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Icicles are a ubiquitous and picturesque feature of cold winter weather. Their familiar form emerges from a subtle interplay between the solidification dynamics of ice and the gravity-driven flow of the thin water film flowing over their evolving surface. The latent heat released by freezing is advected by the water film and ultimately carried away by the surrounding sub-zero air, which is also flowing. Like many processes far from equilibrium, icicle growth can exhibit nonlinear pattern formation. While scaling theory predicts that icicles converge to `platonic', self-similar shapes, natural icicles often exhibit regular ripple patterns about their circumference, which are due to a morphological instability. This thesis presents a comprehensive experimental study of icicles that sheds new light on the dynamics of their growth and the origin of their form. A table-top apparatus was designed and built for the controlled growth of icicles, under different conditions of temperature, water supply rate, ambient air motion, and water purity. Image analysis and Fourier methods were used to examine their morphology. Contrary to theoretical expectations, ripples do not appear on icicles made from pure water. Instead, ripples grow and travel on icicles made from salt solutions, even at very low concentrations. The addition of non-ionic surfactant or dissolved gases does not produce ripples, unless ionic impurities are also present. The ripple wavelength is independent of time and growth conditions. The ripple amplification rate and traveling velocity vary weakly with the ionic concentration, as do the tip and radial growth speeds of the icicle. While the tip and radial growth also depend on the ambient temperature and input mass flux, the ripple dynamics is not correlated with extrinsic conditions. If the ambient temperature or input mass flux is sufficiently low, the tip growth only advances for a short period of time before it ceases. After cessation, the shape of the icicle deviates increasingly from self-similarity. The most self-similar icicles are made from pure water with the surrounding air gently stirred, whereas icicles made from impure water in still air tend to grow multiple tips.

Icicles are a ubiquitous and picturesque feature of cold winter weather. Their familiar form emerges from a subtle interplay between the solidification dynamics of ice and the gravity-driven flow of the thin water film flowing over their evolving surface. The latent heat released by freezing is advected by the water film and ultimately carried away by the surrounding sub-zero air, which is also flowing. Like many processes far from equilibrium, icicle growth can exhibit nonlinear pattern formation. While scaling theory predicts that icicles converge to `platonic', self-similar shapes, natural icicles often exhibit regular ripple patterns about their circumference, which are due to a morphological instability. This thesis presents a comprehensive experimental study of icicles that sheds new light on the dynamics of their growth and the origin of their form. A table-top apparatus was designed and built for the controlled growth of icicles, under different conditions of temperature, water supply rate, ambient air motion, and water purity. Image analysis and Fourier methods were used to examine their morphology. Contrary to theoretical expectations, ripples do not appear on icicles made from pure water. Instead, ripples grow and travel on icicles made from salt solutions, even at very low concentrations. The addition of non-ionic surfactant or dissolved gases does not produce ripples, unless ionic impurities are also present. The ripple wavelength is independent of time and growth conditions. The ripple amplification rate and traveling velocity vary weakly with the ionic concentration, as do the tip and radial growth speeds of the icicle. While the tip and radial growth also depend on the ambient temperature and input mass flux, the ripple dynamics is not correlated with extrinsic conditions. If the ambient temperature or input mass flux is sufficiently low, the tip growth only advances for a short period of time before it ceases. After cessation, the shape of the icicle deviates increasingly from self-similarity. The most self-similar icicles are made from pure water with the surrounding air gently stirred, whereas icicles made from impure water in still air tend to grow multiple tips.

We propose a hypothesis and a numerical model for the formation of branching plagioclase textures visible at both macroscopic (∼cm to ∼m) and microscopic scale within melagabbro of the Isle of Rum, Scotland, based on macroscopic, microscopic observations and relevant geological history. The plagioclase crystals are typically linked as twins and form meshes of planar stellate structures (m-scale) with a large range in geometrical organization from patchy to radiating. Evidence of macroscopic crystal aggregation and alignment is attributed to interfacial free energy minimization at the microscopic scale during growth. Accordingly, a binary immiscible Lattice Boltzmann model was developed to simulate diffusion of simplified plagioclase in the melt phase. Isothermal phase transitions modelled via first order chemical reactions are subsequently coupled with stochastic dynamics at the crystal growth front to simulate energy minimization processes including twinning during crystallization in an igneous environment. The solid phase and the liquid phase are coupled with a temporal flexibility that sets the overall ratio between the rate of diffusion and chemical enrichment in the liquid state and the rate of crystallization. The parameter space of the model is explored extensively, followed by a reasonable transcription of physical parameters and an estimation of other parameters to construct realistic simulation scenarios yielding synthetic plagioclase stellates. The results are presented, analyzed and discussed. They appear to be in reasonable qualitative agreement with observations, and several aspects of the natural stellates such as the stellate spacing and long continuous stretches of plagioclase with epitaxial junctions seem to be in reasonable quantitative agreement with observations.

The success or failure of any criminal investigation often depends on the recognition of physical evidence left at a crime scene and the proper analysis of that evidence. Crime scenes that involve bloodshed often contain a wealth of information in the form of blood patterns, the location, and its cause. Any criminal investigation has specific tasks, from the time when the crime is reported to the reconstruction of crime scenes. A lot of work needs to be done. Once the investigation starts at the crime scene, BPA needs to be done at the crime scene and the investigating officer must identify this evidential tool. The investigating officer should not necessarily have specialised training in blood pattern analysis, but rather know when to use these experts at their bloody crime scenes. With the interviews and docket analysis done, the researcher found that this was a problem as the investigating officers, either had no knowledge on the subject of BPA or very little knowledge on this research. The purpose of this study was to determine the use of BPA to CSR, and for the investigating officer to realise that it is not just a bloody crime scene, but also contains a wealth of evidence. The researcher had two research questions. Once the investigating officer follows the objectives of criminal investigation, they should be able to have a strong case against the perpetrators. How could BPA be used in the reconstructing of a crime scene? The researcher wanted to bring it to the investigating officers’ attention that it is not just a bloody crime scene, but rather that it contains a wealth of evidence, which can give them a perspective of the movement of both the victim and perpetrator during the commencement of the crime. Regardless of the lack of knowledge of BPA, it is proposed that investigating officers are to be informed, either through station lectures or by yearly refresher workshops and courses of the evidential tool of BPA. When the bloody crime scene is reconstructed with the use of BPA, an insight of what transpired at the crime scene will help them to finalise their cases. For recommendations, it is proposed that investigating officers are to be trained in more in depth courses in criminal investigation as well as crime scene reconstruction and evidence collection using FSL. / Criminology and Security Science / M.Tech. (Forensic Investigation)

This thesis consists of three parts: The first and second parts focus on long-time asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling approaches. (1) Keller–Segel-type aggregation-diffusion equations: We study a Keller–Segel-type model with non-linear power-law diffusion and non-local particle interaction: Does the system admit equilibria? If yes, are they unique? Which solutions converge to them? Can we determine an explicit rate of convergence? To answer these questions, we make use of the special gradient flow structure of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the asymptotic behaviour of solutions. (2) Hypocoercivity techniques for a fibre lay-down model: We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in non-woven textile production. Further, we prove convergence to equilibrium with an explicit rate. This part of the thesis is an extension of previous work which considered the case of a stationary conveyor belt. Adding the movement of the belt, the global equilibrium state is not known explicitly and a more general hypocoercivity estimate is needed. Although we focus here on a particular application, this approach can be used for any equation with a similar structure as long as it can be understood as a certain perturbation of a system for which the global Gibbs state is known. (3) Scaling approaches for collective animal behaviour models: We study the multi-scale aspects of self-organised biological aggregations using various scaling techniques. Not many previous studies investigate how the dynamics of the initial models are preserved via these scalings. Firstly, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local kinetic 1D and 2D models to simpler models existing in the literature. Secondly, we investigate how some of the kinetic spatio-temporal patterns are preserved via these scalings using asymptotic preserving numerical methods.

L'identité des organes floraux est définie par l’expression de gènes homéotiques appartenant à la famille des MADS-box au début du développement floral. Un de ces gènes, AGAMOUS (AG), est responsable de l’identité des étamines et des carpelles chez Arabidopsis thaliana. Dans ce manuscrit, je tente de comprendre les propriétés spatiales et temporelles de l’expression d’AG en cherchant à connaître les mécanismes impliqués dans le bon établissement de la dynamique d’expression d’AG pendant les jeunes stades du développement floral.Je débute par développer un modèle de réaction-diffusion qui prend en compte la croissance de la fleur pendant les stades d’intérêt, ainsi que quelques facteurs de transcriptions clefs impliqués dans la régulation d’AG. Ensuite j’ai imagé en direct et en 4D la croissance des fleurs pour quantifier l’activation de l’expression d’AG de son initiation à son patron d’expression stable. Je montre que son expression se déroule en deux phases: une phase de faible expression, et une phase de forte expression. Bien que toutes les cellules du dôme central de la fleur présentent un profil d’activation d’AG similaire, le temps précis au cours du développement où AG est activé est différent pour chacunes d’entre elles et est à l’origine de la stochasticité du patron d’expression. Avec l’aide du modèle, je propose quatres nouvelles hypothèses relatives à la régulation d’AG :AG est capable de maintenir sa propre activation en se liant directement à son second intron au travers d’un complexe protéique contenant au moins deux molécule d'AG, créant ainsi un seuil d'auto-activation.AP2 influence la valeur de ce seuil, restreint l’expression d’AG dans le dôme central de la fleur et produit un retard dans l’activation complète d’AG.LFY et WUS sont nécessaire à l’accumulation des protéines d’AG dans les cellules pour pouvoir atteindre le seuil d’auto-activation et obtenir une expression complète d’AG.Le mouvement d’AG est nécessaire pour obtenir l’expression d’AG dans toutes les cellules du dôme central. Pour prouver ces hypothèses, j’ai réalisé différentes expériences. En premier, utilisant une expérience de FRET-FLIM dans les protoplastes, nous proposons qu’AG est capable de s’associer en homodimer dans les cellules végétales. Néanmoins, sur-exprimer AG pour aider les cellules à atteindre le seuil d’auto-activation plus tôt que dans la plante sauvage ne semble pas modifier la dynamique d’expression de l’AG endogène. En deuxième, j’ai testé le rôle précis de LFY au cours des différentes phases et transitions de la dynamique d’expression d’AG en mutant les sites d'interactions spécifiques pour LFY au sein des séquences de régulation d’AG. Ces mutations retardent l’expression l’expression d’AG et modifient légèrement son patron d’expression. Je montre que seulement d’important retards dans l’activation d’AG induit des modifications phénotypiques. Ensuite, pour tester le rôle de la répression par AP2 dans la dynamique d’expression d’AG, j’analyse le rapporteur d’AG dans le contexte d’un mutant fort d’ap2. Dans ce mutant, l’expression d’AG s’étend à une région plus large et le retard entre l’initiation de l’expression d’AG et la transition entre les phases de faible et forte expressions est diminué. Ces résultats correspondent aux simulations du modèle. Finalement, pour comprendre l’importance du mouvement d’AG d’une cellule à l’autre dans sa propre dynamique, je bloque cette capacité de bouger en utilisant un tag de localisation nucléaire. Bien que cela induit un retard dans l’activation de quelques cellules au stade 3 au moment où toutes les cellules du dôme centrale de la fleur expriment AG dans la plante sauvage, ce retard n’a pas d’effets visible sur le phénotype. / The identity of flower organs is defined by the expression of homeotic genes during early development that belongs to the MADS-box family. One of these genes, AGAMOUS (AG), is responsible for the identity of the stamens and the carpels in Arabidopsis thaliana. In this manuscript, I attempt to fully understand the spatial and temporal properties of AG expression by investigating the mechanisms underlying the proper establishment of AG expression dynamics during the early stages of flower development. I start by developing a reaction-diffusion model that takes into account the growth of the flower at the relevant stages, as well as the few key transcription factors involved in AG regulation. Next I used real-time 4D imaging on growing flowers to quantify the activation of AG expression from its onset to the stable pattern. I show that the AG expression occurs in two phases: a low-expression phase and a high-expression phase. Thus although all cells of the central dome of the flower present similar profiles of AG activation, the precise developmental time at which AG is activated is different in each case, and is the origin of the initial stochastic pattern. With the aid of the model, I also propose four new hypotheses to explain AG regulation: AG is able to maintain its own activation by directly binding its own second intron through a protein complex containing at least two molecules of AG leading to the creation of an auto-activation threshold.AP2 influences the value of this threshold, restraining AG expression to the central dome of the flower and producing a delay in complete AG activation.LFY and WUS are necessary to accumulate AG proteins in cells in order to reach the auto-activation threshold and obtain a full expression of AG.AG movement is necessary to obtain expression of AG in every cell of the central dome. To prove these hypotheses, I have carried out various experiments, using FRET-FLIM in protoplast cells, we suggest that AG is able to form homo-dimers in plant cells. However, overexpressing AG to help cells reach the auto-activation threshold earlier than in the wild-type does not appear to alter the endogenous AG dynamics of expression. Secondly, I test the precise role of LFY in the different phases and transitions in the AG expression dynamics by mutating specific interaction sites for LFY within AG regulatory sequences. These mutations appear to delay AG expression and slightly modify its pattern of expression. I show that only important delays in AG activation induce phenotypic differences. Then, to test the role of AP2 repression in AG expression dynamics, I analyse the AG reporter in the context of a strong ap2 mutant. In these mutants, AG expression spreads to a wider region and reduces the delay between the onset of AG expression and the transition from low- to high-expression. These results match with simulations of the model. Lastly, to understand the importance of AG cell-to-cell movement in AG dynamics, I block its ability to move using a nuclear localisation tag. Although this induces a delay in the activation of few cells at stage 3, when all cells of the central dome of the flower express AG in the WT. This delay has no visible effects on the phenotype.

Nous étudions dans cette thèse le problème de la stabilité d'une goutte à l'état sphérique. La goutte est soumise à forçage qui s'exerce à sa surface de manière purement radiale. Deux configurations sont envisagées : lorsque le forçage est oscillant (avec ou sans une composante constante) et lorsque le forçage est constant. Pour ce faire, nous avons utilisé un code de simulation numérique tridimensionnel pour les écoulements multiphasique incompressibles massivement parallélisé. Le solver combine les méthodes eulériennes et lagrangiennes pour le traitement de la dynamique de l'interface. Le premier problème correspond à l'analogue de l'instabilité de Faraday en présence d'une interface sphérique. Nous avons réalisé une étude de stabilité linéaire en utilisant une décomposition spatiale sur une base d'harmonique sphérique et une généralisation de l'analyse de Floquet de Kumar and Tuckerman (1994) d'une interface plane. Les régions d'instabilités permettent de déterminer le mode sphérique le plus instable. Le mode prédit par la théorie linéaire correspond à celui obtenu à l'aide des simulations numériques. Le second problème est celui d'un forçage radial constant à l'interface de la goutte. En orientant la force dans le sens du gradient de densité, le problème est similaire à l'instabilité de Rayleigh-Taylor en géométrie sphérique. Nous présentons les résultats préliminaires de nos simulations à très haute résolution pour des petits nombres d'onde sur une sphère en tenant compte de la tension de surface durant les premières phases de l'instabilités. La phase turbulente n'est pas abordée. Pour de grand nombre d'onde, nous avons suivi l'évolution de différent motifs de la condition initiale jusque dans la phase non-linéaire. Un troisième problème est considéré pour un forçage horizontal d'une interface plane. Nous avons reproduit à l'aide de notre solver numérique les expériences de Yoshikawa and Wesfreid (2011b). L'interface entre deux fluides stablement stratifiés avec un fort contraste de viscosité est soumise à un cisaillement oscillant horizontal et oscillant . Le problème est celui de l'instabilité de Kelvin-Helmholtz oscillant. Les simulations numériques reproduisent avec succès la croissance et l'évolution de l'interface. nous distinguons deux régimes où l'interface adopte un comportement qualitativement différent dont un nouvel état à saturation est mis en évidence. Nous avons obtenu que pour ce nouvel état l'interface se déstabilise via une première bifurcation fourche supercritique. Cet état semble subir une seconde bifurcation lorsque la fréquence de forçage dépasse un second seuil avec une transition sous-critique, où deux états existent pour les mêmes paramètres de forçages. / We consider in this thesis the stability problem of a spherical drop subjected to a radial bulk force for two different configurations consisting of an oscillating (with or without a constant component) and a constant force. To do so, we use a full three-dimensional parallel front-tracking code for incompressible multiphase flow to calculate the interface motion. The first configuration consist to the spherical analogue of the Faraday instability. We linearize the governing equations about the state of rest and decompose deformations of the interface as spherical harmonics. Generalizing the Kumar & Tuckerman (1994) Floquet procedure to a spherical interface, we present a linear stability analysis for the appearance of standing waves. The most unstable spherical mode at onset predicted by the linear theory agrees with full three-dimensional nonlinear numerical simulations. The second configuration consists to the spherical analogue of the Rayleigh-Taylor instability when the force is oriented from the heavier to the lighter fluid. We performed numerical simulations for both high and low spherical modenumbers and followed their evolutions up to the nonlinear stage. Finally, we consider a plane interface subjected to an horizontal oscillatory forcing which is called the oscillatory Kelvin-Helmholtz instability. We consider the experimental configuration proposed by Yoshikawa and Wesfreid (2011b) for stably stratified fluids with a high viscosity contrast. Numerical simulations reproduce succesfully the growth and the evolution of the interface. We distinguish a new regime for the interface saturation which was not observed by the original experiment. We obtained a subcritical transition between the two different regimes.

Self-organizing patterns arise in a variety of ways in nature, the complex patterning observed on animal coats is such an example. It is already known that the mechanisms responsible for pattern formation starts at the developmental stage of an embryo. However, the actual process determining cell fate has been, and still is, unknown. The mathematical interest for pattern formation emerged from the theories formulated by the mathematician and computer scientist Alan Turing in 1952. He attempted to explain the mechanisms behind morphogenesis and how the process of spatial cell differentiation from homogeneous cells lead to organisms with different complexities and shapes. Turing formulated a mathematical theory and proposed a reaction-diffusion system where morphogens, a postulated chemically active substance, moderated the whole mechanism. He concluded that this process was stable as long as diffusion was neglected; otherwise this would lead to a diffusion-driven instability, which is the fundamental part of pattern formation. The mathematical theory describing this process consists of solving partial differential equations and Turing considered deterministic reaction-diffusion systems.   This thesis will start with introducing the reader to the problem and then gradually build up the mathematical theory needed to get an understanding of the stochastic reaction-diffusion systems that is the focus of the thesis. This study will to a large extent simulate stochastic systems using numerical computations and in order to be computationally feasible a compartment-based model will be used. Noise is an inherent part of such systems, so the study will also discuss the effects of noise and morphogen kinetics on different geometries with boundaries of different complexities from one-dimensional cases up to three-dimensions.

In this thesis we show how reactive processes can be affected by the presence of different types of spatial constraints, so much so that their nonlinear dynamics can be qualitatively altered or that new and unexpected behaviors can be produced. To understand how this interplay can occur in general terms, we theoretically investigate four very different examples of this situation. <p><p>The first system we study is a reversible trimolecular chemical reaction which is taking place in closed one-dimensional lattices. We show that the low dimensionality may or may not prevent the reaction from reaching its equilibrium state, depending on the microscopic properties of the molecular reactive mechanism. <p><p>The second reactive process we consider is a network of biological interactions between pigment cells on the skin of zebrafish. We show that the combination of short-range and long-range contact-mediated feedbacks can promote a Turing instability which gives rise to stationary patterns in space with intrinsic wavelength, without the need of any kind of motion.<p><p>Then we investigate the behavior of a typical chemical oscillator (the Brusselator) when it is constrained in a finite space. We show that molecular crowding can in such cases promote new nonlinear dynamical behaviors, affect the usual ones or even destroy them. <p><p>Finally we look at the situation where the constraint is given by the presence of a solid porous matrix that can react with a perfect gas in an exothermic way. We show on one hand that the interplay between reaction, heat flux and mass transport can give rise to the propagation of adsorption waves, and on the other hand that the coupling between the chemical reaction and the changes in the structural properties of the matrix can produce sustained chemomechanical oscillations. <p><p>These results show that spatial constraints can affect the kinetics of reactions, and are able to produce otherwise absent nonlinear dynamical behaviors. As a consequence of this, the usual understanding of the nonlinear dynamics of reactive systems can be put into question or even disproved. In order to have a better understanding of these systems we must acknowledge that mechanical and structural feedbacks can be important components of many reactive systems, and that they can be the very source of complex and fascinating phenomena.<p> / Doctorat en Sciences / info:eu-repo/semantics/nonPublished