La chromodynamique quantique (QCD) prédit l'existence d'un nouvel état de la matière : le plasma de quarks et de gluons (PQG). Celui-ci aurait existé dans les premiers instants suivant le Big Bang et peut en principe être produit sous les conditions extrêmes de température et de densité atteintes lors de collisions d'ions lourds à haute énergie (au LHC par exemple). Un des marqueurs de sa présence est la suppression des quarkonia (états liés de quark/antiquark lourds), caractérisée par une production inférieure de ces états dans les collisions d'ions lourds relativement aux collisions proton-proton où le PQG ne pourrait être créé. Cette suppression a bien été observée expérimentalement, mais l'évolution de ses tendances aux énergies du RHIC et du LHC est un véritable défi qui requiert une meilleure compréhension théorique. La présente thèse a pour but d’étudier l’évolution en temps réel de paires corrélées de quark/antiquark lourds considérées comme des systèmes quantiques ouverts en interaction permanente avec un PQG en refroidissement. Explicitement, l'interaction continue entre le milieu et les degrés de liberté internes de la paire est obtenue par 1) un écrantage de couleur dit « de Debye » dû à la présence de charges de couleur dans leur voisinage et 2) des mécanismes de fluctuation/dissipation qui reflètent les collisions permanentes. Cela mène à une image dynamique et continue de la dissociation des quarkonia, de leur recombinaison et des transitions entre états liés. L'étude est transversale à différents cadres théoriques : semi-classique, quantique et quantique des champs. Les prédictions du modèle sont comparées aux résultats expérimentaux et aux résultats d'autres modèles théoriques. / The theory of quantum chromodynamics (QCD) predicts the existence of a new state of matter: the Quark-GluonPlasma (QGP). The latter may have existed at the first moments of the Universe following the Big Bang and can be, in theory, re-produced under the extreme conditions of temperature and density reached in high energy heavy ion collisions (at the LHC for instance). One of the QGP observables is the suppression of the quarkonia (heavy quark/antiquark bound states), characterised by a smaller production of these states in heavy ion collisions in comparison to proton-protoncollisions, in which no QGP production would be possible. This suppression has indeed been observed experimentally, but the puzzling evolution of its trend from RHIC to LHC energies requires a better theoretical understanding. The present thesis aims at studying the real-time evolution of correlated heavy quark/antiquark pairs described as open quantum systems which permanently interact with a cooling QGP. More explicitly, the continuous interaction between the medium and the pair internal degrees of freedom is obtained through 1) a temperature dependent color screening (“Debye” like) due to color charges in the irvicinity and 2) some fluctuation/dissipation mechanisms reflecting the continuous collisions. It leads to a dynamical and continuous picture of the dissociation, recombination and possible transitions to other bound states. This investigation is at the crossroads of different theoretical frameworks: semi-classic, quantum and quantum fields. The deduced predictions are compared to experimental data and to the results of other theoretical models.

No description available.

This thesis is concerned with methodologies for the accurate quantitative modelling of molecular biological systems. The first part is devoted to the chemical Langevin equation (CLE), a stochastic differential equation driven by a multidimensional Wiener process. The CLE is an approximation to the standard discrete Markov jump process model of chemical reaction kinetics. It is valid in the regime where molecular populations are abundant enough to assume their concentrations change continuously, but stochastic fluctuations still play a major role. We observe that the CLE is not a single equation, but a family of equations with shared finite-dimensional distributions. On the theoretical side, we prove that as many Wiener processes are sufficient to formulate the CLE as there are independent variables in the equation, which is just the rank of the stoichiometric matrix. On the practical side, we show that in the case where there are m_1 pairs of reversible reactions and m_2 irreversible reactions, there is another, simple formulation of the CLE with only m_1+m_2 Wiener processes, whereas the standard approach uses 2m_1+m_2. Considerable computational savings are achieved with this latter formulation. A flaw of the CLE model is identified: trajectories may leave the nonnegative orthant with positive probability. The second part addresses the challenge when alternative, structurally different ordinary differential equation models of similar complexity fit the available experimental data equally well. We review optimal experiment design methods for choosing the initial state and structural changes on the biological system to maximally discriminate between the outputs of rival models in terms of L_2-distance. We determine the optimal stimulus (input) profile for externally excitable systems. The numerical implementation relies on sum of squares decompositions and is demonstrated on two rival models of signal processing in starving Dictyostelium amoebae. Such experiments accelerate the perfection of our understanding of biochemical mechanisms.

Made available in DSpace on 2015-03-04T18:50:49Z (GMT). No. of bitstreams: 1 tese.pdf: 5590910 bytes, checksum: a89ccd96ade2b696f0e5b9163dc31bf5 (MD5) Previous issue date: 2006-11-13 / Lagrangian stochastic models are a largely used tool in the study of passive substances dispersion inside the Atmospheric Boundary Layer. Its application is related to the trajectory computation of thousands of particles, that numerically simulate the dispersion of suspense substances in the atmosphere. In this study, the basic concepts related to the Lagrangian stochastic modelling are presented and discussed together with its main characteristics and its computational implementation, to the study of particles dispersion in the atmosphere. In a computational experiment, the obtained results are compared with observational data from the TRACT experiment, that took place in Europe in 1992. The input data needed for the dispersion model are extracted from simulations with the numerical weather forecast model RAMS. Dispersion over Rio de Janeiro region is also tested in a second experiment. / Modelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.

In spite of remarkable progress in molecular biology, our understanding of the dynamics and functions of intra- and inter-cellular biological networks has been hampered by their complexity. Kinetics modelling, an important type of mathematical modelling, provides a rigorous and reliable way to reveal the complexity of biological networks. In this thesis, two genetic regulatory networks have been investigated via kinetic models. In the first part of the study, a model is developed to represent the transcriptional regulatory network essential for the circadian rhythms in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not used to describe the regulation of genes, instead the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model is described by a set of ordinary differential equations and the parameters are estimated from the in vitro experimental data of the clocks’ components. The simulation results show that the model reproduces sustained circadian oscillations in mRNA and protein concentrations that are in agreement with experimental observations. It also simulates the entrainment by light-dark cycles, the disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, perS and perL mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in per01, tim01 and clkJrk mutants suggests some differences in the model from reality. Finally, a possible function of VRI/PDP1 loops is proposed to increase the robustness of the clock. In the second part of the study, the sources of intrinsic noise and the influence of extrinsic noise are investigated on an intracellular viral infection system. The contribution of the intrinsic noise from each reaction is measured by means of a special form of stochastic differential equation, the chemical Langevin equation. The intrinsic noise of the system is the linear sum of the noise in each of the reactions. The intrinsic noise arises mainly from the degradation of mRNA and the transcription processes. Then, the effects of extrinsic noise are studied by means of a general form of stochastic differential equation. It is found that the noise of the viral components grows logarithmically with increasing noise intensities. The system is most susceptible to noise in the virus assembly process. A high level of noise in this process can even inhibit the replication of the viruses. In summary, the success of this thesis demonstrates the usefulness of models for interpreting experimental data, developing hypotheses, as well as for understanding the design principles of genetic regulatory networks.

The topic of this thesis is a diffusion process on a potential landscape which is given by a smooth Hamiltonian function in the regime of small noise. The work provides a new proof of the Eyring-Kramers formula for the Poincaré inequality of the associated generator of the diffusion. The Poincaré inequality characterizes the spectral gap of the generator and establishes the exponential rate of convergence towards equilibrium in the L²-distance. This result was first obtained by Bovier et. al. in 2004 relying on potential theory. The presented approach in the thesis generalizes to obtain also asymptotic sharp estimates of the constant in the logarithmic Sobolev inequality. The optimal constant in the logarithmic Sobolev inequality characterizes the convergence rate to equilibrium with respect to the relative entropy, which is a stronger distance as the L²-distance and slightly weaker than the L¹-distance. The optimal constant has here no direct spectral representation. The proof makes use of the scale separation present in the dynamics. The Eyring-Kramers formula follows as a simple corollary from the two main results of the work: The first one shows that the associated Gibbs measure restricted to a basin of attraction has a good Poincaré and logarithmic Sobolev constants providing the fast convergence of the diffusion to metastable states. The second main ingredient is a mean-difference estimate. Here a weighted transportation distance is used. It contains the main contribution to the Poincaré and logarithmic Sobolev constant, resulting from exponential long waiting times of jumps between metastable states of the diffusion.

This doctoral study consists of two parts. In the first part, the quantum statistical effects on the formation process of the heavy ion fusion reactions have been investigated by using the c-number quantum Langevin equation approach. It has been shown that the quantum effects enhance the over-passing probability at low temperatures. In the second part, we have developed a simulation technique for the quantum noises which can be approximated by two-term exponential colored noise.

No description available.

Centro Latino-Americano de Física / Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi. / Multiplicativewhite-noise stochastic processes continuously attract the attention of a wide area of scientific research. The variety of prescriptions available to define it difficults the development of general tools for its characterization. In this thesis, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for this kind of processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. We deduce a functional formalism to derive a generating functional for correlation and response functions of a multiplicative stochastic process represented by a Langevin equation. Representing the stochastic process in this functional (Grassmann) formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicativeMarkovian white-noise process and study some of the constraints it imposes on correlation functions using Ward-Takahashi identities.

Lagrangian stochastic models are a largely used tool in the study of passive substances dispersion inside the Atmospheric Boundary Layer. Its application is related to the trajectory computation of thousands of particles, that numerically simulate the dispersion of suspense substances in the atmosphere. In this study, the basic concepts related to the Lagrangian stochastic modelling are presented and discussed together with its main characteristics and its computational implementation, to the study of particles dispersion in the atmosphere. In a computational experiment, the obtained results are compared with observational data from the TRACT experiment, that took place in Europe in 1992. The input data needed for the dispersion model are extracted from simulations with the numerical weather forecast model RAMS. Dispersion over Rio de Janeiro region is also tested in a second experiment. / Modelos Lagrangianos estocásticos constituem ferramenta muito utilizada no estudo da dispersão de substâncias passivas na Camada Limite Atmosférica. Sua aplicação consiste em calcular a trajetória de milhares de partículas, que simulam numericamente a dispersão de uma substância em suspensão na atmosfera. Nesta tese, são apresentados e discutidos os conceitos básicos relacionados à Modelagem Lagrangiana Estocástica de Partículas, bem como suas principais características e sua implementação computacional, para o estudo da dispersão de partículas na atmosfera. Numa experimentação computacional, comparam-se os resultados obtidos com dados observacionais provenientes do experimento TRACT, realizado na Europa em 1992. Os dados de entrada necessários ao modelo de dispersão são extraídos de simulações do modelo de previsão numérica do tempo RAMS. A dispersão sobre o Estado do Rio de Janeiro é também testada em um segundo experimento.