include the derivation of a low dimensional model including junction conditions and the evaluation of a fracture criterion in the form of a constant in the asymptotic expansion of physical fields near crack tips. The second major application uses the new weight functions to assist in perturbation analysis. In particular, Betti’s formula is applied in an imperfect interface setting, which introduces new conditions and asymptotic behaviour in comparison to previously studied perfect interface cases. We first derive a weight function by employing the Wiener-Hopf technique in a bi-material strip containing a semi-infinite crack and an imperfect interface. We then present an asymptotic algorithm that uses the new weight function to evaluate coefficients in the asymptotics of solutions to problems of wave propagation in a thin bi-material strip containing a periodic array of finite-length cracks situated along an imperfect interface between two materials. We introduce and solve a low dimensional model and give relationships between its solution’s behaviour at junction points and the behaviour of physical fields near the crack tip in the full original model problem. The low dimensional model is then used to estimate eigenfrequencies of the periodic structure. We will find via comparisons against finite element simulations that the model gives excellent estimates in most cases for the frequencies of waves propagating through the strip; however, a small discrepancy is found for standing wave eigenfrequencies. We address this discrepancy by suggesting an improvement to the asymptotic model and perform computations which demonstrate a greatly improved accuracy for standing wave eigenfrequencies in both the imperfect and ideal interface problems. We then move on to consider our second major problem which concerns out-of-plane shear in an infinite domain containing a semi-infinite crack situated on an imperfect interface. We derive a weight function for this geometry and use Betti’s identity to relate the behaviour of physical fields near the crack tip to that of the weight function and prescribed loadings on the crack faces. In particular, the method presented allows for the prescribed tractions to be point forces, as well as continuous loadings. Having obtained the weight function, we then conduct perturbation analysis to determine how small linear defects such as elliptic inclusions influence the forces near the crack tip. Computations are performed which demonstrate how the unperturbed solution depends upon the parameter of interface imperfection, and how the location of defects may shield or amplify the stresses near the crack tip.
25
Hsieh, Mike Hou-Ning. "Mathematical modelling of controlled drug release from polymer micro-spheres : incorporating the effects of swelling, diffusion and dissolution via moving boundary problems." Thesis, Queensland University of Technology, 2012. https://eprints.qut.edu.au/60306/1/Mike_Hsieh_Thesis.pdf.
Full textAbstract:
Controlled drug delivery is a key topic in modern pharmacotherapy, where controlled drug delivery devices are required to prolong the period of release, maintain a constant release rate, or release the drug with a predetermined release profile. In the pharmaceutical industry, the development process of a controlled drug delivery device may be facilitated enormously by the mathematical modelling of drug release mechanisms, directly decreasing the number of necessary experiments. Such mathematical modelling is difficult because several mechanisms are involved during the drug release process. The main drug release mechanisms of a controlled release device are based on the device’s physiochemical properties, and include diffusion, swelling and erosion.
In this thesis, four controlled drug delivery models are investigated. These four models selectively involve the solvent penetration into the polymeric device, the swelling of the polymer, the polymer erosion and the drug diffusion out of the device but all share two common key features. The first is that the solvent penetration into the polymer causes the transition of the polymer from a glassy state into a rubbery state. The interface between the two states of the polymer is modelled as a moving boundary and the speed of this interface is governed by a kinetic law. The second feature is that drug diffusion only happens in the rubbery region of the polymer, with a nonlinear diffusion coefficient which is dependent on the concentration of solvent. These models are analysed by using both formal asymptotics and numerical computation, where front-fixing methods and the method of lines with finite difference approximations are used to solve these models numerically. This numerical scheme is conservative, accurate and easily implemented to the moving boundary problems and is thoroughly explained in Section 3.2. From the small time asymptotic analysis in Sections 5.3.1, 6.3.1 and 7.2.1, these models exhibit the non-Fickian behaviour referred to as Case II diffusion, and an initial constant rate of drug release which is appealing to the pharmaceutical industry because this indicates zeroorder release. The numerical results of the models qualitatively confirms the experimental behaviour identified in the literature. The knowledge obtained from investigating these models can help to develop more complex multi-layered drug delivery devices in order to achieve sophisticated drug release profiles. A multi-layer matrix tablet, which consists of a number of polymer layers designed to provide sustainable and constant drug release or bimodal drug release, is also discussed in this research.
The moving boundary problem describing the solvent penetration into the polymer also arises in melting and freezing problems which have been modelled as the classical onephase Stefan problem. The classical one-phase Stefan problem has unrealistic singularities existed in the problem at the complete melting time. Hence we investigate the effect of including the kinetic undercooling to the melting problem and this problem is called the one-phase Stefan problem with kinetic undercooling. Interestingly we discover the unrealistic singularities existed in the classical one-phase Stefan problem at the complete melting time are regularised and also find out the small time behaviour of the one-phase Stefan problem with kinetic undercooling is different to the classical one-phase Stefan problem from the small time asymptotic analysis in Section 3.3. In the case of melting very small particles, it is known that surface tension effects are important. The effect of including the surface tension to the melting problem for nanoparticles (no kinetic undercooling) has been investigated in the past, however the one-phase Stefan problem with surface tension exhibits finite-time blow-up. Therefore we investigate the effect of including both the surface tension and kinetic undercooling to the melting problem for nanoparticles and find out the the solution continues to exist until complete melting.
The investigation of including kinetic undercooling and surface tension to the melting problems reveals more insight into the regularisations of unphysical singularities in the classical one-phase Stefan problem. This investigation gives a better understanding of melting a particle, and contributes to the current body of knowledge related to melting and freezing due to heat conduction.
26
Wessels, Helena. "Using a modelling task to Elicit Reasoning about data." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-83189.
Full text
27
Gonçalves, Raínne Florisbelo. "Métodos de resolução para o problema de empacotamento de cilindros em níveis." Universidade de São Paulo, 2018. http://www.teses.usp.br/teses/disponiveis/55/55134/tde-29102018-113809/.
Full textAbstract:
O problema de empacotamento de cilindros em níveis é comumente encontrado nas indústrias de cerâmica. Solucionar este problema significa encontrar o posicionamento ideal dos itens cerâmicos cilíndricos dentro do forno de modo que o menor número de fornos seja utilizado e os itens não se sobreponham e obedeçam aos limites do recipiente. Também é considerado o uso de prateleiras para que haja uma melhor ocupação do espaço do forno. Propomos uma formulação matemática não-linear inteira mista e métodos de resolução heurísticos e exato para o problema. Os métodos heurísticos consistem em escolher uma estratégia de ordenação, posicionar os itens em cada nível por meio da heurística Bottom-Left e posicionar os níveis no recipiente utilizando as estratégias Best-Fit, First-Fit ou Worst-Fit. Ao total, propomos seis variações heurísticas para resolução do problema. O método exato consiste em estimar o número de níveis e recipientes necessários e resolver o problema por meio de um solver de otimização global. Os experimentos computacionais foram realizados para um conjunto de instâncias que criamos. Os resultados mostraram que o método exato é capaz de encontrar a solução ótima em um curto período de tempo para instâncias de pequeno porte e que as heurísticas são capazes de resolver o problema em um tempo computacional baixo, para instâncias de pequeno, médio e grande porte, sendo que algumas heurísticas apresentam melhor desempenho que outras.<br>The cylinder packing problem in levels is commonly found in ceramic industries. Solving this problem consists in finding the ideal position of items inside furnaces so that the minimum number of furnaces is used and the items do not overlap and obeying furnaces size. In this case, it is possible to add levels to the furnace. We proposed a non-linear integer mixed mathematical model for the problem and heuristic and exact resolution methods. Heuristic methods consist of choosing a sorting strategy, packing the items at each level by a Bottom-Left heuristic, and positioning the levels in the furnace using Best-Fit, First- Fit or Worst-Fit strategy. In total, it is proposed six heuristic variations to solve the problem. The exact method consists in solving the problem by a global optimization solver. The computational experiments were run over a set of new proposed instances. The results have shown that the exact method is able to find an optimal solution in a short period of time for small instances and that the proposed heuristics are capable of solving the problem in a low computational time for small, medium and large instances. Furthermore, some of them have performed better than others.
28
Martin, D. C. (David Charles). "Selected heat conduction problems in thermomechanical treatment of steel." Doctoral thesis, Oulun yliopisto, 2011. http://urn.fi/urn:isbn:9789514295195.
Full textAbstract:
Abstract This thesis considers two related problems where heat conduction is accompanied by phase transformation during the cooling of carbon steels – phenomena which are fundamental to modern thermomechanical treatment processes. In the first problem, a non-linear heat equation formulation is described which includes linkage between irreversible diffusive and diffusionless phase transformation processes and thermophysical properties. A family of numerical schemes using finite difference methods with diagonally implicit Runge-Kutta method integrators for solving this formulation is present. Sample calculations using these schemes are presented for a mild steel cooled under range of industrially relevant heat transfer conditions. These calculations illustrate the need for careful scheme design and solver selection when coupled heat conduction and microstructure evolution equations become non-linear and stiff. The second section of the thesis extends this heat conduction formulation into the realm of inverse analysis. The problem of temperature reconstruction and boundary condition estimation using temperature measurements obtained thermocouples embedded into laboratory samples undergoing phase transformation is considered. A solution method based on iterative regularization is described for solving the resulting ill-posed problem. An analysis of extremely high rate cooling experiments made on a pilot-plant descaling unit using the inverse method is presented. This analysis highlights some of the practical issues associated with embedded thermocouple temperature measurements made in this fashion<br>Tiivistelmä Väitöstyössä tutkitaan kahta ongelmaa liittyen hiiliteräksen termomekaanisen käsittelyn numeeriseen mallintamiseen. Työssä tarkastellaan teräksessä tapahtuvaa lämmönsiirtoa ja faasimuutoksia jäähdytyksen aikana, eli ensisijaisen tärkeitä ilmiöitä kehittynyttä teräksen valmistusta ja prosessointia ajatellen. Ensimmäisenä ongelmana tutkitaan epälineaarisen energiayhtälön muodostaminen huomioiden teräksen termofysikaaliset materiaaliominaisuudet, diffuusion kontrolloimat ja diffuusiosta riippumattomat irreversiibelit faasimuutokset. Lisäksi huomioidaan näiden väliset kytkennät. Yhtälöt ratkaistaan numeerisesti ja käytetyt menetelmät esitellään differenssimenetelmien ja diagonaalisesti implisiittisten Runge-Kutta-menetelmien osalta. Väitöstyössä näiden käyttöä havainnollistetaan simuloimalla niukkahiilisen teräksen käyttäytymistä teollisia olosuhteita vastaavan jäähdytyksen aikana. Laskentatulokset osoittavat ratkaisumenetelmän suunnittelun ja valinnan tärkeyden erityisesti silloin, kun lämmönjohtuminen, mikrorakenteen kehittyminen ja termofysikaaliset materiaaliominaisuudet muuttavat ratkaistavan ongelman epälineaariseksi ja jäykäksi. Toisena ongelmana tutkitaan edellä esitetyn lämmönsiirtomallin käyttöä osanainversioanalyysiä. Laboratoriokokeiden, termopareilla suoritettujen lämpötilamittausten, työssä kehitetyn lämmönsiirtomallin ja suoritetun inversioanalyysin avulla rekonstruoidaan teräskappaleiden lämpötila- ja faasimuutoskäyttäytymistä sekä estimoidaan mallin reunaehtoja. Näin luotu inversio-ongelma on kuitenkin matemaattisesti tarkasteltuna ns. huonosti asetettu ongelma, ja sen ratkaisemiseksi käytetään iteratiiviseen säännöllistämiseen perustuvaa menetelmää. Väitöstyön inversioanalyysiä havainnollistetaan pilot-mittakaavan kokeiden avulla, joissa hilsepesuria käyttäen koekappaleen jäähtymisnopeus saadaan erittäin korkeaksi. Tulokset nostavat esille inversio-analyysiin liittyviä ongelmia ja rajoitteita nopeaan jäähtymiseen sekä lämpötilamittauksiin liittyen
29
Hegarty-Cremer, Solene G. "Spatial control and cell guidance in evolving biological tissues." Thesis, Queensland University of Technology, 2021. https://eprints.qut.edu.au/207246/1/Solene_Hegarty-Cremer_Thesis.pdf.
Full textAbstract:
In this thesis, a mathematical model for tissue growth under curvature control and directed cell guidance is derived. The model extends previous mathematical work by adding a tangential cell velocity. A numerical solver is implemented to solve the model and the solutions show that new cases of tissue growth can now be simulated thanks to the extension derived in this thesis. Finally, the model is fit to data on bone pore infilling and is used to examine hypotheses about atypical tissue growth.
30
Regnier, Rémi. "Approche de reconstruction d’images fondée sur l’inversion de certaines transformations de Radon généralisées." Thesis, Cergy-Pontoise, 2014. http://www.theses.fr/2014CERG0698/document.
Full textAbstract:
Depuis l'invention de la radiographie au début du vingtième siècle et des premiers radars lors la seconde guerre mondiale, le besoin de connaître notre environnement par différentes techniques d'imagerie n'a cessé de croître. Ce besoin a pris de multiples formes, allant de l'exploration d'une structure interne avec la prolifération des techniques d'imagerie non invasives à l'imagerie par satellite qui accompagna la conquête de l'espace. Nombre de systèmes d'imagerie ont donc été proposés pour arriver à créer les images les plus représentatives des milieux étudiés. Parmi eux la tomodensitométrie, ou scanner médical, a connu un succès remarquable depuis son invention. La raison de ce succès vient du fait que son principe de fonctionnement est fondé sur la transformée de Radon dont l'inversion permet de restituer une image fidèle de l'intérieur du milieu étudié.La transformée de Radon (TR) est une transformée géométrique intégrale, qui intègre une densité physique d'intérêt, le long d'une droite du plan. Il est donc naturel de penser qu'une généralisation de la TR, qui consiste à remplacer la droite, support d'intégration, par une courbe ou par une surface, peut amener à une nouvelle imagerie. Dans cette thèse, nous étudions deux types de transformées de Radon généralisées qui sont définies sur des lignes brisées en V du plan (appelées TRV) et des sphères centrées sur un plan fixe (appelées TRS) ainsi que leurs imageries correspondantes.Les transformées de Radon généralisées sur des lignes brisées (TRV) nous permettent de proposer trois nouvelles modalités tomographiques. La première, comme la tomodensitométrie, exploite le phénomène d'atténuation du rayonnement X lors de sa propagation dans un milieu mais utilise aussi le phénomène de réflexion du rayonnement sur une surface impénétrable. La deuxième exploite le phénomène de diffusion Compton du rayonnement émis par un objet. La troisième combine deux modalités d'imageries par transmission et par émission sous la forme d'une imagerie bimodale à partir du rayonnement ionisant diffusé. Cette étude permet non seulement de faire émerger de nouvelles imageries pouvant concurrencer celles existantes mais aussi d'établir de nouveaux algorithmes pour la correction de l'atténuation (un des facteurs physiques dégradant sérieusement la qualité d'image tomographique actuellement).La transformée de Radon sur des sphères centrées sur un plan fixe (TRS) est une généralisation connue de la transformée de Radon en trois dimensions. Elle a été proposée comme modèle mathématique de l'imagerie radar à synthèse d'ouverture (RSO). On montre par la construction d'algorithmes appropriés que l'inversion de cette TRS donne une solution efficace à la reconstruction d'images de l'environnement directement en 3D.La faisabilité théorique de ces nouvelles imageries modélisées par ces deux classes de transformées de Radon généralisées et la performance des algorithmes de reconstruction d'images basés sur les formules d'inversion de ces transformées ouvrent plusieurs perspectives : extension en 3D de l'imagerie bimodale par rayonnement ionisant diffusé, ou possibilité de détection de cibles mobiles en imagerie RSO par introduction d'autres généralisations de la TR. De plus, les méthodes développés dans cette thèse sont susceptibles d'application dans d'autres imageries : imagerie sismique modélisée par la transformée de Radon définie sur des paraboles, imagerie radar Doppler par la TR sur des hyperboles ou encore imagerie thermo-opto-acoustique modélisée par la TR sur des cercles centrés sur un cercle fixe<br>Since the invention of radiography at the beginning of the 20th century and of the radar during the 2nd world war, the need of information on our environment is ever increasing. This goes from the exploration of internal structures using non-invasive numerous imaging techniques to satellite imaging which rapidly expands with space exploration. A huge number of imaging systems have been conceived to provide faithful images of the objects of interest. Computed Tomography (or the medical scanner) has experienced a tremendous success since it was invented. The reason for this success lies in the fact that its mathematical foundation is the Radon transform (RT), which has an inverse formula allowing the faithful reconstruction of the interior of an object.The Radon transform is a geometric integral transform which integrates a physical density of interest along a straight line in the plane. It is natural to expect that, when the line is replaced by a curve or a surface as an integration support, new imaging processes may emerge. In this thesis, we study two generalized Radon transforms which are defined on broken lines in the form of a letter V (called V-line RT or VRT) and on spheres centered on a fixed plane (called spherical RT or SRT), as well as their resulting imaging processes.The Radon transforms on V-lines (VRT) form the mathematical foundation of three tomographic modalities. The first modality exploits not only the attenuation of X-rays in traversed matter (as in Computed Tomography) but also the phenomenon of reflection on an impenetrable surface. The second modality makes use of Compton scattering for emission imaging. The third modality combines transmission and emission imaging modalities into a bimodal imaging system from scattered ionizing radiation. This study puts forward new imaging systems which compete with the existing ones and develops new algorithms for attenuation corrections (in emission imaging the attenuation is one of factors degrading seriously tomographic image quality up to now).The Radon transform on spheres centered on a fixed plane (SRT) is a generalization of the classical Radon transform in three dimensions. It has been proposed as a mathematical model for Synthetic Aperture Radar (SAR) imaging. We show through the setting up of appropriate algorithms that the inversion of the SRT yields an efficient solution to the landscape reconstruction problem, directly in three dimensions.The theoretical feasibility of these new imaging systems based on generalized Radon transforms and the good performance of inversion algorithms based on inversion formulas open the way to several perspectives: 3D extension of bimodal imaging by scattered radiation or SAR target motion detection through the introduction of other generalized Radon transforms. Moreover the algorithmic methods developed here may serve in other imaging activities such as: seismics with the parabolic Radon transform, Doppler radar with the hyperbolic Radon transform, thermo-opto-acoustic imaging with the Radon transform on circles centered on a fixed circle
31
Tanner, H. F. R. "Using and applying mathematics : developing mathematical thinking through practical problem solving and modelling." Thesis, Swansea University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.639162.
Full textAbstract:
Using and Applying Mathematics in the National Curriculum focuses on the development of reasoning skills through problem solving, and links the processes involved in learning new mathematics with the application of existing knowledge to new situations. This thesis begins by examining how mathematical knowledge is constructed and how children make sense of it. The nature of practical problem solving and modelling is considered and the literature on teaching and learning problem solving and modelling is reviewed with particular emphasis on metacognition and social practices. The research reports a quasi-experiment in which 314 pupils aged between 11 and 13 followed a mathematical thinking skills course and were compared with matched control pupils using pre-tests, post-tests, delayed texts and structured interviews. Assessment instruments were devised to assess pupils' mathematical cognitive development, their metacognitive skills and their metacognitive self knowledge. Statistical data were supported by participant observations. On average, experimental pupils performed slightly better than control pupils in metacognitive skill and mathematical development in the post and delayed-tests. The content of the mathematical development test had not been taught directly by the course and far transfer is claimed. The teachers were divided into four groups according to teaching approach, based on analysis of the qualitative data. The most successful teachers used a flexible form of scaffolding and encouraged reflection. Their classes demonstrated a substantial advantage over their controls in metacognitive skill, metacognitive self knowledge and mathematical development. Recommendations are made about teaching approaches.
32
Chalmers, Alexander David. "Mathematical Modelling of Atherosclerosis." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/14986.
Full textAbstract:
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
33
Morris, Graham Peter. "Parameter recovery in AC solution-phase voltammetry and a consideration of some issues arising when applied to surface-confined reactions." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:1b1d40f3-ef1a-4f64-b500-17ce34630c43.
Full textAbstract:
A major problem in the quantitative analysis of AC voltammetric data has been the variance in results between laboratories, often resulting from a reliance on "heuristic" methods of parameter estimation that are strongly dependent on the choices of the operator. In this thesis, an automatic method for parameter estimation will be tested in the context of experiments involving electron-transfer processes in solution-phase. It will be shown that this automatic method produces parameter estimates consistent with those from other methods and the literature in the case of the ferri-/ferrocyanide couple, and is able to explain inconsistency in published values of the rate parameter for the ferrocene/ferrocenium couple. When a coupled homogeneous reaction is considered in a theoretical study, parameter recovery is achieved with a higher degree of accuracy when simulated data resulting from a high frequency AC voltammetry waveform are used. When surface-confined reactions are considered, heterogeneity in the rate constant and formal potential make parameter estimation more challenging. In the final study, a method for incorporating these "dispersion" effects into voltammetric simulations is presented, and for the first time, a quantitive theoretical study of the impact of dispersion on measured current is undertaken.
34
Ali, Habib K. "Mathematical modelling of the optimal power dispatch problem." Thesis, University of Strathclyde, 1990. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=21285.
Full textAbstract:
This thesis is concerned with the optimum operating conditions in a power system. The various aspects of the problem are modelled and solved as a number of optimization problems applying linear programming techniques. A generalized linear mathematical model has been developed for this purpose. A two-stage formulation is adopted to represent the various problems considered. In each case one power system quantity is chosen as an objective function to be optimized under a number of constraints and operating limits relating to the power system relationships and upper and lower bounds on the variables. These include constraints derived from the power flow equations and transmission network capacity. Limits are also imposed on bus voltage magnitudes and generator outputs. With the appropriate selection of the combination of objective function and constraints, the model can be used to minimize the overall generation cost, the total system losses or the total reactive power generation. The two-stage modelling of the problem also allows optimizing two different objective functions at the same time. Two such combinations are possible. In one case the total system losses can be minimized in the first stage and the generation cost minimized in the second stage. The other combination minimizes the total system reactive power output and the active power generation cost. Using the same model, the problem is then solved using decomposition techniques. These imply breaking up the original problem into a number of smaller problems that can be solved almost independently. The mathematical model has been developed in general terms and the associated computer program is written for a general power system. A sample system of medium size has been used to test the validity of the various aspects of the suggested model and produce numerical results.
35
Guan, Anna. "Mathematical modelling of optical coherence tomography and solutions of the inverse scattering problem." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2024. https://ro.ecu.edu.au/theses/2800.
Full textAbstract:
Optical coherence tomography (OCT) is a non-invasive high-resolution imaging technology. It utilises the coherence property of light to visualise biological tissue cross-sections and produce A-scans. A-scans contain numerous peaks that are associated with layer interfaces in a given sample. Trained medical staff may be able to make a qualitative interpretation of an OCT A-scan. However, this interpretation is not always reliable in terms of identifying the key features of the sample structure. To provide an accurate prognosis and a potential treatment scheme, a more objective measure is in order. The process of inferring sample structure from an A-scan is known as the inverse scattering problem. There are two stages to mathematically solve the OCT inverse scattering problem. The first stage is to establish an OCT model as a means to simulate the A-scan of a known sample structure. This is known as the direct scattering problem. The OCT model is of significant importance in providing a quantitative measure of how well a sample structure fits the available A-scan. The second stage is to develop an efficient and reliable algorithm to infer the sample structure from the A-scan. Solving the inverse scatting problem is about establishing an algorithm to systematically search the space of feasible optical properties of the sample to best fit the available A-scan, thus inferring the tissue structure. Aligning with the two stages, the research proceeds under two main foci. The first focus is the development of the OCT models for the direct scattering problem. This includes extending the first principle OCT model to incorporate absorption, scattering and multiple reflections to create simulated A-scans. The extended OCT model will be used to study the impact of light sources, and the impact of absorption, scattering and multiple reflections on the simulated A-scans. The second focus is the solutions to the inverse scattering problem. This includes investigating and implementing a robust deterministic algorithm to efficiently and accurately solve the inverse scattering problem.
36
Doyle, Katherine Mary. "Mathematical modelling through top-level structure." Thesis, Queensland University of Technology, 2006. https://eprints.qut.edu.au/16391/1/Katherine_Doyle_Thesis.pdf.
Full textAbstract:
Mathematical modelling problems are embedded in written, representational, and graphic text. For students to actively engage in the mathematical-modelling process, they require literacy. Of critical importance is the comprehension of the problems' text information, data, and goals. This design-research study investigated the application of top-level structuring; a literary, organisational, structuring strategy, to mathematical-modelling problems. The research documents how students' mathematical modelling was changed when two classes of Year 4 students were shown, through a series of lessons, how to apply top-level structure to two scientifically-based, mathematical-modelling problems.
The methodology used a design-based research approach, which included five phases.
During Phase One, consultations took place with the principal and participant teachers. As well, information on student numeracy and literacy skills was gathered from the Queensland Year 3 'Aspects of Numeracy' and 'Aspects of Literacy' tests. Phase Two was the initial implementation of top-level structure with one class of students. In Phase Three, the first mathematical-modelling problem was implemented with the two Year 4 classes. Data was collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. During Phase Four, the top-level structure strategy was implemented with the second Year 4 class. In Phase Five, the second mathematical-modelling problem was investigated by both classes, and data was again collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations.
The key finding was that top-level structure had a positive impact on students' mathematical modelling. Students were more focussed on mathematising, acquired key mathematical knowledge, and used high-level, mathematically-based peer questioning and responses after top-level structure instruction.
This research is timely and pertinent to the needs of mathematics education today because of its recognition of the need for mathematical literacy. It reflects international concerns on the need for more research in problem solving. It is applicable to real-world problem solving because mathematical-modelling problems are focussed in real-world situations. Finally, it investigates the role literacy plays in the problem-solving process.
37
Doyle, Katherine Mary. "Mathematical modelling through top-level structure." Queensland University of Technology, 2006. http://eprints.qut.edu.au/16391/.
Full textAbstract:
Mathematical modelling problems are embedded in written, representational, and graphic text. For students to actively engage in the mathematical-modelling process, they require literacy. Of critical importance is the comprehension of the problems' text information, data, and goals. This design-research study investigated the application of top-level structuring; a literary, organisational, structuring strategy, to mathematical-modelling problems. The research documents how students' mathematical modelling was changed when two classes of Year 4 students were shown, through a series of lessons, how to apply top-level structure to two scientifically-based, mathematical-modelling problems. The methodology used a design-based research approach, which included five phases. During Phase One, consultations took place with the principal and participant teachers. As well, information on student numeracy and literacy skills was gathered from the Queensland Year 3 'Aspects of Numeracy' and 'Aspects of Literacy' tests. Phase Two was the initial implementation of top-level structure with one class of students. In Phase Three, the first mathematical-modelling problem was implemented with the two Year 4 classes. Data was collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. During Phase Four, the top-level structure strategy was implemented with the second Year 4 class. In Phase Five, the second mathematical-modelling problem was investigated by both classes, and data was again collected through video and audio taping, student work samples, teacher and researcher observations, and student presentations. The key finding was that top-level structure had a positive impact on students' mathematical modelling. Students were more focussed on mathematising, acquired key mathematical knowledge, and used high-level, mathematically-based peer questioning and responses after top-level structure instruction. This research is timely and pertinent to the needs of mathematics education today because of its recognition of the need for mathematical literacy. It reflects international concerns on the need for more research in problem solving. It is applicable to real-world problem solving because mathematical-modelling problems are focussed in real-world situations. Finally, it investigates the role literacy plays in the problem-solving process.
38
Millien, Pierre. "Mathematical modelling for hybrid and nanoparticle imaging." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0010/document.
Full textAbstract:
Cette thèse a pour sujet la modélisation mathématique de nouvelles méthodes expérimentales d'imagerie. Elle est divisée en deux parties. La première porte sur l'étude de techniques dites hybrides basées sur des interactions entre différents types d'ondes. La deuxième parte est consacrée à l'étude du comportement des nano-particules métalliques soumises à des champs électro-magnétiques. La première partie contient trois chapitres dans lesquels sont étudiés trois techniques d'imagerie différentes : - la tomographie magnéto-acoustique par force de Lorentz ; - la tomographie magnéto-acoustique par induction magnétique ; - l'élastographie par tomographie cohérente optique. Dans les deux premiers chapitres nous donnons un modèle mathématique explicite pour les expériences étudiées, ainsi que des formules explicites pour résoudre les problèmes inverses associés. Nous introduisons une méthode de reconstruction directe dite de « viscosité » permettant de reconstruire la conductivité électrique du milieu étudié. Dans le troisième chapitre nous proposons une méthode d'optimisation pour récupérer le module de cisaillement du milieu à partir de mesures d'un champs de déplacement. La deuxième partie contient deux chapitres dans lesquels sont étudiés la diffraction par de petites particules. Les phénomènes suivant sont abordés : - les résonances plasmoniques ; - la génération de seconde harmonique. Nous étudions les résonances plasmoniques dans le cadre d'une approximation petit volume<br>In this thesis we study the mathematical modelling of new experimental imaging techniques. It is divided in two parts. The first one contains work on hybrid imaging techniques based on the interactions betwenn different types of waves. The second part is devoted to the study of the behavior of metallic nanoparticles embedded in electromagnetic fields. The first part contains three chapters in which three different imaging techniques are studied : - magneto-acoustic tomography by Lorentz force, - magneto-acoustic tomography with magnetic induction, - optical coherence tomography based elastography. In the first two chapters we give a mathematical model for the experiments studied as well as explicit reconstruction formulas for the associated inverse problems. We introduce a new direct reconstruction method ("viscosity method") allowing the recovery of the electrical conductivity of the medium. In the third chapter we give an optimisation method to reconstruct the shear modulus of the medium from a displacement field. The second part contains two chapters in which are studied the diffraction of light by small metallic nanoparticles. We study: - plasmonic resonances, - second harmonic generation. The plasmonic resonances are studied within the Maxwell frame. We give an asymptotic formula for the electromagnetic fields within a small volume approximation
39
Heipcke, Susanne. "Combined modelling and problem solving in mathematical programming and constraint programming." Thesis, University of Buckingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297665.
Full text
40
Biccard, Piera. "An investigation into the development of mathematical modelling competencies of grade 7 learners." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/5301.
Full textAbstract:
Thesis (MEd (Curriculum Studies))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT: Mathematical modelling is becoming a popular teaching and learning approach in
mathematics education. There is however a need within the modelling domain to
identify exactly what modelling competencies are and how these competencies
develop. This study examines how mathematical modelling competencies develop in
Grade 7 students working in groups.
Modelling is placed in the field of mathematics teaching and learning as a significant
means of learning mathematics. Modelling competencies are identified and
characterised from existing literature and explored through empirical generation and
collection of data. The study is qualitative in nature and uses a mixed approach of
design research and some aspects of grounded theory. Students’ progress through a
modelling program is documented while the modelling competencies of students
stereotyped as weak and strong are also investigated. The findings firmly support
earlier research that competencies do develop in students who are exposed to
modelling. A comprehensive picture of the modelling situation is presented since this
study merges competencies from other studies into a detailed analysis of the
modelling situation - it presents an authentic modelling situation of students working
in groups and furthers the discussion on modelling competencies.
The analysis of the data suggests that the development of modelling competencies is
complex and interrelated but that competencies do develop progressively in groups
involved in modelling tasks. Recommendations for additional studies include studies
of a longer duration and a full investigation into the link between modelling and
language ability.<br>AFRIKAANSE OPSOMMING: Wiskundige modellering is besig om ‘n populêre onderrig- en studiebenadering in
wiskundeonderwys te word. Daar is egter ‘n behoefte om die
modelleringsbevoegdhede te identifiseer in hierdie veld en om te weet hoe hierdie
bevoegdhede ontwikkel. Hierdie studie ondersoek watter bevoegdhede in wiskundige
modellering by Gr.7 studente wat in groepe saamwerk ontwikkel.
Modellering is in die studieveld van wiskundeonderrig en -leer geplaas as 'n
betekenisvolle leerwyse in wiskunde. Modelleringsbevoegdhede word vanuit
bestaande literatuur en navorsing geïdentifiseer en beskryf deur empiriese generering
en versameling van data. Die studie is kwalitatief van aard en gebruik ‘n gemengde
benadering van ontwikkelingsondersoek en sekere aspekte van begronde teorie.
Studente se vordering in die modelleringsprogram is gedokumenteer terwyl die
modelleringsbevoegdhede van gestereotipeerde swak en sterk studente ook ondersoek
is. Die resultate bevestig vroeëre navorsing dat bevoegdhede ontwikkel word deur
studente wat blootgestel is aan modellering. ‘n Omvattende beeld van die
modelleringsituasie is in hierdie studie aangebied waardeur
modelleringsbevoegdhede, soos geïdentifiseer in ander studies, tot ‘n gedetailleerde
analise van die modelleringsituasie saamgevoeg word. Dit verteenwoordig dus ‘n
outentieke modelleringsituasie van studente wat in groepe saamwerk en bevorder so
die gesprek oor modelleringsbevoegdhede.
Die analise van die data suggereer dat die ontwikkeling van modelleringsbevoegdhede
kompleks en geïntegreerd is, en dat bevoegdhede progressief ontwikkel in groepe wat
betrokke is by modelleringstake. Aanbevelings vir addissionele studies sluit langer
ondersoektydperke in en 'n dieper ondersoek na die verband tussen modellering en
taalvaardigheid.
41
Narimanyan, Arsen. "Stefan-Signorini moving boundary problem arisen from thermal plasma cutting mathematical modelling, analysis and numerical solution /." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980807719.
Full text
42
Whitbrook, Amanda Marie. "The efficient numerical solution of differential/algebraic boundary value problems arising in detonation modelling." Thesis, Nottingham Trent University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388868.
Full text
43
Xue, Ning. "Modelling and advanced optimisation methods for the multi-shift full truckload vehicle routing problem." Thesis, University of Nottingham, 2017. http://eprints.nottingham.ac.uk/39865/.
Full textAbstract:
This thesis is concerned with a real-world multi-shift drayage problem at a large international port with multiple docks being operated simultaneously. Several important issues in the drayage problem are identified and a set covering model is developed based on a novel route representation. The model adopts an implicit solution representation to reduce the problem size and aims to find a set of vehicle routes with minimum total cost to deliver all commodities within their time windows. As accurate travel time prediction is necessary to construct the vehicle routes, a short-haul travel time prediction model and an algorithm using real-life GPS data are studied. The output of the prediction model can be used as an input for the set covering model. The set covering model for the multi-shift full truckload transportation problem can be directly solved by a commercial solver for small problems, but results in prohibitive computation time for even moderate-sized problems. In order to solve medium- and large-sized instances, we proposed a 3-stage hybrid solution method and applied it to solve real-life instances at a large international port in China. It was shown that the method is able to find solutions that are very close to the lower bounds. In addition, we also proposed a more efficient hybrid branch-and-price approach. Results show the method performed well and is more suited for solving real-life, large-sized drayage operation problems.
44
Biccard, P., and D. C. J. Wessels. "Problem-centred teaching and modelling as bridges to the 21st century in primary school mathematics classrooms." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82321.
Full text
45
Patel, Mayur K. "On the false-diffusion problem in the numerical modelling of convection-diffusion processes." Thesis, University of Greenwich, 1986. http://gala.gre.ac.uk/8697/.
Full textAbstract:
This thesis is concerned with the classification and evaluation of various numerical schemes that are available for computing solutions for fluid-flow problems, and secondly, with the development of an improved numerical discretisation scheme of the finite-volume type for solving steady-state differential equations for recirculating flows with and without sources. In an effort to evaluate the performance of the various numerical schemes available, some standard test cases were used. The relative merits of the schemes were assessed by means of one-dimensional laminar flows and two-dimensional laminar and turbulent flows, with and without sources. Furthermore, Taylor series expansion analysis was also utilised to examine the limitations that were present. The outcome of this first part of the work was a set of conclusions, concerning the accuracy of the numerous schemes tests, vis-a-vis their stability, ease of implementation, and computational costs. It is hoped that these conclusions can be used by `computational fluid-dynamics' practitioners in deciding on an optimum choice of scheme for their particular problem. From the understanding gained during the first part of the study, and in an effort to combine the attributes of a successful discretisation scheme, eg positive coefficients. conservation and the elimination of 'false-diffusion', a new flow-oriented finite-volume numerical scheme was devised and applied to several test cases in order to evaluate its performance. The novel approach in formulating the new CUPID* scheme (for Corner UPw^nDing) underlines the idea of focussing attention at the control-volume corners rather than at the control-volume cell-faces. In two-dimensions, this leads to an eight neighbour influence for the central grid point value, depending on the flow-directions at the corners of the control-volume. In the formulation of the new scheme, false-diffusion is considered from a pragmatic perspective, with emphasis on physics rather than on strict mathematical considerations such as the order of discretisation, etc. The accuracy of the UPSTREAM scheme (for JJPwind in STREAMIines) indicates that although it is formally only first-order accurate, it considerably reduces 'false-diffusion'. Scalar transport calculations (without sources) show that the UPSTREAM scheme predicts bounded solutions which are more accurate than the upwind-difference scheme and the unbounded skew-upstream-difference scheme. Furthermore, for laminar and turbulent flow calculations, improved results are obtained when compared with the performances of the other schemes. The advantage of the UPSTREAM-difference scheme is that all the influence coefficients are always positive and thus the coefficient matrices are suitable for iterative solution procedures. Finally, the stability and convergence characteristics are similar to those of the upwind-difference scheme, eg converged solutions are guaranteed. What cannot be guaranteed, however, is the conservatism of the scheme and it is recommended that future work should be directed towards improving that disadvantage.
46
Puerta, Gabriel Figueiredo. "Restauração de sistemas de distribuição radiais quando existe um número reduzido de chaves de manobra." Ilha Solteira, 2018. http://hdl.handle.net/11449/158269.
Full textAbstract:
Orientador: Rubén Augusto Romero Lázaro<br>Resumo: Neste trabalho, apresenta-se um modelo matemático especializado para a otimização do problema da restauração de redes de distribuição de energia elétrica radiais quando existem poucas chaves manobráveis. A existência de um número reduzido de chaves seccionadoras na rede de distribuição é uma característica típica de sistemas reais. O problema da restauração de redes de distribuição consiste em obter um plano de restauração que restabeleça o máximo possível de cargas presentes na parcela do sistema que foi desenergizada após a ocorrência de uma falta permanente. O plano de restauração deve ser obtido o mais rápido possível. O modelo matemático proposto possui como objetivo maximizar o restabelecimento de energia àqueles setores de carga que estão desenergizados e minimizar o número total de chaveamentos necessários para que a restauração aconteça. O modelo matemático resultante é de programação cônica de segunda ordem inteira mista e é resolvido através de solucionadores comerciais que se baseiam em técnicas de otimização clássicas. Os testes considerando faltas permanentes foram simulados em sistemas de distribuição testes de 53 e 84 barras. Os sistemas foram adaptados e transportados para a problemática do trabalho e os resultados adquiridos qualificam a robustez e a eficácia do modelo matemático especializado proposto para a resolução do problema.<br>Abstract: This work proposes an specialized mathematical model for the optimization of the restoration problem in radial electric power distribution systems with few manageable switches. The existence of a reduced number of switches in the distribution systems it’s a typical characteristic of real systems. The restoration problem in radial electric power distribution systems is to obtain a restoration plan that reestablishes the maximum amount of present loads in the system portion that has been de-energized after the occurrence of a permanent fault. The elaboration of the restoration plan must be as soon as possible. The proposed mathematical model aims at maximizing the power re-establishment to the de-energized load sectors and at minimizing the total amount of operated switches that are required for the restoration happen. The resulting mathematical model is a mixed-integer second-order conic programming problem and it’s solved through commercial solves that use classical optimization techniques as base. The tests considering permanents faults were simulated in 84 and 53-bus distribution systems. The systems were adapted and transported to the work’s problematic and the acquired results show the robustness and the effectiveness of the proposed specialized mathematical model for the problem resolution.<br>Mestre
47
Zequim, Katia Cristina. "A resolução de problemas, a modelagem matemática e desenvolvimento de habilidades matemáticas em alunos do 7º ano do ensino fundamental." Universidade Federal de São Carlos, 2014. https://repositorio.ufscar.br/handle/ufscar/4464.
Full textAbstract:
Made available in DSpace on 2016-06-02T20:02:56Z (GMT). No. of bitstreams: 1
6315.pdf: 4602500 bytes, checksum: 6afec96e16dd04c400431b43a5e636b2 (MD5)
Previous issue date: 2014-03-28<br>In recent years, much has been said of the need to improve the quality of education. Specifically in mathematics, the quest for change has been to approximate contents of schooling of everyday problems of students. Nowadays, teaching mathematics is restricted basically in memorizing formulas and resolution of repetitive exercises. The central question to be answered in this research, level Professional Master, is "learning activities, based on Problem Solving and Mathematical Modelling, contribute to the development of mathematical skills in students of 7th year of elementary school?". To help find the answer to this question, two specific questions were proposed: (1st) "What difficulties encountered during the planning, development and implementation of educational activities of research?", and, (2nd) "What is the contribution that research brought to my teacher training in mathematics, didactic and methodological prospects?". The survey results showed that of the 16 math skills selected for investigation, 6 of them worked and were evaluated at 3 or 4 of the planned and implemented educational activities. These six, five of them are associated with "power to carry out" this basic competence and processes necessary for the development of problem-solving and mathematical modelling. Therefore, the conclusion of research on the key issue is that "yes, problem solving and mathematical modelling contributed much to the development of mathematical skills in students from the 7th year of elementary school, involved in research." About the difficulties faced during the course of the research, the main one was to put on paper, in writing, what was being planned in the teaching activities, the observations made during the applications of these activities on students and everything needed report coherently in this dissertation. Finally, the main contribution that research has brought into my teacher training refers to the teaching perspective. Through research, she realized that the act of teaching mathematics can from practice and contextualized problem situations and, consequently, more meaningful and attractive to students. Came to believe that, at least in formal education, mathematics should be taught as a "tool" that, when used well, helps us to better understand the society in which we live.<br>Nos últimos anos, muito se tem falado da necessidade de melhoria na qualidade da educação. Especificamente na matemática, a busca pela mudança vem sendo no sentido de aproximar os conteúdos escolares de problemas do cotidiano dos alunos. Hoje em dia, o ensino de matemática se restringe, basicamente, a memorização de fórmulas e a resolução de exercícios repetitivos. A questão central a ser respondida nesta pesquisa, em nível de Mestrado Profissionalizante, é: atividades didáticas, baseadas na Resolução de Problemas e na Modelagem Matemática, contribuem para o desenvolvimento de habilidades matemáticas em alunos do 7º ano, do Ensino Fundamental? . Para auxiliar na busca da resposta a esta questão, duas outras questões específicas foram propostas: (1ª) "Quais dificuldades encontrei durante os processos de planejamento, elaboração e aplicação da sequência de atividades didáticas da pesquisa?"; e, (2ª) "Qual a contribuição que a pesquisa trouxe para a minha formação de professora, nas perspectivas matemática, didática e metodológica?". Os resultados da pesquisa mostraram que das 16 habilidades matemáticas selecionadas para investigação, 6 delas foram trabalhadas e avaliadas em 3 ou 4 das atividades didáticas planejadas e aplicadas. Destas seis, 5 delas são associadas a "competência para realizar", competência esta básica e necessária ao desenvolvimento dos processos de resolução de problemas e de modelagem matemática. Portanto, a conclusão da pesquisa quanto à questão central é de que "sim, a resolução de problemas e a modelagem matemática contribuíram em muito para o desenvolvimento de habilidades matemáticas nos alunos do 7º Ano, do Ensino Fundamental, envolvidos na pesquisa". Quanto às dificuldades que enfrentei durante o transcorrer da pesquisa, a principal delas foi a de colocar no papel, por escrito, o planejado nas atividades didáticas, as observações feitas durante as aplicações dessas atividades nos alunos e tudo aquilo que necessitava relatar, coerentemente, nesta dissertação. Finalmente, a principal contribuição que a pesquisa trouxe à minha formação de professora refere-se à perspectiva didática. Com a pesquisa, compreendi que o ato de ensinar matemática pode partir de situações-problema práticas e contextualizadas e, consequentemente, mais significativas e atraentes aos alunos. Passei a acreditar que, ao menos no Ensino Básico, a matemática deva ser ensinada como uma "ferramenta", que, quando bem utilizada, ajuda-nos a melhor compreender a sociedade em que vivemos.
48
Hurdal, Monica Kimberly. "Mathematical and computer modelling of the human brain with reference to cortical magnification and dipole source localisation in the visual cortx." Thesis, Queensland University of Technology, 1998.
Find full text
49
Ivan, Jean-Paul. "Principal Component Modelling of Fuel Consumption ofSeagoing Vessels and Optimising Fuel Consumption as a Mixed-Integer Problem." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-51847.
Full textAbstract:
The fuel consumption of a seagoing vessel is, through a combination of Box-Cox transforms and principal component analysis, reduced to a univariatefunction of the primary principle component with mean model error −3.2%and error standard deviation 10.3%. In the process, a Latin-hypercube-inspired space partitioning sampling technique is developed and successfully used to produce a representative sampleused in determining the regression coefficients. Finally, a formal optimisation problem for minimising the fuel use is described. The problem is derived from a parametrised expression for the fuel consumption, and has only 3, or 2 if simplified, free variables at each timestep. Some information has been redacted in order to comply with NDA restrictions. Most redactions are either names (of vessels or otherwise), units, andin some cases (especially on figures) quantities.<br><p>Presentation was performed remotely using Zoom.</p>
50
Ndiaye, Ndèye Fatma. "Algorithmes d'optimisation pour la résolution du problème de stockage de conteneurs dans un terminal portuaire." Thesis, Le Havre, 2015. http://www.theses.fr/2015LEHA0002/document.
Full textAbstract:
ADans cette thède, nous traitons le problème de stockage de conteneurs dans un terminal portuaire. Dans un premier temps, noux présentons une étude bibliographique dans laquelle sont analysés les travaux qui ont déhà été rélisé dans ce domaine. Ensuite, nous présentons une étude analytique, puis une modélisation mathématique et des méthodes de résolution numérique qui englobent des algorithmes efficaces. Nous proposons une démonstration de la compexité du problème de stockage de conteneurs en considérant différents cas de stockage. Ce problème étant "Np_difficile" peut être difficilement résolu avec le logiciel d'optimisation "ILOG CPLEX". », raison pour laquelle nous proposons un algorithme de banch-and-cut, qui est une méthode de résolution exacte et qui nous a permis de repousser les limites de "ILOG CPLEX". Nous avons aussi proposé des algorithmes métatheuristiques et des hybridations qui procurent des résultats très satisfaisants et qui sont très avantageux en temps de calcul<br>AIn this thesis, we trait the container storage problem at port terminal. Initially, we present a state of the art in which the work that have been previously made in this filed are analyzed. After that, we present an analytical study. Thed we propose a mathematical modelling and some methods of resolution including effective algorithms. We propose a demonstration of the complexity of the problem by considering different cases of storage. This problme is "Np_difficult, so not always easy to solve by using the optimization software "ILOG CPLEX”. This is why we propose a branch-and-cut algorithm, wich is an optimal resolution algorithm and wich enables to go beyong the limits of "ILOG CPLEX". We also proposed meta-heuristic algorithms and hybridizations wich provide satisfactory resulys and wich required less calculation times