Ce travail porte sur la modélisation de problèmes liés au recalage d'images. Le recalage consiste à trouver une déformation optimale de sorte qu'une image déformée s'aligne sur une image de référence. Il s'agit d'une technique que l'on rencontre dans de nombreux domaines, comme l'imagerie médicale, la comparaison de données ou le suivi de formes. Le premier chapitre se concentre sur le problème de préservation de la topologie. Cette condition de préservation de la topologie est importante lorsque la déformation recherchée traduit des propriétés physiques des objets soumis à la déformation. Les chapitres suivants proposent la construction de différentes méthodes de recalage d'images fondées sur la théorie de l'élasticité non linéaire. En effet, les objets à apparier sont supposés être des matériaux hyper-élastiques. Différents termes d'attaches aux données ont été explorés ainsi que deux modèles conjoints de segmentation et recalage. / This work focuses on the modelling of problems related to image registration. Image registration consists in finding an optimal deformation such that a deformed image is aligned with a reference image. It is an important task encountered in a large range of applications such as medical imaging, comparison of data or shape tracking. The first chapter concerns the problem of topology preservation. This condition of topology preservation is important when the sought deformation reflects physical properties of the objects to be distorted. The following chapters propose several methods of image registration based on the nonlinear elasticity theory. Indeed, the objects to be matched are modelled as hyperelastic materials. Different fidelity terms have been investigated as well as two joint segmentation/registration models.

MSc (Mathematics) / Department of Mathematics and Applied Mathematics

Doctor Educationis / The overarching purpose of this research study was to ascertain the deliberations preservice mathematics teachers engage with when they construct alternative mathematical models for social phenomena. The study is situated within the mathematical competencies and, in particular, on the evaluation competency with the possibility of developing alternative models flowing from the evaluation. Twenty fourth-year pre-service mathematics teachers participated in the completion of three different mathematical modelling tasks on which the analysis was based. The data collected was analysed qualitatively. The researcher exploited a thematic analysis design to investigate how pre-service mathematics teachers build alternative models.

>Magister Scientiae - MSc / In this thesis, we consider some interesting mathematical models arising in ecology. Our focus is on the exploration of robust numerical solvers which are applicable to models arising in mathematical ecology. To begin with, we consider a simple but nonlinear second-order time-dependent partial differential equation, namely, the Allen-Cahn equation. We discuss the construction of a class of exponential time differencing methods to solve this particular problem. This is then followed by a discussion on the extension of this approach to solve a more difficult fourth-order time-dependent partial differential equation, namely, Kuramoto-Sivashinsky equation. This equation is nonlinear. Further applications include the extension of this approach to solve a complex predator-prey system which is a system of fourth-order time-dependent non-linear partial differential equations. For each of these differential equation models, we presented numerical simulation results. / 2025

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Operating conditions of the furnaces has the major effect on the quality of steel during steel production process. Furnaces also are the biggest energy consumer in the whole production process  which make them a center of concern, in order to get to the most optimized condition through both energy and quality aspects. Soaking pit furnaces are for heating steel ingots before rolling, in order to provide convenient conditions for ingots for further procedures. These batch furnaces are characterized by heat and temperature conditions that vary in time. The structure permits rapid heating of the metal inside the furnace, since heat is supplied over the entire surface of the ingot. One serious problem that these furnaces might contain is the existence of non-uniform temperature gradient inside the chamber that causes different temperature distribution on the ingots surface which leads to a bad surface quality of them, considering further rolling process. As the first step through obtaining the best temperature gradient inside the chamber, is to ensure the exact temperature condition in the current running procedure. In here as the first step through the problem solving of these furnaces, temperature profile, radiation profile and other effective parameters are investigated with the aid of CFD software. The simulation is done by ICEM and FLUENT programs for geometry and mesh designing, and modeling in respect. Modeling is based on four main steps:         I.            Modeling of the furnace chamber geometry and applying appropriate mesh style with ICEM       II.            Modeling the chamber with fluent, and taking the results (case 0)     III.            Modeling of six cases with different excess air, in order to investigate the best λ magnitude     IV.            Modeling of six cases with different burner capacities in order to investigate its affection on combustion parameters

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Yes / This paper presents an improved mathematical model for calculation of distortion vectors of two aligned surface meshes. The model shows better accuracy when benchmarked to an existing model with exceptional mathematical conditions, such as sharp corners and small radii. The model was implemented into a developed distortion compensation digital tool and applied to an industrial component. The component was made of Inconel 718 and produced by laser powder bed fusion 3D printing technology. The digital tool was utilised to compensate the original design geometry by pre-distortion of its original geometry using the developed mathematical model. The distortion of an industrial component was reduced from approximately ±400 µm to ±100 µm for a challenging thin structure subjected to buckling during the build process.

We illustrate here how a range of fluid and solid mechanics problems relevant to the human eye have been combined in a continuing PhD study. Anterior chamber flow, the solid mechanics of tonometry, the effects of scleral buckle surgery and the mechanics of retinal detachment are all discussed. Finally, a number of other aye problems that are amenable to a theoretical mechanics treatment are proposed.

Cervical cancer is the fourth most common cancer in women. It is caused by the hu- man papillomavirus (HPV). There are many different types of HPV, some of which are high-risk, highly associated with cancer, and low-risk. While HPV is very common— most sexually active individuals will contract some sexually transmitted HPV infec- tion in their lifetime—most infections are cleared without any complication. However, persistent infections may establish and develop into cancerous lesions. Two vaccines have been developed against the two most high-risk types, and have shown high lev- els of efficacy thus far. However, infections are still occurring and it is not clear why some individuals develop persistent infections while others do not. In this thesis, we develop a model to describe how the infection spreads within the host. We express the basic reproduction number R0, a threshold for the establishment of an infection. We solve for the diseased equilibrium, providing insight about whether an infection will persist or not. We develop a spatial model to examine how spatiality of the infec- tion process affects the establishment or clearance. Lastly, we develop a multi-type HPV model to examine whether competitive HPV types are able to coexist in the host for different levels of competition. Ultimately, this work provides groundwork for within-host modelling of HPV and can provide direction for future research. / Thesis / Master of Science (MSc) / The human papillomavirus (HPV) is a sexually transmitted infection that is known to cause cervical cancer in women along with other genital cancers. Cervical cancer is the fourth most common cancer in women, and thus researchers are looking to reduce the number of cervical cancer cases and the number of HPV infections. In order for HPV to cause cervical cancer, the infection must persist for a long time. Most individuals clear the infection without any complication; however, some individuals develop persistent infections. By using mathematical and computation models, we hope to understand why and how HPV infections spread in the host. We develop a criterion for when the infection may be able to establish in the host, and explore conditions that could lead to clearance. Understanding when and how infections will persist could inform treatment and monitoring of cervical cancer development.