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Electromagnetic waves can be used to transmit information over long distances and are therefore often employed for communication purposes. The electromagnetic waves are reflected off material objects on their paths and interact with the medium through which they propagate. For instance, the plasma in the ionosphere can refract and even reflect radio waves propagating through it. By increasing the power of radio waves injected into the ionosphere, the waves start to modify the plasma, resulting in the generation of a wide range of nonlinear processes, including turbulence, in particular near the reflection region. By systematically varying the injected radio waves in terms of frequency, power, polarisation, duty cycle, inclination, etc. the ionosphere can be used as an outdoor laboratory for investigating fundamental properties of the near-Earth space environment as well as of plasma turbulence. In such ionospheric modification experiments, it has been discovered that the irradiation of the ionosphere by powerful radio waves leads to the formation of plasma density structures and to the emission of secondary electromagnetic radiation, a phenomenon known as stimulated electromagnetic emission. These processes are highly repeatable and have enabled systematic investigations of the nonlinear properties of the ionospheric plasma. In this thesis we investigate features of the plasma density structures and the secondary electromagnetic radiation. In a theoretical study we analyse a certain aspect of the formation of the plasma structures. The transient dynamics of the secondary radiation is investigated experimentally in a series of papers, focussing on the initial stage as well as on the decay. In one of the papers we use the transient dynamics of the secondary radiation to reveal the intimate relation between certain features of the radiation and structures of certain scales. Further, we present measurements of unprecedentedly strong secondary radiation, attributed to stimulated Brillouin scattering, and report measurements of the secondary radiation using a novel technique imposed on the transmitted radio waves.

Population projection matrix (PPM) models are a central tool in ecology and evolution. They are widely used for devising population management practises for conservation, pest control, and harvesting. They are frequently employed in comparative analyses that seek to explain demographic patterns in natural populations. They are also a key tool in calculating measures of fitness for evolutionary studies. Yet, demographic analyses using projection matrices have, in some ways, failed to keep up with prevailing ecological paradigms. A common focus on long-term and equilibrium dynamics when analysing projection matrix models fits better with the outmoded view of ecosystems as stable and immutable. The more current view of ecosystems as dynamic and subject to constant extrinsic disturbances has bred new theoretical advances in the study of short-term "transient" dynamics. Transient dynamics can be very different to long-term trends, and given that ecological studies are often conducted over short timescales, they may be more relevant to research. This thesis focuses on the study of transient dynamics using population projection matrix models. The first section presents theoretical, methodological and computational advances in the study of transient dynamics. These are designed to enhance the predictive power of models, whilst keeping data requirements to a minimum, and borrow from the fields of engineering and systems control. Case studies in this section provide support for consideration of transient dynamics in population management. The second section applies some of these new methods to answer pertinent questions surrounding the ecology and evolution of transient dynamics in plants. Results show that transient dynamics exhibit patterns according to life form and phylogenetic history. Evidence suggests that this can be linked to the stage-structuring of life cycles, which opens up the possibility for new avenues of research considering the evolution of transient dynamics in nature.

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.

Codakia orbicularis est un mollusque bivalve appartenant à la famille des Lucinidae et établissant des symbioses avec des bactéries sulfo-oxydantes (symbiotes) au sein de ses branchies. Dans l’hypothèse où toute symbiose nécessite une régulation par des molécules de dialogue, une étude chimique exhaustive pourrait aboutir à la mise en évidence des métabolites impliqués. Le travail de ce manuscrit porte donc sur l'isolement de métabolites secondaires à partir des branchies de ce bivalve et sur l'évaluation de l'activité antibactérienne des molécules isolées. Douze composés ont été isolés des branchies de Codakia orbicularis et leurs structures ont été déterminées par les méthodes spectroscopiques usuelles. Parmi ces molécules, une seule est nouvelle et a été nommée orbicularisine. Elle présente un squelette indolone spirotetracyclique inédit. Parmi les molécules isolées, seules quatre d’entre elles présentent une activité antibactérienne à savoir le soufre S8, la 4-hydroxybenzaldéhyde et deux monoglycérolipides. L'orbicularisine est inactive contre un panel de lignées cellulaires cancéreuses et de kinases. Le nouveau squelette de l’orbicularisine pourrait permettre d'aboutir à une nouvelle famille de molécules par synthèse organique et ainsi d'accroître la diversité moléculaire autour de ce motif inédit. Il sera également intéressant de déterminer l'origine des molécules isolées (procaryote ou eucaryote), particulièrement pour l’orbicularisine, et leurs rôles dans le cadre de la symbiose. Les résultats chimiques obtenus sur C. orbicularis et sur les Lucinidae en général sont intéressants puisque les espèces côtières appartenant aux bivalves ont été peu exploitées en chimie jusqu’à ce jour. / Codakia orbicularis is a bivalve mollusk belonging to the family Lucinidae harboring sulfur-oxidizing bacterial endosymbionts within its gills. Considering that any symbiosis is most likely regulated by dialogue molecules, an exhaustive chemical study could lead to identify the involved metabolites. Thus, the aim of this thesis focuses on the isolation of secondary metabolites from the gills of this bivalve and the evaluation of the antibacterial activity of the isolated molecules. Twelve compounds were isolated from the gills of Codakia orbicularis and their structures were determined by usual spectroscopic methods. Among these molecules, only one presented a new structure and has been named orbicularisine. The latter presents an undescribed spirotetracyclic indolone skeleton. Regarding the biological activities, among the isolated molecules, only four of them identified as S8 sulfur, 4-hydroxybenzaldehyde and two monoglycerolipids presented an antibacterial activity. Orbicularisine was inactive against a panel of cell lines and kinase. The orbicularisine new skeleton is an interesting start for the synthesis of new family of molecules, thus enhancing its molecular diversity. It will be interesting to determine the origin of the isolated molecules (prokaryotic or eukaryotic), especially for the new orbicularisine, and their roles in the frame of the symbiosis. The chemical results obtained on C. orbicularis and on lucinids in general are interesting since the coastal species belonging to Bivalves have not been chemically explored.

In biochemical networks transient dynamics plays a fundamental role, since the activation of signalling pathways is determined by thresholds encountered during the transition from an initial state (e.g. an initial concentration of a certain protein) to a steady-state. These thresholds can be defined in terms of the inflection points of the stimulus-response curves associated to the activation processes in the biochemical network. In the present work, we present a rigorous discussion as to the suitability of finite-time Lyapunov exponents and metabolic control coefficients for the detection of inflection points of stimulus-response curves with sigmoidal shape.

Cette thèse présente l'étude de la réduction de modèles pour les réseaux électriques et les réseaux de transmission. Un point de vue mathématique a été adopté pour la réduction de modèles. Les réseaux électriques sont des réseaux immenses et complexes, dont l'analyse et la conception nécessite la simulation et la résolution de grands modèles non-linéaires. Dans le cadre du développement de réseaux électriques intelligents (smart grids) avec une génération distribuée de puissance, l'analyse en temps réel de systèmes complexes tels que ceux-ci nécessite des modèles rapides,fiables et précis. Dans la présente étude, nous proposons des méthodes de réduction de de modèles à la fois a priori et a posteriori, adaptées aux modèles dynamiques des réseaux électriques.Un accent particulier a été mis sur la dynamique transitoire des réseaux électriques, décrite par un modèle oscillant non linéaire et complexe. La non-linéarité de ce modèle nécessite une attention particulière pour bénéficier du maximum d'avantages des techniques de réduction de modèles.Initialement, des méthodes comme POD et LATIN ont été adoptées avec des degrés de succès divers. La méthode de TPWL, qui combine la POD avec des approximations linéaires multiples, a été prouvée comme étant la méthode de réduction de modèles la mieux adaptée pour le modèle dynamique oscillant.Pour les lignes de transmission, un modèle de paramètres distribués en domaine fréquentiel est utilisé. Des modèles réduits de type PGD sont proposés pour le modèle DP des lignes de transmission. Un problème multidimensionnel entièrement paramétrique a été formulé, avec les paramètres électriques des lignes de transmission inclus comme coordonnées additionnelles de la représentation séparée. La méthode a été étendue pour étudier la solution du modèle des lignes de transmission pour laquelle les paramètres dépendent de la fréquence. / This thesis presents the study of the model order reduction for power grids and transmission networks. The specific focus has been the transient dynamics. A mathematical viewpoint has been adopted for model reduction. Power networks are huge and complex network, simulation for power grid analysis and design require large non-linearmodels to be solved. In the context of developing “SmartGrids” with the distributed generation of power, real time analysis of complex systems such as these needs fast,reliable and accurate models. In the current study we propose model order reduction methods both a-priori and aposteriori suitable for dynamic models of power grids.The model that describes the transient dynamics of the power grids is complex non-linear swing dynamics model. The non-linearity of the swing dynamics model necessitates special attention to achieve maximum benefit from the model order reduction techniques. In the current research, POD and LATIN methods were applied initially with varying degrees of success. The method of TPWL has been proved as the best-suited model reduction method for swing dynamics model ; this method combines POD with multiple linear approximations.For the transmission lines, a distributed parameters model infrequency-domain is used. PGD based reduced-order models are proposed for the DP model of transmission lines. A fully parametric problem with electrical parameters of transmission lines included as coordinates of the separated representation. The method was extended to present the solution of frequency-dependent parameters model for transmission lines.