The main goal of the thesis is to construct explicit, s-stage, strong-stability-preserving (SSP) Hermite–Birkhoff (HB) time discretization methods of order p with nonnegative coefficients for the integration of hyperbolic conservation laws. The Shu–Osher form and the canonical Shu–Osher form by means of the vector formulation for SSP Runge–Kutta (RK) methods are extended to SSP HB methods. The SSP coefficients of k-step, s-stage methods of order p, HB(k,s,p), as combinations of k-step methods of order (p − 3) with s-stage explicit RK methods of order 4, and k-step methods of order (p-4) with s-stage explicit RK methods of order 5, respectively, for s = 4, 5,..., 10 and p = 4, 5,..., 12, are constructed and compared with other methods. The good efficiency gains of the new, optimal, SSP HB methods over other SSP methods, such as Huang’s hybrid methods and RK methods, are numerically shown by means of their effective SSP coefficients and largest effective CFL numbers. The formulae of these new, optimal methods are presented in their Shu–Osher form.

Advancements in spectroscopy rely on the improvement of two fundamental characteristics: spatial and temporal resolutions. High harmonic spectroscopy (HHS) is an emerging technology that promises the capability of studying the fastest processes that exist today: electronic motion with angstrom spatial and attosecond temporal resolution. HHS is based on the process of high harmonic generation (HHG) which arises from the nonlinear interaction between an intense, infrared laser pulse and an atomic or molecular gaseous medium, producing coherent, attosecond-duration bursts of extreme ultraviolet (XUV) light. In order to utilize the attosecond pulses for spectroscopic measurements, it is necessary to improve the conversion efficiency of HHG. Chapter 2 of this thesis describes the improvements we make to the HHG source in order to obtain high XUV photon flux and we report on the nonlinear ionization of atomic systems using these pulses in Chapter 6. In Chapters 3 - 5, we describe several HHG experiments in complex, polyatomic molecules in order to promote the use of HHS as a general spectroscopic tool. Amplitude modulations in high harmonic spectra of complex molecules can be attributed to several types of interference conditions that depend on a system's molecular or electronic structure such as recombination with multiple centres or dynamical interference from multi-orbital contributions to ionization. Our results demonstrate the capability of HHS to extract useful information on molecular and electronic structure from large, polyatomic molecules directly from their high harmonic spectra. Furthermore, we use HHS to investigate the suppression of ionization in complex molecules due to quantum destructive interference during ionization as well as the distinguishability of emitted harmonic spectra from molecular isomers. Chapter 6 explores the study of multi-electron dynamics in complex molecules using XUV multiphoton ionization of atoms and molecules as well as the ionization and fragmentation of C60 which has hundreds of delocalized valence electrons. This thesis also describes the author's role in the design and fabrication of a time-of- flight mass spectrometer (Section 6.1) as well as an HHG detector system (Appendix A).

Understanding the electronic structure and dynamics of cyclic organic molecules is becoming increasingly the subject of investigations from different perspectives due to their unique chemical and physical properties. Since they are largely involved in the biochemistry of living organisms, studies on this class of compounds are also valuable to understand biologically relevant complex systems. Compared to other techniques, high-order harmonic generation (HHG) has been increasingly considered as a powerful spectroscopic tool with Angstrom spatial and attosecond temporal resolutions. This thesis demonstrates that high-order harmonic spectroscopy is capable of providing structural and dynamical information on the electronic systems of representative cyclic organic molecules comprising randomly oriented five-membered or six-membered rings. The first part of this thesis shows that the HHG from these molecules is sensitive to their aromatic character, which results from the de-localized pi electrons, and can potentially be a useful qualitative measure of aromaticity. We show that the advantage of utilizing HHG in this direction stems from the result that only pi molecular orbitals, associated with aromatcity, are responsible for the HHG emission in aromatic systems. The capability of HHG to distinguish cyclic isomers is demonstrated in the case of xylene molecules. Supported by numerical calculations, differences in the isomers are attributed to both tunnel ionization and photorecombination, the first and last steps of HHG. These results enable further HHG-based time-resolved studies of the dynamics associated with isomeric effects that these molecules exhibit. The present work also challenges the well-established prediction that strong field ionization from a molecular orbital is suppressed along nodal planes, where the electron density is zero. In fact, our study shows that considerable tunnel ionization in some cyclic molecules can occur near or along nodal planes. This unusual ionization is reported to have its signature on the quantitative and qualitative dependence of harmonic yield on laser ellipticity. The high symmetry displayed by the cyclic molecule, 1,4 cyclohexadiene, is shown to leave its imprints on the HHG in the form of structural interferences even if the target is randomly oriented. Two-color HHG from this molecule also indicates that hole dynamics could be involved in the generation process. A general study on high harmonic spectroscopy of the Cooper minimum in molecules is also reported. The presence of this minimum could affect the interpretation of harmonics spectra in any molecule containing S or Cl atoms. The molecular environment is shown to influence the position of this spectral modulation.

Many-body quantum dynamics is a challenging problem that has induced the development of many different computational techniques. One powerful technique is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method. This method allows proper consideration of electronic correlation with much less computational overhead compared to other similar methods. In this work, we present our implementation of the MCTDHF method on a non-uniform cylindrical grid. With the one-body limit of our code, we studied the controversial topic of tunneling delay, and showed that our results agree with one recent experiment while disagreeing with another. Using the fully correlated version of the code, we demonstrated the ability of MCTDHF to address correlation by calculating the ground state ionization energies of a few strongly correlated systems.

Au LHC, la collision de particules de très hautes énergies permet d’étudier l’interaction forte. En particulier, lors de la collision de deux noyaux (de plomb pour le LHC), un nouvel état de la matière, appelé Plasma de Quarks Gluons (QGP), est créé. L’étude de ce QGP constitue actuellement un des domaines actif de la recherche en physique. Les sondes dures, telles les quarks lourds ou les photons prompts, sont produit dés les premiers instants des collisions faites au LHC. Cette caractéristique les rend idéales pour l’étude du QGP. Elles vont traverser et interagir avec le milieu créé. En comparant avec un cas sans QGP (collisions proton-proton), il sera possible d’évaluer l’influence du plasma sur ces sondes dures et d’en extraire les propriétés telles la température et la densité. Cette étude nécessite donc d’avoir une bonne connaissance de la production de ces sondes dures dans les collisions proton-proton. Le but de ma thèse est l’implémentation des quarks lourds et des photons prompts dans le générateur d’évènements EPOS (codes informatique simulant les collisions), pour les collisions p-p. Le but final sera d’utiliser ce travail pour l’étude du plasma dans les collisions Pb-Pb / At the LHC, strong interaction is studied by doing collisions of high energy particles. In the case of nucleus-nucleus collision (lead at the LHC), a new state of matter, called Quarks Gluons Plasma (QGP), is created. The study of this QGP is currently a lively research field. Hard probes, like heavy quarks and prompt photons, are produced during early times of collisions done at the LHC. This is why they are ideal probes for the study of the QGP. They will go through and interact with the medium produced by the collision. A comparison with a case without QGP (proton-proton- collision) will allow us to see how hard probes properties are modified by themedium. Then, medium properties like temperature and density can be extracted. This study requires a good understanding of hard probes production in proton-proton collisions. The aim of my thesis is the implementation of heavy quarks and prompt photons in the event generator EPOS (computer code for colliders), for p-p collisions. Our final aim is the study of the QGP in Pb-Pb collisions.

This thesis consists of two parts. We start with some background theory that will be used throughout the thesis. Then, in the first part, we investigate the existence and uniqueness of the solution of the stochastic partial differential equation with two reflecting walls. Then we establish the existence and uniqueness of invariant measure of this equation under some reasonable conditions. In the second part, we study the splitting-up method for approximating the solu- tions of stochastic Stokes equations using resolvent method.

This thesis was funded by the Natural Environment Research Council (NERC) and is presented in an alternative thesis format. The thesis consists of three separate journal articles which form a coherent research project. Paper 1 investigates the development of strong winds in a dry, idealised extratropical cyclone using the horizontal momentum equation. In particular, the southwest wind maximum that develops was found to contain air parcels from three airstreams. The development of the horizontal along-flow forces around the cyclone and along trajectories entering the southwest wind maximum were analysed. An attempt to extend this methodology to a moist, idealised extratropical cyclone was made. However, the effect of adding moisture to the initial condition was found to be negligible. The reasons for this are explored in Paper 2, which documents this finding: that the effect of moisture on the development of an idealised, baroclinic wave is sensitive to the choice of initial condition. Paper 3 applies the horizontal momentum equation diagnostics to an intense, marine extratropical cyclone that brought strong winds to Ireland and the United Kingdom on 12 February 2014. The development of strong winds in Cyclone Tini was investigated by turning off latent heat release and surface fluxes. In the absence of latent heat release a weaker wind maximum developed. However, the simulation without surface fluxes had a very similar vertical structure of the horizontal wind to the full-physics simulation, but a weaker surface wind maximum. The reason for this weaker wind maximum was analysed using the quasigeostrophic omega equation. This analysis demonstrated a maximum in forcing for descent southwest of the low both in the full-physics simulation and in the simulation without surface fluxes, however strong winds were prevented from reaching the surface in the simulation without surface fluxes because of a more stable boundary layer around the bent-back front.

Le travail de recherche qui est rapporté dans ce manuscrit porte sur les couches minces de pérovskites et leur utilisation dans le cadre de la problématique des microcavités en régime de couplage fort. L’arrangement cristallin des pérovskites forme une structure en multi-puits quantiques dans laquelle les états excitoniques présentent une grande force d’oscillateur et une énergie de liaison importante (quelques 100 meV), en raison des effets de confinements quantique et diélectrique. Un premier axe de ce travail a consisté à collecter des informations sur les propriétés excitoniques de ces matériaux. Sur une pérovskite particulière (PEPI), nous avons notamment effectué des mesures de photoluminescence sous excitation impulsionnelle et des mesures pompe-sonde qui semblent suggérer l’existence, sous forte densité d’excitation, d’un processus de recombinaison Auger des excitons. Un deuxième axe de recherche fut de mettre en cavité des couches de certaines pérovskites. Avec les pérovskites PEPI et PEPC, nous avons montré que la réalisation de microcavités présentant un facteur de qualité de l'ordre de la dizaine suffit à obtenir, à température ambiante, le régime de couplage fort en absorption et en émission avec des dédoublements de Rabi pouvant atteindre 220 meV. Un goulet d’étranglement dans la relaxation des polaritons a été clairement mis en évidence pour la microcavité PEPI. Nous avons d’autre part montré que les pérovskites pouvaient également être associées à des semi-conducteurs inorganiques dans des microcavités dites "hybrides". Selon Agranovich et al., ces dernières pourraient, dans le cadre de la problématique du laser à polaritons, constituer une alternative à l'augmentation du facteur de qualité des microcavités. Dans cette optique, le couple ZnO/MFMPB semble particulièrement prometteur. / The research work which is reported in this manuscript focuses on 2D perovskites and their use to obtain microcavities working in the strong coupling regime. Perovskite structure forms a multi-quantum wells in which the excitonic states have a high oscillator strength and a large binding energy (a few 100 meV) due to quantum and dielectric confinement effects. A first axis of this work was to collect information on the excitonic properties of these materials. On a particular perovskite (PEPI), we performed photoluminescence and pump-probe measurements, which seem to suggest the existence, under high excitation density, a process of Auger recombination of excitons. A second research axis was to put in cavity thin layers of some perovskites. With PEPI and PEPC perovskites, we have shown that the realization of microcavities with a quality factor of the order of ten is sufficient to obtain at room temperature, the strong coupling regime in absorption and emission with Rabi splitting up to 220 meV. A bottleneck effect has been clearly demonstrated for the PEPI microcavity. We have also shown that perovskites could be associated with inorganic semiconductors in “hybrid” microcavities. According Agranovich et al., these microcavities could present polariton lasing with lower quality factors. To this end, the ZnO/MFMPB association seems particularly promising.

Equipamentos médicos equipados com interface de rede, classificados como sensores, transmitem informações sensíveis sobre a rede, constituindo uma rede de sensores. Essa rede pode ser utilizada para o acompanhamento remoto de pacientes a domicílio, com a finalidade de propiciar comodidade ao paciente. As informações provenientes desses sensores são vulneráveis, necessitando assim de fortes mecanismos de segurança. Devido às vulnerabilidades, métodos mais eficazes de autenticação vêm sendo desenvolvidos. Porém, as soluções de autenticação existentes obrigam a interação direta dos usuários com o sistema, não respeitando suas individualidades. Dessa forma, esta dissertação propõe uma solução de autenticação forte a qual retira a necessidade de interação do usuário com o sistema, baseando-se nos fatores de biometria e localização. O autenticador desenvolvido, foi testado através de estudos de casos distintos para mostrar sua eficiência e viabilidade para utilização em um ambiente real. / Medical devices equipped with network interfaces, classified as sensors, transmit sensitive information through the network and form a sensor network. This network can be used to monitor patients at home remotely. The information from these sensors is vulnerable and requires strong security mechanisms. Because of vulnerabilities, more effective authentication methods have been developed. However, the current authentication solutions require direct interaction of the user with the system, which does not respect their individuality. Thus, this dissertation proposes a strong authentication solution in which the interaction of the user with the system is removed based on biometrics and location factors. The developed authenticator was tested through different case studies to show its efficiency and feasibility before application in a real environment.

Cette thèse s’intéresse à la photo-ionisation de systèmes atomiques et moléculaires en phase gazeuse à l’aide d’harmoniques d’ordre élevé, un rayonnement cohérent dans le domaine de l’extrême ultraviolet (10-100 eV) sous la forme de trains d’impulsions attosecondes (1 as = 10-18 s). Dans un premier temps, les dynamiques électroniques au cours de l’auto-ionisation de gaz rares sont étudiées par interférométrie électronique. L’auto-ionisation résulte de l’interférence entre un chemin d’ionisation direct et un chemin résonant pour lequel l’atome reste transitoirement piégé dans un état excité.L’amplitude de la transition associée à ces processus est accessible via des expériences de photo-ionisation dans le domaine spectral (sur synchrotron par exemple), mais ce n’est pas le cas de la phase qui est pourtant essentielle à la compréhension de la dynamique électronique.Nous avons développé plusieurs méthodes interférométriques afin de mesurer la phase spectrale associée aux transitions électroniques vers des résonances de Fano dans les gaz rares.A partir des informations dans le domaine spectral, nous avons reconstruit pour la première fois la dynamique d'auto-ionisation ultra-rapide dans le domaine temporel et observé les interférences électroniques donnant lieu au profil de raie asymétrique. Dans un second temps, la photo-ionisation de molécules de NO est étudiée dans le référentiel moléculaire et utilisée comme un polarimètre afin de caractériser complètement l’état de polarisation du rayonnement harmonique, et en particulier de distinguer la partie du rayonnement polarisée circulairement d’une éventuelle partie dépolarisée. Nous présentons les résultats des mesures de polarimétrie moléculaire dans le cas de la génération d’harmoniques par un champ à deux couleurs polarisées circulairement en sens opposé. Ces études, complétées par des simulations numériques, permettent de proposer des conditions optimales de génération de rayonnement harmonique polarisé circulairement et contribuent à ouvrir la voie vers des études de dichroïsme circulaire ultrarapide dans la matière. / In this work, photoionzation of atomic and molecular species in the gas phase is investigated with high-harmonic radiation. In a first part, electronic dynamics in the autoionization process of rare gases in studied with electron interferometry. This method gives access to the spectral phase of the transition to the autoionizing state, and allows there construction of the entire autoionization dynamics. The ultrafast electronic dynamics, as well as the build-up of the celebrated asymmetric Fano profile, are observed experimentally for the first time. In a second part, photoionization of NO molecules in the molecular frame is used as a polarimeter to completeley characterize the polarization state of high-harmonics. In particular, this method can address the challenging disentanglement of the circular and unpolarized components of the light. The experimental results, completed by numerical simulations, allow defining optimal generation conditions of fully circularly-polarized harmonics for advanced studies of ultrafast dichroisms in matte