A prominent feature of many practical flows is the hydrodynamic wave system attached to moving bodies or concentrations of vorticity. Sound waves are usually present, and these act as a mechanism for energy and momentum transport. With their source rooted in the unsteadiness of the flow, they can sometimes play an important role in determining the general flow structure, particularly if the flow is unstable. In this thesis we investigate the basic connection between sound, and hydrodynamic waves. By analysing the waves attached to boundaries which are in prescribed unsteady motion, details emerge concerning the linear production of sound from hydrodynamic motions. We show that the abrupt arrest or commencement of a steady hydrodynamic wave causes the production of a quantity of sound energy exactly equalling that of the hydrodynamic wave. For more gentle modulations of the steady state, we identify those aspects of the evolving hydrodynamic field which determine how much sound is produced. These results are used to suggest ways to improve procedures for minimising the noise from vibrating surfaces. According to linear theory, when waves on an infinite fluid boundary travel at sonic speed the fluid response is infinite. We use the ideas developed to cope with the sound generation problem to investigate the effects of unsteady transonic motion. We give a detailed analysis of acoustic 'Cerenkov radiation', which would occur if a body travelled through an inviscid medium supersonically, and decelerated to a subsonic speed. We assess the degree to which non-linear transonic effects are important. Sound waves are known to be a critical factor leading to the destabilisation of line vortices, and we were intrigued to know whether compressibility has a corresponding effect on the stability of a rigid body moving steadily in an irrotational, inviscid flow. Our investigation reveals that the motion is always stable.

Energy Benefit in Tidal Power Schemes' by Helen Suckling Abstract Predictions of energy output from a barrage in the Severn Estuary can be made by using a mathematical model describing the operation of the barrage linked to one of tidal flow. Estimates of the likely energy production from such a barrage have been made using a flat surface model of the estuary which incorporates real machinery operating characteristics. The flow through the barrage can be controlled optimally in order to obtain the greatest amount of energy from the tides. The energy predictions made by using the flat surface model are examined using a hydrodynamic model of flow in the estuary. A simple one-dimensional hydrodynamic model of the tidal flow in the Severn Estuary is presented. The area of the estuary under consideration is that which lies between approximately Berkeley in Gloucestershire and 11 fracombe on the North Devon coast. The only open boundary is assumed to be the seaward boundary. No account is taken of flow into the estuary from rivers. Finite amplitude shallow water wave equations, together with a representation of bottom friction, are used to describe the tidal behaviour in the estuary. The crosssectional topography of the estuary is assumed to be a rectangle. The boundary conditions are that there is no flow through the landward boundary and the water level at the seaward boundary is a known function of time. The equations are solved numerically as a system of ordinary differential equations. A simple Runge-Kutta method is used. The mqdel is used to obtain predictions of the level and time of high and low tide at certain points along the estuary. The results are compared with those obtained by using another, but more complex, onedimensional model. In the region of computation, the accuracy of the results of the two models are comparable. The effect of varying both the coefficient of friction and the form of the friction term is examined. The effect of linearizing the governing equations is also studied. A model of a tidal power barrage, sited between Weston-super-Mare and Cardiff, is then incorporated into the hydrodynamic model. The operation 'of the barrage is determined by using an open loop control, obtained by using a flat surface model of the estuary. The extent to which hydrodynamic effects may modify the energy predictions made by the flat surface are examined. variation of the time at which generation is allowed to start is found to affect the amount of energy predicted by the hydrodynamic model. The costate equations, which are necessary for the solution of the optimal control problem are derived, but the solution of these equations is not presented

This thesis focuses on the analysis of the role of adhesion between substrate and cell and factors of Quorum sensing on the migration of Dictyostelium amoeba. Tools to automate the recordings of videomicroscopy and image analysis have been developed to work with very large samples of cells and toquantify cell migration. A microfluidic device for cell detachment in hydrodynamic flow combined witha motorized stage has allowed a statistical study of adhesion but also the dynamics of detachment. The analysis of the migration of Dictyostelium in non nutritive medium highlights the role of density on celldifferentiation and migration capacity. We observe the presence of a maximum speed of migration after6 hours of starvation. We show that the adhesion to glass is twice as low in deprivation buffer as inthe nutrient medium. The experiences of migration in growth medium revealed the presence of a factorof detection of density secreted by the cells and regulating their random migration. The diffusion coefficient, the persistence of the movement and morphology of cells vary depending on the concentrationof this factor. This factor does not affect cell adhesion but only the dynamics of detachment. Finally, the testing protocol developed allowed us to make a comparative study of migration by varying otherparameters such as surface or the chemical composition of experimental medium. This work concludesby outlining the possible role of adhesion to the migration of Dictyostelium in nutrient medium.

Cette thèse est centrée sur l’analyse du rôle de l’adhésion cellule-substrat et des facteurs de détectionde Quorum sur la migration amibienne de Dictyostelium . Des outils pour automatiser les enregistrementsde vidéoomicroscopie et l’analyse d’image ont été développés afin de travailler avec de trèsgrands échantillons de cellules et de quantifier la migration cellulaire. Un dispositif microfluidique dedétachement cellulaire sous flux hydrodynamique combiné une platine motorisée a permis une étude statistique de l’adhésion mais aussi de la dynamique de détachement. L’analyse de la migration de Dictyostelium en milieu non nutritif met en évidence le rôle de la densité sur la différentiation des celluleset leur capacité de migration. Nous observons la présence d’une vitesse maximale de migrationaprès 6h de carence. Nous montrons que l’adhésion sur verre est deux fois plus faible en milieu carenc´equ’en milieu nutritif. Les exp´eriences de migration en milieu nutritif ont révélé la présence d’un facteur de détection de densité sécrété par les cellules et régulant leur migration aléatoire. Le coefficient de diffusion, la persistance du mouvement et la morphologie des cellules varient en fonction de la concentrationde ce facteur. Ce facteur ne modifie pas l’adhésion cellulaire mais uniquement la dynamique de d´etachement. Enfin, le protocole d’analyse développé nous a permis de faire une étude comparative de la migration en faisant varier d’autres paramètres tel que la surface ou la composition chimique du milieu expérimental. Ce travail se conclue en exposant le possible rôle de l’adhésion sur la migrationchez Dictyostelium en milieu nutritif. / This thesis focuses on the analysis of the role of adhesion between substrate and cell and factors of Quorum sensing on the migration of Dictyostelium amoeba. Tools to automate the recordings of videomicroscopy and image analysis have been developed to work with very large samples of cells and toquantify cell migration. A microfluidic device for cell detachment in hydrodynamic flow combined witha motorized stage has allowed a statistical study of adhesion but also the dynamics of detachment. The analysis of the migration of Dictyostelium in non nutritive medium highlights the role of density on celldifferentiation and migration capacity. We observe the presence of a maximum speed of migration after6 hours of starvation. We show that the adhesion to glass is twice as low in deprivation buffer as inthe nutrient medium. The experiences of migration in growth medium revealed the presence of a factorof detection of density secreted by the cells and regulating their random migration. The diffusion coefficient, the persistence of the movement and morphology of cells vary depending on the concentrationof this factor. This factor does not affect cell adhesion but only the dynamics of detachment. Finally, the testing protocol developed allowed us to make a comparative study of migration by varying otherparameters such as surface or the chemical composition of experimental medium. This work concludesby outlining the possible role of adhesion to the migration of Dictyostelium in nutrient medium.

In this thesis the interplay between hydrodynamic transport and specific adhesion is theoretically investigated. An important biological motivation for this work is the rolling adhesion of white blood cells experimentally investigated in flow chambers. There, specific adhesion is mediated by weak bonds between complementary molecular building blocks which are either located on the cell surface (receptors) or attached to the bottom plate of the flow chamber (ligands). The model system under consideration is a hard sphere covered with receptors moving above a planar ligand-bearing wall. The motion of the sphere is influenced by a simple shear flow, deterministic forces, and Brownian motion. An algorithm is given that allows to numerically simulate this motion as well as the formation and rupture of bonds between receptors and ligands. The presented algorithm spatially resolves receptors and ligands. This opens up the perspective to apply the results also to flow chamber experiments done with patterned substrates based on modern nanotechnological developments. In the first part the influence of flow rate, as well as of the number and geometry of receptors and ligands, on the probability for initial binding is studied. This is done by determining the mean time that elapses until the first encounter between a receptor and a ligand occurs. It turns out that besides the number of receptors, especially the height by which the receptors are elevated above the surface of the sphere plays an important role. These findings are in good agreement with observations of actual biological systems like white blood cells or malaria-infected red blood cells. Then, the influence of bonds which have formed between receptors and ligands, but easily rupture in response to force, on the motion of the sphere is studied. It is demonstrated that different states of motion-for example rolling-can be distinguished. The appearance of these states depending on important model parameters is then systematically investigated. Furthermore, it is shown by which bond property the ability of cells to stably roll in a large range of applied flow rates is increased. Finally, the model is applied to another biological process, the transport of spherical cargo particles by molecular motors. In analogy to the so far described systems molecular motors can be considered as bonds that are able to actively move. In this part of the thesis the mean distance the cargo particles are transported is determined. / In der vorliegenden Arbeit wird das Zusammenspiel zwischen hydrodynamischem Transport und spezifischer Adhäsion theoretisch untersucht. Eine wichtige biologische Motivation für diese Arbeit ist die rollende Adhäsion weißer Blutkörperchen, die experimentell in Flusskammern untersucht wird. Die spezifische Adhäsion wird durch schwache Bindungen zwischen komplementären molekularen Bausteinen vermittelt, die sich einerseits auf der Zelloberfläche, Rezeptoren genannt, andererseits auf der unteren begrenzenden Platte der Flusskammer, Liganden genannt, befinden. Das untersuchte Modellsystem besteht aus einer festen Kugel, die mit Rezeptoren bedeckt ist und sich unter dem Einfluss einer einfachen Scherströmung, deterministischer Kräfte und der Brownschen Molekularbewegung oberhalb einer mit Liganden bedeckten Wand bewegt. Es wird ein Algorithmus angegeben, mit dessen Hilfe diese Bewegung sowie das Entstehen und Reißen von Bindungen zwischen Rezeptoren und Liganden numerisch simuliert werden kann. In der numerischen Modellierung werden die Positionen von Rezeptoren und Liganden räumlich aufgelöst, wodurch sich die Möglichkeit ergibt, die Ergebnisse auch mit Flusskammerexperimenten, in denen moderne nanotechnologisch strukturierte Substrate verwendet werden, zu vergleichen. Als Erstes wird der Einfluss von Strömungsrate sowie Zahl und Form der Rezeptoren bzw. Liganden auf die Wahrscheinlichkeit, mit der es zu einer Bindung kommen kann, untersucht. Hierfür wird die mittlere Zeit bestimmt, die vergeht bis zum ersten Mal ein Rezeptor mit einem Liganden in Kontakt kommt. Dabei stellt sich heraus, dass neben der Anzahl der Rezeptoren auf der Kugel insbesondere der Abstand, welchen die Rezeptoren von der Oberfläche haben, eine große Rolle spielt. Dieses Ergebnis ist in sehr guter Übereinstimmung mit tatsächlichen biologischen Systemen wie etwa weißen Blutkörperchen oder mit Malaria infizierten roten Blutkörperchen. Als Nächstes wird betrachtet, welchen Einfluss Bindungen haben, die sich zwischen Rezeptoren und Liganden bilden, aber unter Kraft auch leicht wieder reißen. Dabei zeigt sich, dass verschiedene Bewegungstypen auftreten, beispielsweise Rollen, deren Erscheinen in Abhängigkeit wichtiger Modellparameter dann systematisch untersucht wird. Weiter wird der Frage nachgegangen, welche Eigenschaften von Bindungen dazu führen können, dass Zellen in einem großen Bereich von Strömungsraten ein stabiles Rollverhalten zeigen. Abschließend wird das Modell auf einen etwas anderen biologischen Prozess angewendet, nämlich den Transport kugelförmiger Lastpartikeln durch molekulare Motoren. In Analogie zu den bisher beschriebene Systemen können diese molekularen Motoren als sich aktiv bewegende Bindungen betrachtet werden. In diesem Teil der Arbeit wird ermittelt, wie weit die Lastpartikel im Mittel transportiert werden.