In order to rationally optimize a reaction, it is necessary to have a thorough understanding of its mechanism. Consequently, great effort has been made to elucidate a variety of reaction mechanisms. However, the fundamental ideas needed to understand reaction mechanisms are not yet fully developed. Throughout the literature, one encounters numerous examples of experimental observations that are not explainable by conventional mechanistic ideas and methods. The research described in this dissertation employs a unique approach towards the identification and analysis of systems whose observations cannot be explained by conventional transition state theory (TST). The nucleophilic substitution of 4,4-dichloro-but-3-en-2-one by sodium-para-tolyl-thiolate was explored. It was deduced that the reaction was concerted and consequently, the product selectivity observed in the reaction cannot be explained by TST. Dynamic effects play a major role in the observed selectivity and this is further supported by the results of dynamic trajectory simulations. Using computational studies, the ethanolysis of symmetric aryl carbonates was also shown to be concerted, provided that the substrate possesses good leaving groups. Furthermore, extensive precedence has been set by Gutthrie, Santos, Schelgel, and others, detailing concerted substitutions at acyl carbon. The Fujiwara hydroarylation is thought to occur by either a C-H activation mechanism or an electrophilic aromatic substitution (EAS). The KIEs associated with this reaction have been determined and provide strong support for the latter. Computational studies also displayed fair agreement with experimentally determined KIEs, further supporting the EAS mechanism. Isotopic perturbation of equilibria is invaluable in helping to determine whether a structure exists as a single structure or whether it is a time average of two equilibrating structures. The bromonium cation of tetramethylethylene and hydrogen pthalate have been wrongly reported as existing as equilibrating structures. The time averaged geometries have been determined in each case, via a variety of methods and the myth of equilibrating structures in the above cases has been debunked.

Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations.

Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations.

Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations.

Numerical simulations of Mach shock reflections have shown that the Mach stem can bifurcate as a result of the slip line jetting forward. Numerical simulations were conducted in this study which determined that these bifurcations occur when the Mach number is high, the ramp angle is high, and specific heat ratio is low. It was clarified that the bifurcation is a result of a sufficiently large velocity difference across the slip line which drives the jet. This bifurcation phenomenon has also been observed after triple point collisions in detonation simulations. A triple point reflection was modelled as an inert shock reflecting off a wedge, and the accuracy of the model at early times after reflection indicates that bifurcations in detonations are a result of the shock reflection process. Further investigations revealed that bifurcations likely contribute to the irregular structure observed in certain detonations.

Shallow marine environments from the Lower Cambrian period were very different to shallow marine environments of today. Tubes of what was thought to be silica recovered from a partly dolomitized carbonate sample collected form a site near Indian Springs, Nevada could help further understand the chemistry and characteristics of such environments. The aim of this study is to present a detailed morphological description of the tubular structures found in the rock sample as well as to give a description of the environment in which they were produced. This was achieved by first studying the samples with several different analytical techniques including Scanning Electron Microscopy (SEM) and Energy-dispersive X-ray spectroscopy (EDS) and subsequent evaluation of the obtained data. This resulted in the discovery that the tubular structures have a wall mainly consisting of non-detrital silica crystals. The crystals are arranged in string-like structures which overlap to form tube walls of varying thicknesses. The observed tubular structures are typically straight and ca. 0,23 to 0,25 mm long, but slightly curved and rare bifurcating tubes were also seen. The elemental mapping of a thin section of tubes showed that the wall-forming crystals consist mainly of silica (SiO2), however, small concentrations of calcium (Ca) were found inside many of the silica crystals leading to the conclusion that positive calcium ions may have acted as a seed for the silica crystals. A comparison of the tubular structures with other tubular fossils of the same geological time period is presented as well as a discussion of whether the specimens are of biological origin, and consequently a biosignature, as these could be used in future research when studying material from other planetary bodies. / Grunda marinmiljöer i nedre Kambrium var väldigt annorlunda från grunda marinmiljöer som finns idag. Små rör av vad som hypotiserades vara kiseloxid upptäckta i en dolomitiserad kalkstenstuff från Indian Springs, Nevada skulle kunna hjälpa att förstå kemin inblandad i bildandet av dessa samt bildningsmiljön i mer detalj. Syftet med detta projekt är att presentera en detaljerad morfologisk beskrivning av dessa rör samt försöka beskriv miljön i vilken de bildades. Undersökningen gjorde genom att först studera rören med olika mikroskoperingsmetoder inklusive ett optiskt mikroskop samt med ett svepelektronmikroskop (SEM), sedan analyserades proverna med Energidispersiv röntgenspektroskopi (EDS) för att detektera och kartera de grundämnena som fanns i rören. Resultaten av dessa metoder är att rören är cylindriska eller cigarrformade samt har en väggstruktur av kiseldioxidkristaller som sitter ihop som strängar av pärlor. Rören är huvudsakligen raka och har en längd på mellan 0,23 och 0,25mm, även böjda och förgrenade rör hat hittats, dock var mer sällsynta än de raka. Den kemiska analysen av ett tunnslip på några rör visade att de består till mestadels av kiseldioxid (SiO2) men koncentrationer av kalcium (Ca) hittades som indikerar att dessa kanske agerade som små frön för kiseldioxid att växa runt. En jämförelse av dessa rör med andra liknande fossilmed samma struktur och från samma tidsperiod är presenterad samt en diskussion kring rören som biosignatur och dess potentiella biologiskt ursprung samt användning i framtida forskning inom ämnet.

Cette thèse étudie la stabilité linéaire et le contrôle linéaire optimal d’écoulements périodiques en temps. Le cadre d'étude développé a été appliqué au jet rond pulsé.Lorsqu'un jet rond laminaire est forcé au niveau de sa buse périodiquement et de façon axisymétrique, une allée régulière d'anneaux de vorticité se forment. Dans cette configuration, nous étudions deux types d’instabilités. D'une part, de façon intrinsèque, un appariement tourbillonnaire peut parfois survenir. D'autre part, l'ajout d'un terme hélicoïdal sous-harmonique au forçage axisymétrique peut générer un jet bifurqué. Ces deux phénomènes conduisent à une importante augmentation de l'évasement du jet et à une amélioration de ses propriétés de mélange.Tout d'abord, nous présentons une méthode de stabilisation d’orbites périodiques instables, basée sur un contrôle avec un retard temporel. Cette technique, appliquée au cas du jet pulsé, fournit un écoulement périodique non-apparié, dans des gammes de paramètres où l'appariement surgit naturellement. Cet écoulement non-apparié forme la base des études de stabilité et d’optimisation suivantes.Ensuite, nous étudions la dynamique intrinsèque des perturbations de cet état. D'une part, grâce à la théorie de Floquet, nous calculons sa stabilité modale, ce qui prédit le comportement à long-terme de ces perturbations. Pour ce faire, une base de Krylov est construite à l'aide d'une méthode d'Arnoldi par blocs à partir de simulations temporelles. D'autre part, nous caractérisons sa croissance transitoire, qui contrôle le comportement à court-terme des perturbations. Tandis que l'analyse de Floquet prédit avec précision les nombres de Reynolds et de Strouhal critiques pour observer une croissance modale sur le long terme des perturbations puis un appariement, la croissance non-modale contrôle entièrement la bifurcation entre l’état non-apparié et l’état apparié.Enfin, nous optimisons le déclenchement de la bifurcation du jet. Ainsi, le forçage hélicoïdal maximisant l'évasement et le mélange du jet dans un plan préférentiel est calculé. Nous comparons ensuite par simulation numérique directe l'efficacité de ce forçage avec des forçages ad hoc utilisés dans des études précédentes. Le forçage optimal déclenche la bifurcation beaucoup plus tôt, avec un évasement bien plus marqué, et pour une gamme de nombres de Strouhal bien plus large que les forçages précédents. / This thesis describes the linear instability analysis and the design of linear optimal control of time-periodic flows. The numerical framework developed is applied to the study of pulsed jets.When a laminar round jet is forced axisymmetrically and time-periodically at the inlet, a regular street of vortex rings is formed. Two instability phenomena of such arrays are investigated. Firstly, intrinsic mechanisms may trigger vortex pairing. Secondly, if an additional subharmonic helical component is superposed onto the fundamental axisymmetric forcing, jet bifurcation is induced. Both phenomena result in strongly increased spreading and mixing in the mean flow.In a first step, a numerical stabilisation technique is devised, allowing the computation of exact periodic flow solutions, even when they are subject to instrinsic instabilities. This method, based on a time-delayed feedback, is then applied in order to recover unpaired periodic flow states of pulsed jets, in parameter regimes where vortex pairing naturally occurs. These unpaired flow states form the basis for the following instability and optimal control calculations.In a second step, the instrinsic perturbation dynamics in pulsed jets is investigated. Modal instability properties, governing the long-time flow behaviour, are examined in the framework of Floquet theory. Numerically, a Krylov basis is constructed from linear time-stepping using a block-Arnoldi algorithm to maximise efficiency. Transient dynamics, governing the short-time growth of initial perturbations, are characterised by an optimal perturbation analysis. While the modal Floquet analysis accurately predicts the critical Reynolds and Strouhal numbers of the long-time occurrence of vortex pairing, transient growth dynamics dominates the bifurcation.Finally, the optimal way to trigger jet bifurcation through subharmonic inlet forcing is computed. Inlet helical forcing is identified that maximises the jet spreading and mixing in one privileged meridional plane. This optimal forcing is implemented in direct numerical simulations, and its efficiency in the nonlinear regime is compared to that of ad hoc forcing used in previous studies. The optimal forcing results in bifurcation further upstream, at higher spreading angles, and over a much wider range of Strouhal numbers than found previously.

Cette thèse porte essentiellement sur l'étude des solutions stationnaires, en dimension 1 d'espace, d'unmodèle de champs de phase cristallin introduit par Elder en 2002. Ainsi, nous prouvons, par la méthode deréduction de Lyapunov-Schmidt et la technique des multiparamètres, l'existence de courbes de solutionsbifurquantes stationnaires lorsque le noyau de l'opérateur linéarisé, au voisinage de la solution triviale estde dimension 2. Une parenthèse est ouverte pour la comparaison de l'énergie de la solution bifurquantepar rapport à celle la solution triviale. Aussi, grâce au principe de la stabilité réduite, nous fournissonsdes ensembles précis de valeurs des paramètres de bifurcation pour lesquelles les solutions obtenues sontstables ou instables. Ces résultats théoriques sont corroborés par plusieurs tests numériques.Par ailleurs, dans le cas classique du noyau unidimensionel, nous établissons des diagrammes de phasespermettant de comprendre les différentes orientations de courbes de solutions non triviales au voisinage dechaque point de bifurcation. / This thesis is devoted to the study of stationary solutions of a Phase Field Crystal model, in one spacedimension, introduced by Elder in 2002. Thus, we prove by the Lyapunov-Schmidt method of reductionand the multiparameter technique, the existence of the curves of bifurcating stationary solutions whenthe kernel of the linearized operator near to trivial solution is of two dimension. A parenthesis is open forcomparing the energies of the bifurcating solution and the trivial solution. Also, thanks to the principle ofreduced stability, we provide specific sets of parameter values for wich the obtained solutions are stable orunstable. These theoretical results are confirmed by several numerical tests.Moreover, in the classical case of a one dimensional kernel, we establish the phase diagrams allowing tounderstand the different orientations of non-trivial solutions curves near to of each bifurcation point.

Numerical simulations of the complex flows of complex (viscoelastic) fluids are investigated. The primary fluid investigated in this thesis is human blood, a complex fluid which can be modelled via viscoelastic constitutive models. The most commonly used constitutive models for viscoelastic fluids include the OldroydB, Giesekus, Johnson-Segalman, Finitely Extensible Non-Linear Elastic (FENE), Phan-Thein-Tanner (PTT) models etc. Our Numerical approach is based on the finite volume methods implemented on the OpenFOAM platform. We employ the Giesekus, Oldroyd-B, and Generalized Oldroyd-B viscoelastic constitutive models in this thesis, depending on the underlying context. Numerical validation of our results is conducted via the most used benchmark flow problems for viscoelastic fluid flow. The robust and efficient numerical methodologies are then deployed to investigate the flow characteristics, and hence illustrate various novel behavior, for blood flow in stenosed and bifurcated arteries. The present work took advantage of the availability of a reasonable set of viscoelastic constitutive model solvers within OpenFOAM, specifically the viscoelasticFluidFoam solver which we modified and developed to suit our focused needs for blood flow computations. The modified computational algorithms were successfully validated against well-known benchmark flow problems in the literature. Noting that the Giesekus viscoelastic constitutive model is a generalization of both the Oldroyd-B and Generalized Oldroyd-B models, the validation of results is carried out via the Giesekus model enabling us to develop a general-purpose code capable of simulating several viscoelastic constitutive models. The main results were otherwise presented for the Oldroyd-B and Generalized Oldroyd-B models as these are the most applicable to blood flow modelling. The results demonstrate that the velocity spurt through the stenosis is directly proportional to the constriction caused by the stenosis. The higher the blockage from the constriction, the higher the corresponding velocity spurt through the constriction. This velocity behavior, as the constriction blockage increases, correspondingly increase the wall shear stresses. High wall shear stresses significantly increase the possibility of rupture of the stenosis/blockage. This can lead to catastrophic consequences in the usual case where the stenosis is caused by tumor growth.

Cette étude théorique est pensée en lien étroit avec un champ d'application : il s'agit de modéliser la croissance d'une population de cellules qui se divisent selon un taux de division inconnu, fonction d’une variable dite structurante – l’âge et la taille des cellules étant les deux exemples paradigmatiques étudiés. Le champ mathématique afférent se situe à l'interface de la statistique des processus, de l’estimation non-paramétrique et de l’analyse des équations aux dérivées partielles. Les trois objectifs de ce travail sont les suivants : reconstruire le taux de division (fonction de l’âge ou de la taille) pour différents schémas d’observation (en temps généalogique ou en temps continu) ; étudier la transmission d'un trait biologique général d'une cellule à une autre et étudier le trait d’une cellule typique ; comparer la croissance de différentes populations de cellules à travers le paramètre de Malthus (après introduction de variabilité dans le taux de croissance par exemple). / This work is concerned with growth-fragmentation models, implemented for investigating the growth of a population of cells which divide according to an unknown splitting rate, depending on a structuring variable – age and size being the two paradigmatic examples. The mathematical framework includes statistics of processes, nonparametric estimations and analysis of partial differential equations. The three objectives of this work are the following : get a nonparametric estimate of the division rate (as a function of age or size) for different observation schemes (genealogical or continuous) ; to study the transmission of a biological feature from one cell to an other and study the feature of one typical cell ; to compare different populations of cells through their Malthus parameter, which governs the global growth (when introducing variability in the growth rate among cells for instance).