Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic--quintic Ginzburg--Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non--integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse--type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this dissertation, we develop a theoretical framework for these novel classes of solutions. In the first part, we use a traveling wave reduction or a so--called spatial approximation to comprehensively investigate the bifurcations of plane wave and periodic solutions of the CGLE. The primary tools used here are Singularity Theory and Hopf bifurcation theory respectively. Generalized and degenerate Hopf bifurcations have also been considered to track the emergence of global structure such as homoclinic orbits. However, these results appear difficult to correlate to the numerical bifurcation sequences of the dissipative solitons. In the second part of this dissertation, we shift gears to focus on the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. For this part, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the two alternative starting formulations for the Lagrangian are recent and not well explored. Also, after extensive discussions with David Kaup, the trial functions have been generalized considerably over conventional ones to keep the shape relatively simple (and the trial function integrable!) while allowing arbitrary temporal variation of the amplitude, width, position, speed and phase of the pulses. In addition, the resulting Euler--Lagrange equations are treated in a completely novel way. Rather than consider the stable fixed points which correspond to the well--known stationary solitons or plain pulses, we use dynamical systems theory to focus on more complex attractors viz. periodic, quasiperiodic, and chaotic ones. Periodic evolution of the trial function parameters on stable periodic attractors constructed via the method of multiple scales yield solitons whose amplitudes are non--stationary or time dependent. In particular, pulsating, snake (and, less easily, creeping) dissipative solitons may be treated in this manner. Detailed results are presented here for the pulsating solitary waves --- their regimes of occurrence, bifurcations, and the parameter dependences of the amplitudes, widths, and periods agree with simulation results. Finally, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Results will be presented for the pulsating and snake soliton cases. Chaotic evolution of the trial function parameters in chaotic regimes identified using dynamical systems analysis would yield chaotic solitary waves. The method also holds promise for detailed modeling of chaotic solitons as well. This overall approach fails only to address the fifth class of dissipative solitons, viz. the exploding or erupting solitons.

No description available.

No description available.

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」 / 京都大学 / 新制・課程博士 / 博士(理学) / 甲第23694号 / 理博第4784号 / 新制||理||1685(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 川上 則雄, 教授 柳瀬 陽一, 教授 高橋 義朗 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Utilizing an interdisciplinary, multi-level perspective analysis this thesis reviews niche- regime-landscape interactions (analogous to the clusters of actors working at the local level of Gotland representing niche; the regime being national governance goals; and the landscape incorporating global level affairs and institutions such as the European Union (EU)) and their (mis)alignments within the biogas/biofertilizer production system of Gotland, Sweden, a small-island case study for energy-food-transportation transition and sustainable destination development. The study analyzes the heterarchical and polycentric development of biogas on Gotland—a socio-technical niche, nested within a larger energy regime and global landscape for transition—developing an understanding of (mis)alignments of pressures interacting on, at, and between the niche-regime- landscape as they combine with the peculiar competencies, as Loorbach describes, “creative minds, strategists, and visionaries” of a cluster of actors working in the food- energy-transport nexus on the island (2010, p. 6). These peculiar competencies, defined in section two, incorporate, and explore trust, storytelling, crisis, agency, cognitive features, influence, orchestration, social learning, perception, emotion, and expectation dynamics, operating within a strategic niche management context meeting goals for the region, as well as national and international goals set by actors such as the EU and Swedish national government. This is further problematized by landscape-level pressures due to crisis. The purpose is to investigate how clusters of actors with different competencies— connected to the socio-technical niche-level of biogas and biofertilizer production on Gotland—are initiating and accelerating real-world, incremental transition for a region, aligned with niche-, regime- and landscape-level pressures. This research will answer what peculiar competencies are required of key cluster actors within the socio-technical niche of biogas production on Gotland, needed to activate a waste management system, aligned with niche-, regime-, and landscape-level pressures. The study identifies a cluster of actors working in the domains of food, energy, and waste recovery on the island. Through semi-structured interviews and informal participant observation the research describes the political economy of socio-technical governance at the local level of Gotland; the soft features of this domain and their socio-cultural foundations; and expressions of necropolitical power, repurposing the hard features of the niche-regime-landscape to accelerate transition. By identifying the frontrunners for energy transition; their peculiar competencies in this small-island context; and what alignments they foster between the niche, regime and the landscape, the work aims to offer innovative and replicable paths to accelerate transition in small-island contexts. By offering a descriptive overview—and prescriptive recommendations for transition in a variety of regional contexts—the research can provide possible recommendations to increase collaborative initiators, coherence, orchestration, and trust, replicable across regions in Sweden, while transitioning transition research.

This dissertation presents innovative unified approaches to understand and predict the motion between potential wells. The theoretical-computational framework, based on the tube dynamics, will reveal how the dissipative and gyroscopic forces change the phase space structure that governs the escape (or transition) from potential wells. In higher degree of freedom systems, the motion between potential wells is complicated due to the existence of multiple escape routes usually through an index-1 saddle. Thus, this dissertation firstly studies the local behavior around the index-1 saddle to establish the criteria of escape taking into account the dissipative and gyroscopic forces. In the analysis, an idealized ball rolling on a surface is selected as an example to show the linearized dynamics due to its special interests that the gyroscopic force can be easily introduced by rotating the surface. Based on the linearized dynamics, we find that the boundary of the initial conditions of a given energy for the trajectories that transit from one side of a saddle to the other is a cylinder and ellipsoid in the conservative and dissipative systems, respectively. Compared to the linear systems, it is much more challenging or sometimes impossible to get analytical solutions in the nonlinear systems. Based on the analysis of linearized dynamics, the second goal of this study is developing a bisection method to compute the transition boundary in the nonlinear system using the dynamic snap-through buckling of a buckled beam as an example. Based on the Euler-Bernoulli beam theory, a two degree of freedom Hamiltonian system can be generated via a two mode-shape truncation. The transition boundary on the Poincar'e section at the well can be obtained by the bisection method. The numerical results prove the efficiency of the bisection method and show that the amount of trajectories that escape from the potential well will be smaller if the damping of the system is increasing. Finally, we present an alternative idea to compute the transition boundary of the nonlinear system from the perspective of the invariant manifold. For the conservative systems, the transition boundary of a given energy is the invariant manifold of a periodic orbit. The process of obtaining such invariant manifold compromises two parts, including the computation of the periodic orbit by solving a proper boundary-value problem (BVP) and the globalization of the manifold. For the dissipative systems, however, the transition boundary of a given energy becomes the invariant manifold of an index-1 saddle. We present a BVP approach using the small initial sphere in the stable subspace of the linearized system at one end and the energy at the other end as the boundary conditions. By using these algorithms, we obtain the nonlinear transition tube and transition ellipsoid for the conservative and dissipative systems, respectively, which are topologically the same as the linearized dynamics. / Doctor of Philosophy / Transition or escape events are very common in daily life, such as the snap-through of plant leaves and the flipping over of umbrellas on a windy day, the capsize of ships and boats on a rough sea. Some other engineering problems related to escape, such as the collapse of arch bridges subjected to seismic load and moving trucks, and the escape and recapture of the spacecraft, are also widely known. At first glance, these problems seem to be irrelated. However, from the perspective of mechanics, they have the same physical principle which essentially can be considered as the escape from the potential wells. A more specific exemplary representative is a rolling ball on a multi-well surface where the potential energy is from gravity. The purpose of this dissertation is to develop a theoretical-computational framework to understand how a transition event can occur if a certain energy is applied to the system. For a multi-well system, the potential wells are usually connected by saddle points so that the motion between the wells generally occurs around the saddle. Thus, knowing the local behavior around the saddle plays a vital role in understanding the global motion of the nonlinear system. The first topic aims to study the linearized dynamics around the saddle. In this study, an idealized ball rolling on both stationary and rotating surfaces will be used to reveal the dynamics. The effect of the gyroscopic force induced by the rotation of the surface and the energy dissipation will be considered. In the second work, the escape dynamics will be extended to the nonlinear system applied to the snap-through of a buckled beam. Due to the nonlinear behavior existing in the system, it is hard to get the analytical solutions so that numerical algorithms are needed. In this study, a bisection method is developed to search the transition boundary. By using such method, the transition boundary on a specific Poincar'e section is obtained for both the conservative and dissipative systems. Finally, we revisit the escape dynamics in the snap-through buckling from the perspective of the invariant manifold. The treatment for the conservative and dissipative systems is different. In the conservative system, we compute the invariant manifold of a periodic orbit, while in the dissipative system we compute the invariant manifold of a saddle point. The computational process for the conservative system consists of the computation of the periodic orbit and the globalization of the corresponding manifold. In the dissipative system, the invariant manifold can be found by solving a proper boundary-value problem. Based on these algorithms, the nonlinear transition tube and transition ellipsoid in the phase space can be obtained for the conservative and dissipative systems, respectively, which are qualitatively the same as the linearized dynamics.

Thulium (Tm)-doped ultrafast fiber lasers with emission wavelengths around 2 μm are desirable sources for scientific, industrial, medical, and environmental applications and flexible testbeds for investigating nonlinear pulse dynamics. Although exceptional research attention has been drawn by Tm-doped ultrafast fiber lasers in recent years, their designs and dynamics are significantly less explored compared to other fiber laser systems. Despite the broad emission spectrum of Tm-doped fibers, power scaling of Tm-doped ultrafast fiber lasers has been limited at shorter wavelengths of their emission spectrum (<1920 nm) due to challenges including signal re-absorption. However, compact, high-energy ultrafast sources at these less-exploited wavelengths can enable various applications including nonlinear microscopy. Further, due to the challenges of implementing real-time characterization around 2 μm, transient nonlinear pulse dynamics have rarely been reported from Tm-doped ultrafast fiber lasers. Resolving these dynamics can not only provide insights into new laser designs but also guide the generation of novel pulse profiles which can benefit a wide range of applications depending on their parameters. This dissertation focuses on developing various novel Tm-doped ultrafast fiber laser systems with unprecedented performance: High-energy operation is demonstrated at less-exploited wavelengths and unique waveforms are generated with their nonlinear dynamics investigated in real-time. First, a high-energy (394-nJ) Tm-doped chirped-pulse-amplification fiber laser system is designed and optimized for operation at the wavelength of 1900 nm and supports the generation of 950-nm ultrashort (390-fs) pulses via frequency-doubling. The system represents the highest pulse-energy (138 nJ) in the femtosecond regime for any fiber-based systems around this wavelength to date, which can be highly attractive for two-photon microscopy with spatiotemporal-multiplexing. To gain deeper insights into the operation of ultrafast Tm-doped fiber lasers, various new nonlinear dynamics are investigated by a home-built real-time characterization setup based on dispersive Fourier transform for 2 μm pulses: A new mode-locking regime is demonstrated which can deliver both up-chirped and close-to-chirp-free dissipative pulses with a 10-fold difference in their pulse energies/durations, providing a versatile source that can switch between different pulse profiles. Following that, soliton molecules with unique partial spectral modulation patterns are synthesized based on two dissimilar pulses from the same cavity, which represent an interesting analogy to ‘heteronuclear’ chemical molecules and hold great potential for optical information processing. Further, mode-locking evolution between dissimilar coherent pulses are studied in Tm-doped ultrafast fiber lasers. Finally, combining both high-energy operation and novel waveform-generation, we present a Tm-doped fiber laser source delivering amplified (~ 200 nJ) noise-like pulses without requiring any feedback mechanism. / 2025-09-10T00:00:00Z

La thèse est consacrée à la modélisation discrète et continue des écoulements sanguins et des phénomènes connexes tels que la coagulation du sang et l'athérosclérose. Ce travail comprend l'élaboration des modèles mathématiques et numériques de la coagulation du sang, des simulations numériques et l'analyse mathématique d'un modèle d'inflammation chronique au cours d'athérosclérose. Une partie importante de la thèse est liée à la programmation, la mise en œuvre et l'optimisation des codes numériques. La partie principale de la thèse concerne la modélisation de la coagulation du sang in vivo tenant compte des écoulements sanguins, les réactions biochimiques dans le plasma et l'agrégation de plaquettes. La nouveauté principale de ce travail est l'élaboration d'un modèle hybride (discret-continu) de la coagulation du sang et de la formation de caillot sanguin dans le flux. La partie théorique de la thèse est consacrée à l'analyse mathématique d'un modèle d'inflammation chronique liée à l'athérosclérose. Les simulations numériques réalisées dans le cadre de cette thèse impliquent l'élaboration des algorithmes numériques pour les modèles mathématiques et le d´développement des logiciels. Vu le fait que les simulations numériques ont été coûteuse en temps de calcul, des efforts considérables ont été consacrés à la parallélisation des logiciels et à leur optimisation / The thesis is devoted to discrete and continuous modelling of blood flows and related phenomena such as blood coagulation and atherosclerosis. It includes the development of mathematical and numerical models of blood coagulation, numerical simulations and the mathematical analysis of a model problem of chronic inflammation during atherosclerosis. The main part of the thesis concerns modelling of blood coagulation in vivo which takes into account blood flows, biochemical reactions in plasma and platelet aggregation. The main novelty of this work is the development of a hybrid (discrete-continuous) model of blood coagulation and clot formation in flow. The model is used to study several aspects of blood coagulation in flow : platelet aggregation and its interaction with coagulation pathways, influence of the flow speed on the clot development, a possible mechanism by which clot stops growing. The theoretical part of the thesis is devoted to the mathematical analysis of a model of chronic inflammation related to atherosclerosis. In this thesis we study a model problem which describes the propagation of a reaction-diffusion wave in the 2D case with non-linear boundary conditions. For that we use the Leray-Schauder method and a priori estimates of solutions in order to prove the existence of waves in the bistable case. Numerical simulations carried out in the framework of this thesis were based on the numerical implementation of the corresponding models and on the software development. Since the numerical simulations were computationally expensive, a substantial effort was directed to software parallelization and optimization

No description available.

Dans cette thèse, nous étudions expérimentalement la génération d'impulsions carrées très énergétiques et accordable à l’échelle nanosecondes et d'impulsions ultracourtes à haute puissance moyenne de sortie dans les lasers à fibre utilisant les nanomatériaux comme absorbant saturable. Tout d'abord, puisque la dynamique des impulsions est dominée par l'interaction de la non linéarité et de la dispersion chromatique cubique de la fibre avec un mécanisme de discrimination d'intensité appelé absorbant saturable, la stabilité d'une distribution harmonique en mode verrouillé est étudiée par injection externe d'une onde continue.Enfin, nous avons utilisés des absorbant saturable à base de nanomatériaux déposés sur des tapers optiques dans les lasers à fibre pour générer des impulsions ultracourtes avec une puissance de sortie moyenne élevée. / In this thesis, we investigate experimentally the generation of high energy nanosecond tunable square pulses and high output power ultrashort pulses in fiber lasers. First, since pulse dynamics are dominated by the interaction of the fiber's cubic Kerr nonlinearity and chromatic dispersion with an intensity-discriminating mechanism referred to as a saturable absorber, the stability of a harmonic mode-locked distribution is studied by external injection of a continuous wave. Finally, we implemented nanomaterial based saturable absorbers in fiber laser configuration to generate ultrashort pulses with high average output power. Different techniques of achieving such components are explicitly detailed: ultrashort pulse generation in ring cavities where graphene and topological insulators are deposited on optical tapers to form a saturable absorber.