The Casimir force for charge-neutral, perfect conductors of non-planar geometric configurations have been investigated. The configurations were: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical shell. The resulting Casimir forces for these physical arrangements have been found to be attractive. The repulsive Casimir force found by Boyer for a spherical shell is a special case requiring stringent material property of the sphere, as well as the specific boundary conditions for the wave modes inside and outside of the sphere. The necessary criteria in detecting Boyer's repulsive Casimir force for a sphere are discussed at the end of this thesis. / Ph. D.

Casimir forces originating from vacuum fluctuations of the electromagnetic fields are of increasing importance in many scientific and technological areas. The manifestations of these long-range forces at the nanoscale have led to the need of better understanding of their contribution in relation to the stability of different physical systems as well as the operation of various technological components and devices. This dissertation presents mathematical and theoretical methods to calculate the Casimir interaction in various infinitely long cylindrical nanostructures. A dielectric-diamagnetic cylindrical layer immersed in a medium is first considered. The layer has a finite thickness characterized with specific dielectric and magnetic properties. Another system considered is that of perfectly conducting concentric cylindrical shells immersed in a medium. The electromagnetic energy between two infinitely long straight parallel dielectric-diamagnetic cylinders immersed in a medium is also considered. The mode summation method is used to calculate the Casimir energy of all these systems. The energy dependence on the cylindrical radial curvature and dielectric response of the cylinders is investigated. The fundamental effects of these long range interactions are studied in the form of exciton-plasmon interactions in carbon nanotubes and this is achieved by looking at the dielectric response of carbon nanotubes.

Casimir force is a cause of stiction (adhesion) between metal surfaces in Micro-Electro Mechanical Systems (MEMS). Casimir Force depends strongly on the separation of the two surfaces and the contact area. This thesis reviews the theory and prior experimental demonstrations of the Casimir force. Then the Casimir attractive force is calculated for a particular MEMS cantilever device, in which the metal cantilever tip is required to repeatedly touch and release from a metal tip pad on the substrate surface in response to a periodic driving electrostatic force. The elastic force due to the bending of the cantilever support arms is also a consideration in the device operation. The three forces are calculated analytically and compared as a function of cantilever tip height. Calculation of the electrostatic force uses coefficients of capacitance and electrostatic induction determined numerically by the finite element method, including the effect of permittivity for the structural oxide. A condition on the tip area to allow electrostatic release of the tip from the surface against Casimir sticking and elastic restoring forces is established.

The physical reasons why the Drude dielectric function is not compatible with the Lifshitz formula, as opposed to the generalized plasma-like permittivity, are presented. Essentially, the problem is connected with the applicability conditions of the Lifshitz theory. It is shown that the Lifshitz theory combined with the generalized plasma-like permittivity is thermodynamically consistent.

This thesis considers the problem of determining Casimir-Lifshitz forces in inhomogeneous media. The ground-state energy of the electromagnetic field in a piston-geometry is discussed. When the cavity is empty, the Casimir pressure on the piston is finite and independent of the small-scale physics of the media that compose the mirrors. However, it is demonstrated that, when the cavity is filled with an inhomogeneous dielectric medium, the Casimir energy is cut-off dependent. The local behavior of the stress tensor commonly used in calculations of Casimir forces is also determined. It is shown that the usual expression for the stress tensor is not finite anywhere within such a medium, whatever the temporal dispersion or index profile, and that this divergence is unlikely to be removed by modifying the regularisation. These findings suggest that the value of the Casimir pressure may be inextricably dependent on the detailed behavior of the mirror and the medium at large wave vectors. This thesis also examines two exceptions to this rule: first, the case of an idealised metamaterial is considered which, when introduced into a cavity, reduces the magnitude of the Casimir force. It is shown that, although the medium is inhomogeneous, it does not contribute additional scattering events but simply modifies the effective length of the cavity, so the predicted force is finite and can be stated exactly. Secondly, a geometric argument is presented for determining a Casimir stress in a spherical mirror filled with the inhomogeneous medium of Maxwell's fish-eye. This solution questions the idea that the Casimir force of a spherical mirror is repulsive, but prompts additional questions concerning regularisation and the role of non-local effects in determining Casimir forces.

The Planck constant is one of the most important constants in nature, as it describes the world governed by quantum mechanics. However, it cannot be derived from other natural constants. We present a model from which it is possible to derive this constant without any free parameters. This is done utilizing the force between two oscillating electric dipoles described by an extension of Weber electrodynamics, based on a gravitational model by Assis. This leads not only to gravitational forces between the particles but also to a newly found Casimir-type attraction. We can use these forces to calculate the maximum point mass of this model which is equal to the Planck mass and derive the quantum of action. The result hints to a connection of quantum effects like the Casimir force and the Planck constant with gravitational ones and the origin of mass itself.

The Planck constant is one of the most important constants in nature, as it describes the world governed by quantum mechanics. However, it cannot be derived from other natural constants. We present a model from which it is possible to derive this constant without any free parameters. This is done utilizing the force between two oscillating electric dipoles described by an extension of Weber electrodynamics, based on a gravitational model by Assis. This leads not only to gravitational forces between the particles but also to a newly found Casimir-type attraction. We can use these forces to calculate the maximum point mass of this model which is equal to the Planck mass and derive the quantum of action. The result hints to a connection of quantum effects like the Casimir force and the Planck constant with gravitational ones and the origin of mass itself.

À l'approche d'un point critique, la divergence de la longueur de corrélation des fluctuations peut être tronquée par le confinement du système. Cette troncature engendre des effets de taille finie présentant des caractères universels au sein d'un classe de transitions de phases.Nous nous sommes intéressés particulièrement à la classe d'universalité du modèle d'Ising, regroupant notamment les transitions de phase ferro/paramagnétique pour les systèmes magnétiques uniaxiaux, la transition liquide/gaz et encore la démixtion de mélanges binaires. Nous présentons tout d'abord une introduction aux phénomènes critiques, à l'universalité, au « finite-size scaling » et aux simulations Monte Carlo du modèle d'Ising, sur lesquelles se fondent la majeur partie de ce travail.Un effet de taille finie ayant attiré une grande attention durant les dernières dizaines d'années est la force de Casimir critique. Les travaux théoriques et numériques concernant cette force ont, dans leur quasi totalité, été menés dans des systèmes magnétiques modèles, tel que les modèles d'Ising ou XY. Par contre, les approches expérimentales ont toutes été réalisées dans des systèmes fluides, tels que des mélanges binaires ou de l'hélium IV proche de la transition superfluide.Une motivation de ce travail a été de chercher a résoudre cette situation paradoxale en proposant, d'une part, un protocole expérimental pour la mesure de la force de Casimir dans une couche mince magnétique et, d'autre part, une approche numérique dans un mélange binaire de type Lennard-Jones. Cette dernière approche présente l'avantage d'ouvrir la porte à des études des fluctuations de la force de Casimir ou encore hors-équilibre. / Approaching a critical point, the divergence of the correlation length of fluctuations can be cut-off by a confinement of the system. This truncation fosters finite size effects with universal features in a class of continuous phase transitions. We are particularly interested in the Ising universality class, regrouping transitions such as the ferromagnetic/paramagnetic transition for uniaxial magnetic systems, the liquid/gas tran- sition and the demixing of binary mixtures. We will first present an introduction to critical phenomena, universality, finite-size scaling and Monte Carlo simulations of the Ising model, on which a major part of this work relies.A finite size effect that has particularly drawn attention in the past decades is the critical Casimir force. On the one hand, theoretical and numerical works on the subject have almost systematically been performed in magnetic model systems, such as the Ising or XY models. On the other hand, experimental approaches were all realized in fluid systems, such as binary mixtures or helium IV close to the superfluid transition.A motivation of this work was to bridge this gap by proposing, firstly, an experimental protocol for measuring the critical Casimir force in a magnetic layer and, secondly, a numerical approach in a Lennard-Jones binary mixture. The latter is of particular interest as it could lead the way to studying fluctuations of the Casimir force or out-of-equilibrium phenomena.

La toxine bactérienne de Shiga se lie au glycosphingolipide (GSL) globotriaosylcéramide (Gb3) afin d’entrer par endocytose dans les cellules en utilisant une voie dépendante et indépendante de la clathrine. Dans la voie indépendante de la clathrine, la toxine de Shiga réorganise les lipides de la membrane de façon à imposer une contrainte mécanique sur la bicouche, conduisant ainsi à la formation de pic d’invagination d'endocytose profonds et étroits. Mécaniquement ce phénomène n’est pas encore compris, notamment il reste énigmatique, comment se traduisent les propriétés géométriques de l’agrégation des glycosphingolipides GSLS et de la toxine. Dans mon travail de thèse, via l’utilisation de la sous-unité B de la toxine de Shiga (STxB) comme un modèle, différentes espèces moléculaires de son récepteur Gb3 ont été synthétisés avec des structures délibérément choisis. Les études réalisées par imagerie de haute résolution et par la modélisation informatique ont permis d’élucider les contraintes mécano-chimique sous-jacente conduisant à une réorganisation efficace qui a pour résultat l’agrégation de la toxine et la réorganisation des lipides. En combinant des expériences de simulation sur ordinateur de dynamique des particules dissipatives (DPD) et des expériences sur des modèles de membranes cellulaires, nous avons fourni la preuve de l’induction d’une force de fluctuation-membrane, de type « force de Casimir », conduisant à l'agrégation des molécules de toxines associées à la membrane à des échelles de longueur mésoscoiques. Nous avons observé et mesuré, en outre la condensation lipidique induite par la toxine, quantitativement sur des monocouches de Langmuir en utilisant la réflectivité des rayons X (XR) et par la mesure de la diffraction des rayons X par incidence rasante (GIXD), fournissant ainsi une preuve directe de l'hypothèse que la toxine a le potentiel de réduire de façon asymétrique la surface moléculaire sur la partie membranaire exoplasmique, ce qui conduit à une déformation locale de la membrane. Durant ma thèse, nos efforts ont été consacrés à la réalisation de nouveaux glycosphinolipides (GSL) comme outils chimiques à visée biologique. Par ailleurs, une nouvelle stratégie de reconstitution de GSL fonctionnels sur la membrane cellulaire, basée sur une réaction de ligation de type « click » entre un glycosyl-cyclooctyne et un azido-sphingosine a été étudiée. Les résultats obtenus sur les cellules se sont avérés beaucoup moins efficace que ceux in vitro. Une poursuite de l'optimisation de cette méthodologie est actuellement en cours. Une sonde fluorescente du glycosphinolipide Gb3, marquée à l’Alexa Fluor 568 lui-même lié par l'intermédiaire d'un bras PEG-α à la position de la chaîne acyle, a été synthétisée. Cette sonde se lie à la STxB sur couche mince de TLC, mais pas sur des membranes modèles. D'autres améliorations sont discutées. / Bacterial Shiga toxins bind to the glycosphingolipid (GSL) globotriaosylceramide (Gb3) to enter cells by clathrin-dependent and independent endocytosis. In the clathrin-independent pathway, Shiga toxin reorganizes membrane lipids in a way such as to impose mechanical strain onto the bilayer, thus leading to the formation of deep and narrow endocytic pits. Mechanistically how this occurs is not yet understood, and notably how the geometric properties of toxin-GSLs complexes translate into function has remained enigmatic. In my thesis work, using the B-subunit of Shiga toxin (STxB) as a model, different molecular species of its receptor Gb3 have been synthesized with deliberately chosen structures, coupled with high resolution imaging and computational modeling, to understand the underlying mechano-chemical constraints leading to efficient toxin clustering and lipids reorganization. By combining dissipative particle dynamics (DPD) computer simulation and experiments on cell and model membranes, we provided evidence that a membrane fluctuation-induced force, termed Casimir-like force, drives the aggregation of tightly membrane-associated toxin molecules at mesoscopic length scales. Furthermore, toxin-induced lipid condensation was observed and measured quantitatively on Langmuir monolayers using X-ray reflectivity (XR) and grazing incidence x-ray diffraction (GIXD), thereby providing direct evidence for the hypothesis that the toxin has the potential to asymmetrically reduce the molecular area of the exoplasmic membrane leaflet, leading to local membrane deformation. During my PhD, effort was also invested to develop new GSL tools applied to the biological setting. A novel strategy based on the Cu-free click reaction between glycosyl-cyclooctyne and azido-sphingosine was designed with the goal to functionally incorporate GSLs into cellular membranes. Following the synthesis work, click reactions have been performed in solution and on cells. Compared to the former, results on cells were far less efficient. Further optimization is currently ongoing. A fluorescently labeled Gb3 probe with Alexa Fluor 568 coupled via a PEG linker to the α-position of the acyl chain, was synthesized, to which STxB bound on TLCs, but not on model membranes. Further improvements are discussed.