Les systèmes complexes se caractérisent par l’émergence de phénomènes macroscopiques qui ne s’expliquent pas uniquement par les propriétés de leurs composantes de base. La synchronisation est l’un de ces phénomènes par lequel les interactions entre des oscillateurs engendrent des mouvements collectifs coordonnés. Une représentation sous forme de graphe permet de modéliser précisément les interactions, alors que les oscillations se décrivent par des dynamiques non linéaires. Étant donné le lien subtil entre le graphe et la dynamique des oscillateurs, il est difficile de prédire l’émergence de la synchronisation. L’objectif de ce mémoire est de développer de nouvelles méthodes pour simplifier les systèmes complexes d’oscillateurs afin de révéler les mécanismes engendrant la synchronisation. À cette fin, nous introduisons des notions de la théorie des graphes et des systèmes dynamiques pour définir la synchronisation sur des bases mathématiques. Nous présentons ensuite des approches existantes sophistiquées pour réduire la dimension de dynamiques d’oscillateurs. Ces techniques sont toutefois limitées lorsque les dynamiques évoluent sur des graphes plus complexes. Nous développons alors une technique originale—spécialement adaptée pour les graphes aux propriétés plus hétérogènes—pour réduire la dimension de dynamiques non linéaires. En plus de généraliser des approches récentes, notre méthode dévoile plusieurs défis théoriques reliés à la simplification d’un système complexe. Entre autres, la réduction de la dimension du système se bute à une trichotomie : il faut favoriser la conservation des paramètres dynamiques, des propriétés locales du graphe ou des propriétés globales du graphe. Finalement, notre méthode permet de caractériser mathématiquement et numériquement l’émergence d’états exotiques de synchronisation. / Complex systems are characterized by the emergence of macroscopic phenomena that cannot be explained by the properties of their basic constituents. Synchronization is one of these phenomena in which the interactions between oscillators generate coordinate collective behaviors. Graphs allow a precise representation of the interactions, while nonlinear dynamics describe the oscillations. Because of the subtle relationship between graphs and dynamics of oscillators, it is challenging to predict the emergence of synchronization. The goal of this master’s thesis is to develop new methods for simplifying complex systems of oscillators in order to reveal the mechanism causing synchronization. To this end, we introduce notions of graph theory and dynamical systems to define synchronization on sound mathematical basis. We then present existing sophisticated approaches for reducing the dimension of oscillator dynamics. Yet, the efficiency of these techniques is limited for dynamics on complex graphs. We thus develop an original method—specially adapted for graphs with heterogeneous properties—for reducing the dimensions of nonlinear dynamics. Our method generalizes previous approaches and uncovers multiple challenges related to the simplification of complex systems. In particular, the dimension reduction of a system comes up against a trichotomy: one must choose to conserve either the dynamical parameters, the local properties of the graph, or the global properties of the graph. We finally use our method to characterize mathematically and numerically the emergence of exotic synchronization states.

Concentration oscillations are a ubiquitous characteristic of intracellular dynamics. The period of these oscillations can vary from few seconds to many hours, well known examples being calcium oscillations (seconds to minutes), glycolytic oscillations (minutes) and circadian rhythms (1 day). Considerable advances into understanding the mechanisms and functionality of concentration oscillations have been made since glycolytic oscillations were observed in the late 1950s, and mathematical methods have been an essential part of this process. With increasing ability to experimentally measure oscillations in single cells as well as in cell ensembles, the gold standard of modelling is to provide tools that can elucidate how the system-wide dynamics in complex organisms emerge from a system of single cells. Both abstract and detailed mechanistic models are complementary in the insight they can bring, and for networks of coupled cells considerations such as intrinsic intracellular noise, cellular heterogeneity and coupling strength are all expected to play a part. Here, we investigate separately the potential roles played by intrinsic noise arising from finite numbers of interacting molecules and by coupling among cellular oscillators. Regarding the former, it is well known that internal or molecular noise induces concentration oscillations in chemical systems whose deterministic models exhibit damped oscillations. We show, using the linear-noise approximation of the chemical master equation, that noise can also induce oscillations in biochemical systems whose deterministic descriptions admit no damped oscillations, i.e., systems with a stable node. This non-intuitive phenomenon is remarkable since, unlike noise-induced oscillations in systems with damped deterministic oscillations, it cannot be explained by noise excitation of the deterministic resonant frequency of the system. We here prove the following general properties of stable-node noise-induced oscillations for systems with two species: (i) the upper bound of their frequency is given by the geometric mean of the real eigenvalues of the Jacobian of the system, (ii) the upper bound of the Q-factor of the oscillations is inversely proportional to the distance between the real eigenvalues of the Jacobian, and (iii) these oscillations are not necessarily exhibited by all interacting chemical species in the system. The existence and properties of stable-node oscillations are verified by stochastic simulations of the Brusselator, a cascade Brusselator reaction system, and two other simple chemical systems involving autocatalysis and trimerization. We also show that external noise induces stable node oscillations with different properties than those stimulated by internal noise. Having demonstrated and explored this non-intuitive effect of noise, we extend the work to investigate the phenomenon of noise induced oscillations in cellular reaction systems characterised by the ‘bursty’ production of one or more species. Experiments have shown that proteins are typically translated in sharp bursts and similar bursty phenomena have been observed for protein import into subcellular compartments. We investigate the effect of such burstiness on the stochastic properties of downstream pathways by considering two identical systems with equal mean input rates, except in one system molecules (e.g., proteins) are input one at a time and in the other molecules are input in bursts according to some probability distribution. We find that the stochastic behaviour falls in three categories: (i) both systems display or do not display noise-induced oscillations; (ii) the non-bursty input system displays noiseinduced oscillations whereas the bursty input system does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify pathways involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production. We go on to investigate roles played by intercellular coupling in whole organ-level oscillations with an experimental analysis of circadian rhythms in Arabidopsis thaliana †. Circadian clocks in animals are known to be tightly coupled among the cells of some tissues, and this coupling profoundly affects cellular rhythmicity. However, research on the clock in plant cells has largely ignored intercellular coupling. Our research group used luciferase reporter gene imaging to monitor circadian rhythms in leaves of Arabidopsis thaliana plants, with both a lower resolution, high throughput method and a high-resolution (cellular level), lower throughput method. Leaves were grown and imaged in a variety of light conditions to test the relative importance of intercellular coupling and cellular coupling to the environmental signal. We analysed the high throughput data and described the circadian phase by the timing of peak expression. Leaves grown for three weeks without entrainment reproducibly showed spatio-temporal waves of gene expression, consistent with intercellular coupling. A range of patterns was observed among the leaves, rather than a unique spatio-temporal pattern, although some patterns were more often observed. All of the measured leaves exposed to lightdark entrainment cycles had fully synchronised rhythms, which could desynchronise rather quickly when placed in a non-entraining environment (i.e., constant light conditions). After four days in constant light some of these leaves were as desynchronised as leaves grown without any rhythmic input, as described by the phase coherence across the leaf. The same fast transition was observed in the reverse experimental scenario, i.e., applying light-dark cycles to leaves grown in constant light resulted in full synchronisation within two to four days. From these results we conclude that single-cell circadian oscillators were coupled far more strongly to external light-dark cycles than to the other cellular oscillators. Leaves did not spontaneously completely desynchronise, which is consistent with a presence of intercellular coupling among heterogeneous clocks. We also developed a methodology, based on the notion of two functional spatial scales of expression across the leaf, to analyse the high-resolution microscope data and determine whether there is a difference in the phase of circadian expression between vein cells and mesophyll cells in the leaf. The result from a single leaf suggests that the global phase wave dominates the phase behaviour but that there are small delays in the veins compared to their nearby mesophyll cells. This result can be validated by applying the methodology developed here to new microscope leaf data which is currently being collected in the research group. † This work was performed as a collaboration between David Toner (DT) and Benedicte Wenden (BW). BW designed and carried out the experiments, DT performed the data analysis and led on data visualisation.

Solar seismology is a relatively new field in solar astrophysics. It provides us a way of "looking" into the deep interior of the Sun. The goal of solar seismology is to derive information about the internal structure of the Sun from the observed properties of solar oscillations. This is called the inverse problem of solar seismology. This project is to explore a new set of methods and algorithms to solve the inverse problem. The continuous orthonormalization (CON) method and the adjoint method adapted by Rosenwald can be used to compute the eigenfrequency sensitivities to the solar structure parameters in a very efficient way. In this work, the computational algorithm for using these methods has been modified and improved. Continuous parametrization for the internal structure of the Sun is introduced. The solar interior is subdivided into sections, and polynomial fits are applied to the solar structure parameters in each section. The eigenfrequency sensitivities to these polynomial coefficients--the continuous parameters--are computed. These sensitivities can be used to predict the change in solar eigenfrequencies when the structure parameters are perturbed (with the necessary physical constraints satisfied). The inverse problem for the solar internal structure is formulated by using these sensitivities. The generalized inverse technique is used to solve the nonlinear inverse problem in an iterative process. Observed data of low-degree g-modes have been used for a preliminary inversion. The nonlinearity of the solar seismic inverse problem is demonstrated. A nonlinear inversion process has been successfully performed and the results analysed. The inversion results indicate that the standard solar model is a good approximation of the real Sun. Only relatively small perturbations to the model are needed to explain the frequency deviations between observation and theory.

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No description available.

In this thesis, the question of neutrino mass hierarchy is investigated. For this purpose, possibilities of neutrino mass origin are mentioned and phenomenology of neutrino oscillations within three active neutrino framework is introduced. Using that, it is described what neutrino mass hierarchy is and why it would be good to know it. After that, an overview of approaches to this problem is provided, including outline of the JUNO experiment. The approach based on comparison of mass splitting measured in experiments with reactor antineutrinos and accelerator neutrinos is investigated in great detail. The final part of this thesis is measurement of resistive plate chamber properties, as this type of detector was considered to be used in the JUNO experiment (but eventually other type will be used instead).

by Lin Lap-Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [105]-109). / Text in English; abstracts in English and Chinese. / by Lin Lap-Ming. / Abstract --- p.i / Acknowledgement --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Physical Motivation --- p.1 / Chapter 1.2 --- Quasi-Normal Modes --- p.3 / Chapter 1.3 --- Superfluidity in Neutron Stars --- p.7 / Chapter 1.4 --- Outline of this Thesis --- p.9 / Chapter Chapter 2. --- The Ordinary Perfect Fluid Neutron Stars --- p.11 / Chapter 2.1 --- The Equilibrium Neutron Star Models --- p.11 / Chapter 2.2 --- Non-Radial Oscillations of Neutron Stars --- p.14 / Chapter 2.3 --- The Quasi-Normal Modes of Stars --- p.17 / Chapter 2.3.1 --- The Fluid Modes --- p.17 / Chapter 2.3.2 --- The Spacetime Modes --- p.18 / Chapter Chapter 3. --- The General Relativistic Superfluid Formalism --- p.22 / Chapter 3.1 --- The Carter Formalism --- p.22 / Chapter 3.2 --- The Master Function --- p.25 / Chapter Chapter 4. --- The Equilibrium Superfluid Neutron Stars --- p.27 / Chapter 4.1 --- The Equilibrium Configurations --- p.27 / Chapter 4.2 --- Initial and Boundary Conditions --- p.34 / Chapter 4.3 --- Polytropic Models --- p.36 / Chapter Chapter 5. --- Non-Radial Oscillations of Superfluid Neutron Stars --- p.40 / Chapter 5.1 --- The Linearized Field Equations Inside the Star --- p.40 / Chapter 5.1.1 --- Equations for Even-Parity Perturbations --- p.45 / Chapter 5.1.2 --- Equations for Odd-Parity Perturbations --- p.48 / Chapter 5.2 --- Initial and Boundary Conditions --- p.49 / Chapter 5.2.1 --- Radial Integration Initial Conditions --- p.49 / Chapter 5.2.2 --- Boundary conditions at the Surface --- p.55 / Chapter 5.3 --- The Linearized Field Equations Outside the Star --- p.57 / Chapter 5.4 --- Numerical Technique --- p.60 / Chapter Chapter 6. --- Quasi-Normal Modes Extraction --- p.62 / Chapter 6.1 --- Numerical Techniques for Quasi-Normal Modes Extraction --- p.62 / Chapter 6.2 --- The Leaver Series --- p.64 / Chapter 6.3 --- The Graphical Method --- p.67 / Chapter Chapter 7. --- The Quasi-Normal Modes of Superfluid Neutron Stars --- p.69 / Chapter 7.1 --- Polytropic Models --- p.69 / Chapter 7.1.1 --- The w-modes --- p.70 / Chapter 7.1.2 --- The f- and p-modes --- p.74 / Chapter 7.2 --- Ideal Neutron-Proton-Electron Gas --- p.82 / Chapter 7.3 --- Convergence Tests and Accuracy --- p.92 / Chapter Chapter 8. --- Conclusion --- p.95 / Appendix A. Speeds of Sound --- p.97 / Appendix B. Equations for Radial Oscillations --- p.99 / Appendix C. Numerical Technique for Solving Leaver's Series --- p.101 / Appendix D. Scaling in Numerical Calculations --- p.103 / Bibliography --- p.105

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Wong, Ka Sin Jamie = 超流性對中子星振盪的影響 / 黃家倩. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 212-215). / Abstract also in Chinese. / Wong, Ka Sin Jamie = Chao liu xing dui zhong zi xing zhen dang de ying xiang / Huang Jiaqian. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivations --- p.1 / Chapter 1.2 --- Outline of Thesis --- p.3 / Chapter 1.3 --- Notation and Conventions --- p.4 / Chapter 2 --- The Relativistic Superfluid Star --- p.7 / Chapter 2.1 --- The Carter Formalism --- p.7 / Chapter 2.2 --- The Equilibrium Superfluid Star Models --- p.9 / Chapter 2.3 --- Non-Radial Oscillations of Superfluid Neutron Star --- p.13 / Chapter 2.3.1 --- Equations for Even-Parity Perturbations --- p.16 / Chapter 2.3.2 --- Equations for Odd-Parity Perturbations --- p.18 / Chapter 2.3.3 --- Linearised Equations Outside the Star --- p.19 / Chapter 2.3.4 --- Boundary Conditions for Quasinormal Modes --- p.21 / Chapter 2.3.5 --- Quasinormal Mode Spectrum of Superfluid Stars --- p.22 / Chapter 3 --- Universality in Superfluidf-mode --- p.25 / Chapter 3.1 --- What is an f-mode? --- p.25 / Chapter 3.2 --- Uncoupled Polytropic Master Function for Superfluid Stars --- p.27 / Chapter 3.3 --- Reparametrising the Uncoupled Polytropic Master Function --- p.29 / Chapter 3.4 --- f-mode Frequency of Uncoupled Polytropic Superfluid Stars --- p.30 / Chapter 3.5 --- "Derivation of Superfluid Mode Frequency for a Newtonian Sphere of Two Homogeneous, Incompressible, Uncoupled Fluids" --- p.40 / Chapter 4 --- Effects of Entrainment on Superfluid Mode Frequencies --- p.45 / Chapter 4.1 --- What is entrainment? --- p.45 / Chapter 4.2 --- Numerical Results --- p.48 / Chapter 4.3 --- Newtonian Variational Formalism --- p.51 / Chapter 4.4 --- Deriving the Approximate First Order Shift --- p.54 / Chapter 5 --- Variational Principle for Polar Modes --- p.60 / Chapter 5.1 --- Alternative Set of Perturbed Equations for Superfluid Neutron Star --- p.60 / Chapter 5.2 --- Boundary Conditions for Polar Quasinormal Modes --- p.64 / Chapter 5.3 --- Deriving the Variational Principle --- p.65 / Chapter 5.4 --- Recasting the Principle in Abstract Notation --- p.67 / Chapter 5.5 --- Doing Away with the Constraint Equations --- p.70 / Chapter 5.6 --- Regarding the Purely Real Nature of the First Order Term --- p.71 / Chapter 5.7 --- First Order Shift in Mode Frequency due to Entrainment --- p.74 / Chapter 6 --- Excitation of Quasinormal Modes --- p.77 / Chapter 6.1 --- Perturbed Equations Inside the Star --- p.77 / Chapter 6.2 --- Perturbed Equations Outside the Star --- p.78 / Chapter 6.3 --- Circular Orbits in Schwarzschild Spacetime --- p.80 / Chapter 6.4 --- Calculation of Source Term --- p.82 / Chapter 6.5 --- Determination of Amplitude --- p.85 / Chapter 6.6 --- Numerical Procedures --- p.86 / Chapter 6.7 --- Numerical Results --- p.89 / Chapter 7 --- Stability of Non-rotating Newtonian Superfluid Stars to Non-radial Oscillations --- p.91 / Chapter 7.1 --- Introduction --- p.91 / Chapter 7.2 --- Two-fluid Systems --- p.93 / Chapter 7.3 --- A Review of Basic Thermodynamics --- p.96 / Chapter 7.4 --- Perturbed System of Equations --- p.100 / Chapter 7.5 --- Schwarzschild Discriminant --- p.102 / Chapter 7.6 --- Variational Principle for Mode Frequency --- p.105 / Chapter 7.7 --- Stability of Polar Oscillations --- p.108 / Chapter 7.7.1 --- A Sufficient Condition for Stability --- p.109 / Chapter 7.7.2 --- A Necessary and Sufficient Condition for the Occurrence of Zero-frequency Modes --- p.112 / Chapter 7.7.3 --- Conditions for Instability --- p.119 / Chapter 7.8 --- A Little Application to Zero-temperature Superfluid Star --- p.121 / Chapter 7.9 --- Inclusion of Non-dissipative Magnus-typed Force --- p.122 / Chapter 7.10 --- Conclusion --- p.123 / Chapter 8 --- A Single Scalar Governing Stability of Newtonian Superfluid Neutron Stars to Non-radial Oscillations --- p.125 / Chapter 8.1 --- Introduction --- p.125 / Chapter 8.2 --- Summary of Results of the Last Chapter --- p.126 / Chapter 8.3 --- Motivation --- p.129 / Chapter 8.4 --- Occurrence of Neutral Modes --- p.131 / Chapter 8.5 --- S> 0 Implies Stability to Non-radial Oscillations --- p.133 / Chapter 8.6 --- S < 0 On a Finite Interval of r Implies Instability --- p.135 / Chapter 8.7 --- Conclusion --- p.137 / Chapter 9 --- Lagrangian Perturbation Theory for Rotating Non-relativistic Superfluid Stars --- p.138 / Chapter 9.1 --- Perturbation Operators --- p.139 / Chapter 9.2 --- Perturbing the Dynamical Equations --- p.143 / Chapter 9.3 --- Variational Principle and Symplectic Structure --- p.147 / Chapter 9.4 --- Showing Antisymmetry of B --- p.149 / Chapter 9.5 --- Showing Symmetry of C --- p.154 / Chapter 9.6 --- Canonical Displacement --- p.157 / Chapter 9.7 --- Using Canonical Energy in Stability Calculation --- p.163 / Chapter 9.8 --- Instability of r-mode for a Superfluid Star --- p.164 / Chapter 9.9 --- CFS Instability of Normal Modes --- p.169 / Chapter 10 --- Conclusion --- p.172 / Chapter A --- Some Useful Relations --- p.174 / Chapter B --- Derivation of Equations Given in Section 5.1 --- p.176 / Chapter C --- Order Analysis of Quantities at Stellar Radius --- p.179 / Chapter D --- Condition for the Occurrence of Non-radiating Modes --- p.182 / Chapter E --- Perturbed Equations for Polar Oscillations and Boundary Conditions --- p.186 / Chapter F --- Deriving the Variational Principle --- p.191 / Chapter G --- Discerning Similarity with Ordinary-fluid Variational Expression --- p.195 / Chapter G.l --- T'=0 --- p.195 / Chapter G.2 --- T'=0 --- p.199 / Chapter H --- A Condition for Instability of a Dynamical System --- p.202 / Chapter I --- Derivation of Zeroth-order r-mode Frequency --- p.205 / Chapter J --- Spin-s Spherical Harmonics --- p.207 / Chapter J.1 --- Spin-s Quantities --- p.207 / Chapter J.2 --- Motivation of Spin-s Spherical Harmonics --- p.208 / Chapter J.3 --- Proof of a Relation --- p.210 / Bibliography --- p.212

Chan, Pak On = 星體震動的分析方法 / 陳柏安. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (p. 117-119). / Abstracts in English and Chinese. / Chan, Pak On = Xing ti zhen dong de fen xi fang fa / Chen Boan. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Outline of the Content --- p.3 / Chapter 2 --- Preliminaries --- p.5 / Chapter 2.1 --- Einstein Equation --- p.5 / Chapter 2.1.1 --- Hydrostatic Equilibrium --- p.6 / Chapter 2.1.2 --- Linearized Stellar Pulsation --- p.7 / Chapter 2.1.3 --- Gravitational Radiation --- p.11 / Chapter 2.2 --- Classification of Modes --- p.13 / Chapter 2.2.1 --- Fundamental Mode --- p.14 / Chapter 2.2.2 --- Pressure Modes --- p.14 / Chapter 2.2.3 --- Gravity Modes --- p.14 / Chapter 2.3 --- Relativistic Cowling Approximation --- p.15 / Chapter 3 --- Stellar Structure of Quark Stars --- p.19 / Chapter 3.1 --- Ordinary Quark Stars --- p.19 / Chapter 3.1.1 --- Stellar Profile --- p.20 / Chapter 3.1.2 --- Radius and Mass --- p.27 / Chapter 3.1.3 --- Moment of Inertia --- p.30 / Chapter 3.2 --- Effects of Finite Strange Quark Mass and Finite Temperature --- p.32 / Chapter 3.2.1 --- Sommerfeld's Expansions --- p.33 / Chapter 3.2.2 --- Static EOS for Quark Matter --- p.35 / Chapter 3.2.3 --- Corrections to Ordinary Quark Stars --- p.37 / Chapter 3.2.4 --- Induced Buoyancy under Adiabaticity --- p.40 / Chapter 3.2.5 --- Induced Buoyancy under Fixed Composition --- p.45 / Chapter 3.3 --- Addition of Nuclear Crust --- p.47 / Chapter 4 --- Pressure Modes --- p.52 / Chapter 4.1 --- Sturm-Liouville Equation for p-modes --- p.52 / Chapter 4.2 --- Asymptotic Expansion --- p.54 / Chapter 4.3 --- "P""modes for Quark Stars" --- p.57 / Chapter 4.4 --- p-modes for Neutron Stars --- p.62 / Chapter 4.5 --- p-modes for Hybrid Stars --- p.65 / Chapter 5 --- Gravity Modes --- p.74 / Chapter 5.1 --- Sturm-Liouville Equation for modes --- p.74 / Chapter 5.2 --- Asymptotic Expansion --- p.76 / Chapter 5.3 --- g-modes for Quark Stars --- p.78 / Chapter 5.4 --- modes for Hybrid Stars --- p.83 / Chapter 5.5 --- Conditions on the modes --- p.88 / Chapter 6 --- Fundamental Mode --- p.93 / Chapter 6.1 --- Overview of the f-mode Universalities --- p.93 / Chapter 6.2 --- Relation between Real Part and Imaginary Part of Mwf --- p.95 / Chapter 6.3 --- New Universalities of f-mode --- p.96 / Chapter 7 --- Conclusions and Remarks --- p.104 / Chapter A --- Scattering Approximation --- p.106 / Chapter B --- Series Solution to Stellar Profile of Quark Stars --- p.108 / Chapter C --- AAKAS Formalism under Cowling Approximation --- p.113 / Chapter D --- Series Solutions to the Spectra of p-modes and g-modes --- p.114 / Bibliography --- p.117