Rozprawy doktorskie na temat „GEP EQUATION”

The subject of this thesis is a study of the two-component nonlinear Schrodinger equation (NSE) in (1+1)-dimension. Two aitemative cases are possible, referred to as the focusing and defocusing cases in applications to studies in nonlinear optics. The main focus of the work in this thesis is on the defocusing case, but results known for the focusing case are also discussed and compared, where relevant. This thesis is comprised of two themes. The first is the effective integration of the NSE, using techniques of algebrogeometric theory. Here, the Baker-Akheizer formalism is developed and applied to the Manakov system. This formalism is used to derive the finite-gap solution, expressed in terms of Riemann theta-functions. The second is the derivation of soliton solutions from these finite-gap solutions, by considering an important limit; namely, the closing ofthe gap in the Riemanu surface associated with. the spectral curve yields explicit representations for soliton solutions. The scalar NSE is first considered by way of introducing and discussing relevant techniques. Then, it is shown how these methods can be extended to the vector case. Next, two particular cases are considered. Firstly, it is shown that the genus 1 case yields a dark-dark soliton solution in the limiting case. An aspect of the vector problem not found with the scalar case is the existence of dark-bright solitons. A single dark-bright soliton can be obtained by considering genus 2, not genus 1, in the soliton limit. A discussion of these derivations is an important feature of the thesis. We discuss next a solution obtained elsewhere introducing a separable ansatz for both components shown to be a genus 2 solution. We discuss the fact that the appropriate curve is hyperelliptic, and indicate how it is related to our trigonal curve by a birational map.

The vector nonlinear Schrödinger equation is an envelope equation which models the propagation of ultra-short light pulses and continuous-wave beams along optical fibres. Previous work has focused almost entirely on soliton solutions to the equation using a Lax representation originally developed by Manakov. We prove recursion formulae for the family of higher-order nonlinear Schrödinger equations, along with its associated Lax hierarchy, before investigating finite gap solutions using an algebrogeometric approach which introduces Baker-Akhiezer functions defined upon the Riemann surface of the relevant spectral curve. We extend this approach to account for solutions of arbitrary genus and compare it with an alternative method describing solutions of genus two. The scalar nonlinear Schrödinger and Heisenberg ferromagnet equations were shown to be equivalent following work by Lakshmanan; we generalise this idea by introducing the Heisenberg ferromagnet hierarchy and show it is entirely gauge equivalent to the scalar nonlinear Schrödinger hierarchy in the attractive case. We also investigate the polarisation state evolution of general solutions to the vector nonlinear Schrödinger equation and study possible degenerations to the Heisenberg ferromagnet equation.

In this paper, we obtain convergence of solutions of stochastic differential systems with memory gap to those with full finite memory. More specifically, solutions of stochastic differential systems with memory gap are processes in which the intrinsic dependence of the state on its history goes only up to a specific time in the past. As a consequence of this convergence, we obtain a new existence proof and approximation scheme for stochastic functional differential equations (SFDEs) whose coefficients have linear growth. In mathematical finance, an option pricing formula with full finite memory is obtained through convergence of stock dynamics with memory gap to stock dynamics with full finite memory.

We can classify several quite different calculi for automated reasoning in first-order logic as instantiation-based methods (IMs). Broadly speaking, unlike in traditional calculi such as resolution where the first-order satisfiability problem is tackled by deriving logical conclusions, IMs attempt to reduce the first-order satisfiability problem to propositional satisfiability by intelligently instantiating clauses. The Inst-Gen-Eq method is an instantiation-based calculus which is complete for first-order clause logic modulo equality. Its distinctive feature is that it combines first-order reasoning with efficient ground satisfiability checking, which is delegated in a modular way to any state-of-the-art ground solver for satisfiability modulo theories (SMT). The first-order reasoning modulo equality employs a superposition-style calculus which generates the instances needed by the ground solver to refine a model of a ground abstraction or to witness unsatisfiability. The thesis addresses the main issue in the Inst-Gen-Eq method, namely efficient extraction of instances, while providing powerful redundancy elimination techniques. To that end we introduce a novel labelled unit superposition calculus with sets, AND/OR trees and ordered binary decision diagrams (OBDDs) as labels. The different label structures permit redundancy elimination each to a different extent. We prove completeness of redundancy elimination from labels and further integrate simplification inferences based on term rewriting. All presented approaches, in particular the three labelled calculi are implemented in the iProver-Eq system and evaluated on standard benchmark problems.

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Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap completa, composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento constante e corredora. Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento constante feito por Doff, Machado e Natale [2]
Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a complete gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of constant coupling and running coupling constant. This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]

Orientador: Adriano Antonio Natale
Banca: Adriano Doff Sotta Gomes
Banca: Alex Gomes Dias
Resumo: Alguns aspectos da quebra de simetria quiral para quarks na representação fundamental são discutidos no contexto das equações de Schwinger-Dyson. Estudamos a equação de gap fermionica incluindo o efeito de uma massa dinêmica para os gluons. Ao estudar esta equação de gap verificamos que a intenção não é forte o suficiente para gerar uma massa dinâmica dos quarks compatível com os dados experimentais. Também discutimos como a introdução de um propagador confinante pode mudar este cenário, exatamente como foi proposto por Cornwall [1] recentemente, desta forma estudamos uma equação de gap "completa", composta pela troca de um gluon massivo e por um termo confinante; M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). Encontramos soluções assintótica desta equação de gap nos casos de constante de acoplamento "constante" e "corredora". Este último caso corresponde a um aprimoramento do cálculo com constante de acoplamento "constante" feito por Doff, Machado e Natale [2]
Abstract: Some aspects of chiral symmetry breaking for quarks in the fundamental representation are discussed in the framework of the Schwinger-Dyson equations. We study the fermionic gap equation including effects of dynamical gluon mass. Studying the bifurcation equation of this gap equation we verify that the interaction is not strong enough to generate a satisfactory dynamical quark mass. We also discuss how the introduction of a confining propagator may change this scenario as recently pointed out by Cornwall [1], so we study a "complete" gap equation composed by the one-dressed-gluon exchange term and a confining term: M('p POT 2') = 'M IND. c('p POT 2') + 'M IND. 1g'('p POT 2'). We find asymptotic solutions for this gap equation in the cases of "constant coupling" and "running coupling constant". This last case is an improvement of the constant coupling calculation of Doff, Machado and Natale [2]
Mestre

This thesis is concerned with the preparation of mixed silicon-titanium oxides (Ti02=4.1-21.9wt%) and silicon-zirconium oxides (Zr02=4.1-22.Iwt%) by the sol-gel route. Methods of preparing homogeneous Si02-TiO2 gels and SiO2-Zr02 gels have been explored. In this work bis(acetylacetonato)titanium diisopropoxide or bis(acetylacetonato)zirconium dipropoxide and tetraethyl orthosilicate (TEOS) have been hydrolysed simultaneously in iso-propanol to form homogeneous gels. Using these systems, the effects of the reaction conditions, amount of titania/zirconia present in the gel, drying conditions and thermal treatment of the dry gels on the bulk and structural properties have been investigated by a variety of experimental methods including X-ray diffraction, mid- and near-infrared spectroscopy and gas adsorption techniques. For SiO2-TiO2 powders and monoliths, and SiO2-ZrO3 monoliths, thermal treatment has been found to significantly reduce the surface area (from 750-1.0m2g-1), pore volume (from 0.56-0.001cm3g-1') and relative number of silanol groups on the surface of the sample above 700°C. Average pore diameters remain constant at temperatures below 900°C (ca 54-21Å for monoliths), although the micropore volume does decrease (0.04-0.0cm3g-1) suggesting that smaller pores are destroyed by the heating process. For SiO2-TiO2 powders, the average pore diameter was ca IOÅ larger than for the corresponding monolith suggesting that small pores are destroyed during powdering. At 1100°C, gas adsorption data indicate that the samples are fully densified. This is supported by NIR spectra which detect no silanol groups on the surface of the sample. Structural changes arising from compositional changes and differing thermal treatment regimes have been monitored using mid-infrared spectroscopy and X-ray diffraction. With increasing temperature the silica matrix strengthens and titanium/zirconium are incorporated into the matrix. Monolithic SiO2-TiO2 gels (Ti02=6.34 weight%) remained amorphous at 1100°C, whereas powders began to exhibit diffraction patterns predominantly from anatase at 700°C. Anatase crystallite sizes have been calculated using the Scherrer equation and have been found to be between 16.3 and 5.4nm. Monolithic SiO2-ZrO2 gels containing 4.1 and 4.9 weight% zirconia were found to be amorphous after treatment at 1100°C. Increasing the zirconia content to 6.4 and 22.1 weight% resulted in gels that were amorphous up to 900°C. Further treatment at 1100°C, resulted in tetragonal zirconia and some cristobalite being formed. Crystallite sizes have been calculated as being between 2.7 and 1.6nm for tetragonal zirconia and from 4.1 to 2.8nm for cristobalite. Increasing the levels of titania/zirconia in the sample resulted in higher relative levels of hydrogen-bonded silanol groups. On hydration, the increased levels of titania/zirconia resulted in no observable free silanol groups on the surface suggesting that the surface becomes more hydrophilic as the amount of titania/zirconia present in the sample increases. This suggests that water becomes more tightly bound to Ti-OH /Zr-OH groups on the surface and within the pores, resulting in fewer free silanol type groups. A double alkoxide bis(acetylacetonato)titanium di(triethoxysilane) [Ti(acac)2(OSi(OC2H5)3)2] has also been synthesised and characterised. Mixed Si02-TiO2 gels have also been prepared by the simultaneous hydrolysis of Ti(acac)2(OSi(OC2H5)3)2 and TEOS under acidic conditions in ethanol. The effects of reaction conditions and thermal treatment of the dry gels have been investigated. Increasing the treatment temperature of the samples resulted in the progressive decrease in surface area (533-3.0m2g-1), pore volume (0.18-0.003cm3g-1), micropore volume (0.06-0.00cm3g-1) and relative number of silanol groups on the surface. However, the average pore diameter remained constant at temperatures up to 700°C. Changes in pore volume (0.07-0.005cm3g-1), surface area (300-3.0m2g-1) and average pore diameter (26.9-91.9Å) were largest at 900°C, and the samples were found to be almost completely dense. This was confirmed by the absence of observable silanol groups by NIR spectroscopy. After heating at temperatures up to 900°C, the samples were found to be amorphous by XRD. However increasing the temperature to 1100°C resulted in the formation of some crystalline anatase. The anatase crystal sizes have been calculated as being from 16.3 to 10.8nm in diameter. NIR studies of silica-zirconia and silica-titania gels (prepared by both methods), indicate that decreasing the amount of acid used in the hydrolysis reaction resulted in higher relative levels of hydrogen bonded silanol species. Similarly, decreasing the amount of acid increased the micropore volume and decreased the mesoporosity of the resulting samples. Generally, decreasing the amount of acid used for the hydrolysis for silica-zirconia and silica-titania gels (prepared by both methods), results in a decrease in the overall surface area and pore volume of the resulting material. The resulting isotherms indicate that the samples became less mesoporous as the amount of acid used in the hydrolysis reaction decreased. This was accompanied by an increase in the micropore volume. For SiO2-TiO2 monoliths prepared from a double alkoxide and Si02-ZrO2 monoliths the resulting pore structure is more rigid and composed of smaller pores than that of SiO2-TiO2 powders and monoliths prepared from bis(acetylacetonato)titanium diisopropoxide.

The removal of milk fouling deposits often requires the diffusion of electrolyte solutions such as sodium hydroxide through a gel. Very often more than one single anion and one single cation are involved and thus the modelling of such diffusion requires a multicomponent description. Diffusion of electrolyte solutions through gels can be modelled using the Maxwell-Stefan equation. The driving forces for diffusion are the chemical potential gradients of ionic species and the diffusion potential, i.e., the electrostatic potential induced by diffusion of the ions. A model based on the Maxwell-Stefan equation was applied to electrolyte solutions and electrolyte solutions with a gel. When modelling the diffusion of electrolyte solutions, the resulting equations were found to be a partial differential algebraic equation system with a differentiation index of two. The identification of this characteristic of the system enabled a solution method using the method of lines to be developed. When modelling the diffusion of electrolyte solutions through a gel an explicit expression for diffusion potential was developed and hence the diffusion equations were solved. Numerical solutions were presented for a number of case studies and comparisons were made with solutions from literature and between different electrolyte systems. It was found that the results of diffusion of electrolytes were in good agreement with those of experiments and literature. In the case of diffusion of electrolytes through a gel, swelling of the gel was predicted. The model can be improved by adding thermodynamic factors and can be easily extended to multiple ion systems.

An inertial manifold (IM) is one of the key objects in the modern theory of dissipative systems generated by partial differential equations (PDEs) since it allows us to describe the limit dynamics of the considered system by the reduced finite-dimensional system of ordinary differential equations (ODEs). It is well known that the existence of an IM is guaranteed when the so called spectral gap conditions are satisfied, whereas their violation leads to the possibility of an infinite-dimensional limit dynamics, at least on the level of an abstract parabolic equation. However, these conditions restrict greatly the class of possible applications and are usually satisfied in the case of one spatial dimension only. Despite many efforts in this direction, the IMs in the case when the spectral gap conditions are violated remain a mystery especially in the case of parabolic PDEs. On the one hand, there is a number of interesting classes of such equations where the existence of IMs is established without the validity of the spectral gap conditions and, on the other hand there were no examples of dissipative parabolic PDEs where the non-existence of an IM is rigorously proved. The main aim of this thesis is to bring some light on this mystery by the comprehensive study of three model examples of parabolic PDEs where the spectral gap conditions are not satisfied, namely, 1D reaction-diffusion-advection (RDA) systems (see Chapter 3), the 3D Cahn-Hilliard equation on a torus (see Chapter 4) and the modified 3D Navier-Stokes equations (see Chapter 5). For all these examples the existence or non-existence of IM was an open problem. As shown in Chapter 3, the existence or non-existence of an IM for RDA systems strongly depends on the boundary conditions. In the case of Dirichlet or Neumann boundary conditions, we have proved the existence of an IM using a specially designed non-local in space diffeomorphism which transforms the equations to the new ones for which the spectral gap conditions are satisfied. In contrast to this, in the case of periodic boundary conditions, we construct a natural example of a RDA system which does not possess an IM. In Chapters 4 and 5 we develop an extension of the so-called spatial averaging principle (SAP) (which has been suggested by Sell and Mallet-Paret in order to treat scalar reaction-diffusion equation on a 3D torus) to the case of 4th order equations where the nonlinearity loses smoothness (the Cahn-Hilliard equation) as well as for systems of equations (modified Navier-Stokes equations).

We study dynamics of Bragg grating solitons in a system of linearly coupled Bragg gratings with Kerr nonlinearity. The effects of dispersive reflectivity on the behaviour of solitons in the system are investigated by solving the coupled mode equations numerically. Gap solitons, are found to exist throughout the bandgap of the structure. The system supports two types of symmetric and asymmetric solitons that can have any velocities from zero to the speed of light in the medium. At given soliton parameters a critical coupling coefficient is found above which only symmetric solitons exist. Below the critical point however, both types of gap solitons may exist at the same time. Linear forms of coupled mode equations are solved analytically. The results are in excellent agreement with the gap soliton tails. Also, using the linear analysis a condition is found for the solitons to have sidelobes in their tails. Stability of solitons are investigated using systematic simulations. Generally, when dispersive reflectivity is zero, asymmetric solitons are stable for ω≥0. While with increase of dispersive reflectivity the stable region expands into the negative frequencies. Symmetric solitons on the other hand are found to be stable where they exist on their own. Interactions of quiescent gap solitons in the model are studied numerically. The outcomes generally depend on the initial separation (Δx) and phase difference. However, when the dispersive reflectivity is small, Δx-dependence is very weak. Interactions are found to result in a number of outcomes including merger into a single quiescent soliton, destruction, formation of a bound state that eventually breaks up into two separating solitons, formation of two moving and one quiescent solitons, and repulsion. The most interesting outcomes of the collisions of counter-propagating in-phase moving solitons are merger and 2→3 transformation. On the contrary, out-of-phase collisions generally result in the repulsion of the pulses.

Objective: In recent years there has been an increasing interest within the clinical (medical) science in measuring people’s health. When estimating quality of life, present practise is to use the EQ-5D questionnaire and an index which weighs the different questions. The question is what happens if the individuals estimate there own health, would it differ from the public preferences? The aim is to make a new prediction model based on the opinion of patients and compare it to the present model based on public preferences. Method: A sample of 362 patients with unstable coronary artery disease from the Frisc II trial, valued their quality of life in the acute phase and after 3, 6 and 12 months. The EQ-5D question form and also the Time Trade-off method (TTO), a direct method of valuing health was used. A regression technique managing panel data had to be used in estimating TTO by the EQ-5D and other variables like gender and age. Result: Different regression techniques vary in estimating parameters and standard errors. A Generalized Estimating Equation approach with empirical correlation structure is the most suitable regression technique for the data material. A model based on the EQ-5D question form and a continuous age variable proves to be the best model for an index derived by individuals. The difference between heart patients own opinion of health and the public preferences differs a great amount in the severe health conditions, but are rather small for healthy patients. Of the total 243 health conditions, only eight of the conditions were estimated higher by the public index. Conclusions: As the differences between the approaches are significantly large the choice of index could affect the decision making in a health economic study.

This thesis presents a mathematical model of the evaporation of colloidal sol droplets suspended within an atmosphere consisting of water vapour and air. The main purpose of this work is to investigate the causes of the morphologies arising within the powder collected from a spray dryer into which the precursor sol for Synroc™ is sprayed. The morphology is of significant importance for the application to storage of High Level Liquid Nuclear Waste. We begin by developing a model describing the evaporation of pure liquid droplets in order to establish a framework. This model is developed through the use of continuum mechanics and thermodynamic theory, and we focus on the specific case of pure water droplets. We establish a model considering a pure water vapour atmosphere, and then expand this model to account for the presence of an atmospheric gas such as air. We model colloidal particle-particle interactions and interactions between colloid and electrolyte using DLVO Theory and reaction kinetics, then incorporate these interactions into an expression for net interaction energy of a single particle with all other particles within the droplet. We account for the flow of material due to diffusion, advection, and interaction between species, and expand the pure liquid droplet models to account for the presence of these species. In addition, the process of colloidal agglomeration is modelled. To obtain solutions for our models, we develop a numerical algorithm based on the Control Volume method. To promote numerical stability, we formulate a new method of convergence acceleration. The results of a MATLAB™ code developed from this algorithm are compared with experimental data collected for the purposes of validation, and further analysis is done on the sensitivity of the solution to various controlling parameters.

Class of 2013 Abstract
Specific Aims: To assess the association between marginal tax rates (MTR) and innovative output of biotechnology firms. The MTR plays an important role in firms’ financing choices. Assessment of a firm’s tax status may reveal how firms decide on investment policies that affect R&D. Methods: A retrospective database analysis was used. Subjects included were firms within the biotechnology sector with the Standard Industrial Classification code of 2836 from 1980 - 2011. MTR Data was obtained from the S&P Compustat database, and Patent data was obtained from the U.S. Patent and Trademark Office. Changes in MTR’s on outcomes of patents were analyzed by performing an inferential analysis. Generalized estimating equations (GEE) were used, specifically utilizing a GEE regression with a negative binomial distributional family with log link, independent correlation structure and robust standard error variance calculation. Patents were regressed by the lagged change in MTR, after interest deductions. Main Results: The lag years 2 and 5 of the MTR change were statistically significant, (p = 0.031) and (p = 0.026) for each model respectively. Every one unit increase in the change of the MTRs was associated with large and significant drops in patents 78.8% (IRR = 0.212), 90.7% (IRR = 0.093), 92.7% (IRR = 0.073) at year 2 lag and 84.8% (IRR = 0.152), 92.6% (IRR = 0.074) at year 5 lag. Conclusion: An increase in the change of the MTR results in significant drops in patenting activity.

We study numerical stability for interior-point methods applied to Linear Programming, LP, and Semidefinite Programming, SDP. We analyze the difficulties inherent in current methods and present robust algorithms.

We start with the error bound analysis of the search directions for the normal equation approach for LP. Our error analysis explains the surprising fact that the ill-conditioning is not a significant problem for the normal equation system. We also explain why most of the popular LP solvers have a default stop tolerance of only 10^-8 when the machine precision on a 32-bit computer is approximately 10^-16.

We then propose a simple alternative approach for the normal equation based interior-point method. This approach has better numerical stability than the normal equation based method. Although, our approach is not competitive in terms of CPU time for the NETLIB problem set, we do obtain higher accuracy. In addition, we obtain significantly smaller CPU times compared to the normal equation based direct solver, when we solve well-conditioned, huge, and sparse problems by using our iterative based linear solver. Additional techniques discussed are: crossover; purification step; and no backtracking.

Finally, we present an algorithm to construct SDP problem instances with prescribed strict complementarity gaps. We then introduce two measures of strict complementarity gaps. We empirically show that: (i) these measures can be evaluated accurately; (ii) the size of the strict complementarity gaps correlate well with the number of iteration for the SDPT3 solver, as well as with the local asymptotic convergence rate; and (iii) large strict complementarity gaps, coupled with the failure of Slater's condition, correlate well with loss of accuracy in the solutions. In addition, the numerical tests show that there is no correlation between the strict complementarity gaps and the geometrical measure used in [31], or with Renegar's condition number.

2006/2007
Lo scopo di questa tesi di dottorato è la stima del moto forte del suolo nell’area delle Alpi Sud-Orientali. A tal fine sono state proposte delle relazioni empiriche che stimano i parametri del moto in funzione della magnitudo, della distanza dall’epicentro e della classificazione geologica del suolo; successivamente tali relazioni sono state usate per calibrare il software ShakeMaps con il fine di generare in tempo reale le mappe di scuotimento del terreno per la regione Friuli-Venezia Giulia. Le GMPEs (Ground Motion Predictive Equations) per PGA, PGV e SA sono state calcolate nell’area delle Alpi Sud-Orientali utilizzando registrazioni del moto forte del terreno. Sono state selezionate 900 forme d’onde accelerometriche filtrate tra 0.1 Hz e 30 Hz; la distanza epicentrale varia tra 1 km a 100 km, mentre la magnitudo locale, opportunamente calibrata confrontando diversi cataloghi, varia in un intervallo relativamente ampio (3.0 <= ML <= 6.3). Sono stati testati diversi modelli di attenuazione e il miglior risultato è stato individuato utilizzando specifici criteri di valutazione derivanti da considerazioni di carattere statistico (valore di R2, uso dell’ANOVA test, analisi dei residui). I coefficienti del modello finale sono stati determinati oltre che da ML, dalla distanza epicentrale e dagli effetti dovuti al sito, anche dalla saturazione della magnitudo, dalla correlazione tra magnitudo e distanza e dagli effetti di “near-source”. I coefficienti delle GMPEs sono stati calcolati per le componenti verticali ed orizzontali (rappresentata sia con la componente maggiore sia con la somma vettoriale delle due componenti); la tecnica dell’analisi dei gruppi ha permesso di ridurre l’incertezza finale sulle relazioni empiriche. Il confronto con i risultati ottenuti precedentemente evidenzia come le relazioni ottenute in questa tesi abbiano una maggiore attenuazione a basse magnitudo e a grandi distanze; risultati analoghi sono stati ottenuti per le relazioni ricavate dai dati registrati in tutta l’Italia Settentrionale. L’evoluzione recente delle reti sismiche rende oggi disponibile una grossa mole di dati acquisiti in tempo reale, per cui risulta fattibile stimare velocemente lo scuotimento del terreno tramite mappe; il software “ShakeMap” è stato adattato alle Alpi Sud-Orientali implementato allo scopo di ottenere una stabile interfaccia con il sistema di acquisizione dati “Antelope” che garantisca l’estrazione dei parametri del moto dalle forme d’onda e la creazione delle mappe di scuotimento entro 5 minuti dall’evento sismico. Questa procedura richiede una fitta e uniforme distribuzione spaziale degli strumenti di registrazione sul territorio e una classificazione geologica del suolo fatta usando le velocita’ medie, Vs30, dei primi 30m del mezzo immediatamente sotto gli strumenti. La classificazione geologica del suolo prevede la suddivisione in tre categorie (suolo rigido, suolo addensato e suolo soffice) mentre i coefficienti di amplificazione sono stati calcolati usando le relazioni proposte da Borcherdt (1994). Le relative mappe vanno calcolate usando le GMPEs e le relazioni empiriche che legano il moto del terreno all’intensità macrosismica, basate ambedue su dati registrati nella regione alpina. Le GMPEs discusse in precedenza sono state inserite nel software “ShakeMap” per la produzione delle mappe di scuotimento in tempo reale e quasi-reale nell’Italia Nord-Orientale. Per valutare l’effetto della densità di stazioni sulle mappe di scuotimento sono stati calcolati dei sismogrammi sintetici relativi al terremoto di Bovec 2004 variando il passo di griglia e la geometria dei ricevitori. I risultati ottenuti indicano come una distribuzione fitta e uniforme di strumenti sul territorio e una scelta accurata delle dimensioni della griglia dei ricevitori siano cruciali per calibrare le mappe di scuotimento in una ben determinata area geografica. Le mappe di scuotimento del suolo sono state generate per otto terremoti avvenuti nell’area considerata negli ultimi 30 anni; inoltre per gli eventi del Friuli 1976 e Bovec 1998 è stato utilizzato il modello di faglia finita con i parametri di sorgente stimati in precedenti studi. La validazione del modello è stata fatta calcolando il misfit tra le intensità macrosismiche osservate (catalogo DBMI04) e quelle “strumentali” che sono state ottenute dai sismogrammi sintetici tramite relazioni empiriche tra moto del suolo ed intensità. L’analisi è stata fatta per i terremoti del Cansiglio (1936), del Friuli (1976) e di Bovec (1998). I sismogrammi sintetici sono stati calcolati ad una frequenza massima di 10 Hz applicando il modello della riflettività; i parametri del moto sono stati estratti dai segnali sintetici calcolati nelle attuali stazioni di registrazione e successivamente sono state generate le mappe di scuotimento. L’intensità macrosismica “strumentale” è stata ricavata applicando diverse relazioni; il minor misfit è stato ottenuto usando le relazioni proposte da Kästli and Fäh (2006) per tutti e tre i terremoti considerati, il che sembra validare il nostro modello di Shake Maps.
The aim of this PhD thesis is to estimate ground motions in the South-Eastern Alps area. For this purpose we purposed empirical relationships that estimate the ground motion parameters as function of the magnitude, the epicentral distance and the soil geological characterization. Later on these relationships are used to calibrate the ShakeMaps software to generate ground motion shake maps in real time for the Friuli-Venezia Giulia region. The GMPEs (Ground Motion Predictive Equations) for PGA, PGV and SA are computed in the South-Eastern Alps area using strong motion observations. 900 accelerometric waveforms are selected and filtered between 0.1 Hz and 30 Hz; the epicentral distance varies from 1 km to 100 km, while the local magnitude, calibrated by comparison with various catalogues, varies in a relatively wide range (3.0 <= ML <= 6.3). Various attenuation models are tested and the best result is selected by the adoption of specific evaluation criteria derived from statistical considerations (R2 value, ANOVA test, residuals analysis). The coefficients of the final model are determined from ML, the epicentral distance, the site effects, the magnitude saturation, the correlation between the distance and the magnitude and the near-source effects. The coefficients of the GMPEs are computed from vertical and horizontal components (the latter represented both as the largest horizontal component and the vectorial addiction); the cluster analysis reduces the final uncertainties on the empirical relations. The comparison with the previous results evidences that the obtained relationships are characterized by a strong attenuation at low magnitudes and large distances. Similar results are obtained for the relationships derived from data recorded all over Northern Italy. The recent evolution of the seismic networks provides a large number of data, available in real time, so it is possible to quickly estimate shake maps. The “ShakeMap” software has been adapted to the South-Eastern Alps region and implemented to obtain a stable interface with the “Antelope” acquisition system in order to extract the ground motion parameters from the waveforms and the generation of the shake maps within 5 minutes from the earthquake occurrence. This procedure requires a dense and uniform spatial distribution of the recording instruments in the field and a geological classification of the soil derived from the average velocities of the S waves in the first 30m below the recording instruments (Vs30). In the geological classification the soil is divided into three classes (bedrock, stiff soil and soft soil), and the amplification coefficients are computed using the relationships proposed by Borcherdt (1994). The related maps are generated using the GMPEs and the empirical relations that predict the macroseismic intensity from the ground motion, both derived from data observed in the Alpine region. The GMPEs that are obtained in this thesis are inserted in the ShakeMap software to generate shake maps in real time or quasi real time in North-Eastern Italy. To evaluate the effects of the station coverage on the shake maps, synthetic seismograms are computed for the Bovec 2004 earthquake by varying the grid size and the network geometry. The results indicate that a dense and uniform spatial distribution in the field and a careful choice of the grid size are crucial to calibrate the shake maps in a given geographical area. The shake maps are generated for eight earthquakes occurred in the studied area in the last 30 years. Furthermore, the finite-fault model is utilized for the seismic events of the Friuli 1976 and Bovec 1998 selecting the source parameters proposed in previous studies. The model validation is done computing the misfit value between the observed macroseismic data (DBMI04 catalogue) and the “instrumental” intensities that are obtained from the synthetic seismograms using empirical relationships between the ground motion and intensity. This analysis has been done for the earthquakes of Cansiglio (1936), Friuli (1976) and Bovec (1998). The synthetic seismograms are calculated for an upper cutoff frequency of 10 Hz applying the reflectivity model. The ground motion parameters are extracted from synthetic signals computed at the presently operating seismic stations and the shake maps are generated. The macroseismic intensity is derived from various relationships; the lowest misfit is obtained using the relation proposed by Kästli and Fäh (2006) for all considered seismic events and this seem to validate our Shake Maps model.
XX Ciclo
1978

This dissertation consists of three essays studying the effects of collective household decisions on early childhood development from both empirical and theoretical perspectives. The first chapter outlines the dissertation, by presenting the motivations, methods, conclusions, and policy implications for the entire dissertation. Chapter two examines early childhood development using a collective model with children's cognitive production. We jointly estimate the home input demand with children's cognitive production functions based on a simultaneous equations model. Biases are considered that are caused by the non-random selection of time inputs and possible correlations across inputs and outcomes functions. A direct measure of time inputs relying on children's time diaries from the Child Development Supplement of the Panel Study of Income Dynamics (PSID-CDS) has been constructed. We thereby relax the assumption that there is no difference between parental time spent on children and leisure. Our results show that parental time inputs, especially the active time interacting with children's daily activities, have substantial effects on both children's math and reading test scores. The time inputs vary across parents' age, race, and eduction levels. In chapter three, we conduct a standard Blinder-Oaxaca decomposition to evaluate the role of home inputs in the black-white test score gaps based on the empirical model presented in chapter two. Aside from the finding that children's ability accounts for a large proportion of the differences, we find that home inputs can also explain a significant portion of the gap. When the maternal time is equalized at the average levels of white children, the racial differences in children's reading and math test scores can be closed by approximately 30%-50%. The last chapter extends a collective model with household production to the general equilibrium framework. We concentrate on the impacts of a global bargaining power shift within the household on children's cognitive achievement, especially on those who live with single mothers. The model shows that a global bargaining power change in favor of the female may not necessarily be beneficial to the children living with their single mothers. An increase of female's market equilibrium wage rate as a result of reduced labor supply by married women may induce single mothers to work longer hours, spend less time with children, and compensate them with more monetary investment compared with the case when the equilibrium wage rate stays constant.
Ph. D.

De nombreuses études cliniques ou interventions de lutte ont été faites ou sont en cours en Afrique pour la lutte contre le fléau du paludisme. En zone d'endémie, le paludisme est une maladie récurrente. La revue de littérature indique une application limitée des outils statistiques appropriés existants pour l'analyse des données récurrentes de paludisme. Nous avons mis en oeuvre des méthodes statistiques appropriées pour l'analyse des données répétées d'essais thérapeutiques de paludisme. Nous avons également étudié les mesures répétées d'hémoglobine lors du suivi de traitements antipaludiques en vue d'évaluer la tolérance ou sécurité des médicaments en regroupant les données de 13 essais cliniques.Pour l'analyse du nombre d'épisodes de paludisme, la régression binomiale négative a été mise en oeuvre. Pour modéliser la récurrence des épisodes de paludisme, quatre modèles ont été utilisés : i) Les équations d'estimation généralisées (GEE) utilisant la distribution de Poisson; et trois modèles qui sont une extension du modèle Cox: ii) le modèle de processus de comptage d'Andersen-Gill (AG-CP), iii) le modèle de processus de comptage de Prentice-Williams-Peterson (PWP-CP); et iv) le modèle de Fragilité partagée de distribution gamma. Pour l'analyse de sécurité, c'est-à-dire l'évaluation de l'impact de traitements antipaludiques sur le taux d'hémoglobine ou la survenue de l'anémie, les modèles linéaires et latents généralisés mixtes (« GLLAMM : generalized linear and latent mixed models ») ont été mis en oeuvre. Les perspectives sont l'élaboration de guides de bonnes pratiques de préparation et d'analyse ainsi que la création d'un entrepôt des données de paludisme
Numerous clinical studies or control interventions were done or are ongoing in Africa for malaria control. For an efficient control of this disease, the strategies should be closer to the reality of the field and the data should be analyzed appropriately. In endemic areas, malaria is a recurrent disease. Repeated malaria episodes are common in African. However, the literature review indicates a limited application of appropriate statistical tools for the analysis of recurrent malaria data. We implemented appropriate statistical methods for the analysis of these data We have also studied the repeated measurements of hemoglobin during malaria treatments follow-up in order to assess the safety of the study drugs by pooling data from 13 clinical trials.For the analysis of the number of malaria episodes, the negative binomial regression has been implemented. To model the recurrence of malaria episodes, four models were used: i) the generalized estimating equations (GEE) using the Poisson distribution; and three models that are an extension of the Cox model: ii) Andersen-Gill counting process (AG-CP), iii) Prentice-Williams-Peterson counting process (PWP-CP); and (iv) the shared gamma frailty model. For the safety analysis, i.e. the assessment of the impact of malaria treatment on hemoglobin levels or the onset of anemia, the generalized linear and latent mixed models (GLLAMM) has been implemented. We have shown how to properly apply the existing statistical tools in the analysis of these data. The prospects of this work remain in the development of guides on good practices on the methodology of the preparation and analysis and storage network for malaria data

2008/2009
Gli OBS (Ocean Bottom Seismometer) sono ampiamente utilizzati negli studi sismici crostali attraverso l’utilizzo delle registrazioni di onde rifratte e riflesse a grande offset (Wide Angle Reflection/Refraction, WAR/R). L'analisi di questi dati comporta, solitamente, l'impiego di modellistica diretta e/o inversa al fine di giungere alle velocità dei singoli strati e alle profondità delle interfacce. In questa tesi, invece, si presenta un approccio diverso che prevede: 1) costruzione di modelli di velocità dall’analisi dei segnali rifratti; 2) elaborazione dei dati OBS al fine di ottenere immagini sismiche a riflessione. In particolare, gli OBS e gli scoppi sono stati riportati ad uno stesso datum (superficie del mare), utilizzando il Wave Equation Datuming (WED). Dopo il WED è stato possibile applicare l'elaborazione tipica della sismica a riflessione. I profili OBS analizzati sono stati acquisiti nell'area dell'Arco Ellenico e, i risultati ottenuti, hanno permesso di riconoscere le strutture geologiche principali e i meccanismi dell’evoluzione tettonica. L'utilizzo del WED ha migliorato la risoluzione delle sezioni finali rispetto a quanto ottenibile con le correzioni statiche classiche. Per confronto è stata applicata la metodologia WED anche a dati simici ad alta risoluzione a terra, risolvendo problemi di correzioni statiche e di strutturazioni tettoniche apparenti nell'area della Bassa Pianura Friulana.
XXII Ciclo
1979

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.

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Dissertação (Mestrado)
IPEN/D
Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

Cette thèse est centrée sur l’étude d’équations issues de la théorie cinétique des gaz. Dans tous les problèmes qui y sont explorés, une analyse des problèmes linéaires ou linéarisés associés est réalisée d’un point de vue spectral et du point de vue des semi-groupes. A cela s’ajoute une analyse de la stabilité non linéaire lorsque le modèle est non linéaire. Plus précisément, dans une première partie, nous nous intéressons aux équations de Fokker-Planck fractionnaire et Boltzmann sans cut-off homogène en espace et nous prouvons un retour vers l’équilibre des solutions de ces équations avec un taux exponentiel dans des espaces de type L1 à poids polynomial. Concernant l’équation de Landau inhomogène en espace, nous développons une théorie de Cauchy de solutions perturbatives dans des espaces de type L2 avec différents poids (polynomiaux ou exponentiels) et nous prouvons également la stabilité exponentielle de ces solutions.Nous démontrons ensuite pour l’équation de Boltzmann inélastique inhomogène avec terme diffusif le même type de résultat dans des espaces L1 à poids polynomial dans un régime de faible inélasticité. Pour finir, nous étudions dans un cadre général et uniforme des modèles qui convergent vers l’équation de Fokker-Planck du point de vue de l’analyse spectrale et des semi-groupes
The topic of this thesis is the study of models coming from kinetic theory. In all the problems that are addressed, the associated linear or linearized problem is analyzed from a spectral point of view and from the point of view of semigroups. Tothat, we add the study of the nonlinear stability when the equation is nonlinear. More precisely, to begin with, we treat the problem of trend to equilibrium for the fractional Fokker-Planck and Boltzmann without cut-off equations, proving an exponential decay to equilibrium in spaces of type L1 with polynomial weights. Concerning the inhomogeneous Landau equation, we develop a Cauchy theory of perturbative solutions in spaces of type L2 with various weights such as polynomial and exponential weights and we also prove the exponential stability of these solutions. Then, we prove similar results for the inhomogeneous inelastic diffusively driven Boltzmann equation in a small inelasticity regime in L1 spaces with polynomial weights. Finally, we study in the same and uniform framework from the spectral analysis point of view with a semigroup approach several Fokker-Planck equations which converge towards the classical one

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this dissertation we work with the Horava-Lifshitz-like Gross-Neveu model in (2+1) dimensions in the Large N expansion. Firstly we make an article revision [6] where it is shown that the Gross-Neveu Model in the 1/N expansion presents a dynamic mass generation by means of the introduction of an auxiliary field, which results in the dynamical parity broken. We calculate the gap equation where we will see the generated mass dependence with the coupling constant. After that, we will put a gauge field to the model and study the polarization tensor which will generate an induced Chern-Simons term in the Effective Lagrangian. As a novelty, we work with the Gross-Neveu Model in the context of Horava-Lifshitz, where anisotropic scaling is done, thus breaking the Lorentz invariance. We introduce an auxiliary field and we study the cases which the value of the critical dynamic exponent Z is even and when it is odd. In the case where z is even, there is no dynamic mass generation so the parity symmetry is conserved and we will not have the term induced of Chern-Simons either. In the case where z is odd, we will have the dynamic mass generation and the dynamic parity symmetry will occur. Finally we couple a gauge field in the model and find the Chern-Simons term, which clearly shows the anisotropy of space and time for values of z> 1
Nesta dissertacao trabalhamos corn o modelo de Gross-Neveu ern (2+1) dimensoes na expansao 1/N no contexto de Horava-Lifshitz. Primeiro, faremos uma revisao do artigo [6], onde se mostra que o Modelo de Gross-Neveu na expansao 1/N apresenta uma geracao dinamica de massa mediante a introducao de urn campo auxiliar, o que traz como consequencia a quebra dinamica da simetria de paridade. Calculamos a equacao de gap, onde veremos a dependencia da massa gerada corn a constante de acoplamento. ApOs isso, acoplaremos urn campo de gauge ao modelo, estudamos o tensor de polarizacao, o qual vai gerar urn termo induzido de tipo Chern-Simons na lagrangiana efetiva. Como novidade, trabalhamos corn o Modelo de Gross-Neveu no contexto de Horava-Lifshitz, onde se faz urn escalonamento anisotrOpico, quebrando, assim, a invariancia de Lorentz. Introduzimos urn campo auxiliar e estudamos os casos ern que o valor do exponente dinamico critico z é par quando é Impar. No caso ern que z é par, nao ha geracao dinamica de massa pelo que a simetria de paridade é conservada e tambern nao teremos o termo induzido de Chern-Simons. No caso ern que z é impar, vamos ter a geracao dinamica de massa vai ocorrer a quebra dinamica de simetria de paridade. Finalmente, acoplamos urn campo de gauge no modelo e encontramos o termo tipo Chern-Simons, o qual mostra claramente a anisotropia do espaco tempo para valores de z > 1.

The aim of this thesis is the application of the GPS technology to the investigation of crustal deformations, in order to exploit data from a GPS network to improve the knowledge of seismic phaenomena. We attack this problem at different levels: from weekly GPS data processing to normal equations stacking, in order to compute the velocity field and the deformations field of the crust. As a EUREF LAC (Local Analysis Centre) we carry out the weekly processing following the EUREF guidelines: we process data from a cluster of 34 stations. Besides this, we process data from another (non EUREF) cluster of stations, deployed on the Italian and Austrian regions. The aim of this second processing activity is to densify the EUREF network using stations whose quality is comparable to the EUREF stations. For both of the networks raw data are made up of daily phase and code measuremente, at 30 seconds sampled, stored as RINEX observation files. We download these data every week, using PERL scripts to automate the procedure. The data processing is also done in an automatic way, trough Bernese 5 and the Bernese Processing Engine. To produce daily normal equations and coordinates estimates we use the processing strategy defined by RNX2SNX PCF. This Process Control File is made of a list of statements activating the Bernese programs; the main features of this procedure are 1) Rejecting of RINEX containing large gaps or big residuals, 2) Ambiguity resolution through quasi-ionosphere-free strategy, 3) alignement of the network to the ITRF2000 (ITRF2005, now) using a set of fiducial stations. Weekly coordinates are estimated by stacking the daily normal equations; daily tropospheric delays are estimated by fixing the coordinates of the site to their weekly mean values.The velocity field is computed by a multi years solution. At this level we must ensure that all the discontinuities and the outliers are eliminated from the time series of each station. This is done by editing a Bernese input file (.STA) which stores all the information needed to remove discontinuities and reject outliers. Once continous EUREF time series have been obtained, we densify the velocity field by using the information stored in Austrian and Italian regions normal equations files. In order to estimate a reliable velocity field we solve the problem of multi-year normal equations stacking. First of all, we stack the EUREF weekly normal equations; in order to solve this issue it is necessary to screen the time serie of each site in order to find all the offsets and the outliers. The information collected is stored in a input file (.STA file) for the Bernese 5 stacking programme ADDNEQ2. The EUREF normal equations (neq's) stacking is essential for the definition of the reference frame. The second issue is the densification of the EUREF velocity field. This step is essential because the EUREF network is a cartographic network, so its data are not suitable to be used in crustal deformation studies. But this network can be densified using the data belonging to others GPS local networks through the stacking of their normal equations. In this view, each weekly (local) normal equation must be stacked with the related EUREF weekly normal equation, hence the resulting neq's must be stacked in a multi-year solution. We use weekly neq's belonging to two networks, namely UPA and GP, to densify the velocity field in the Italian and Austrian areas. During the EUREF multi-year stacking the programme ADDNEQ2 showed poor speed performance and repeatedly crashed, so we decided to use a faster and more stable software. We moved to CATREF (Combination and Analysis of Terrestrial Reference Frames, see altamimiitrf2000, altamimiitrf2005 and noquet). The stacking strategy we used to carry out the multi-year densified solution is made of 4 steps: 1.Removal of the a-priori constraints from EUREF, UPA and GP weekly neq's, and imposition of new constraints. 2.Preliminary multi-year solution for each network, in order to find offsets and outliers. 3.Stacking of each UPA and GP neq with the related EUREF neq. 4.Multi-year stacking of the resulting neq's. Step 1 is very important to define a reference frame which is common for each neq involved in a stacking procedure. It is well known the neq's deriving from GPS observables are not full rank: the rank deficit is 7 and is strictly related to the poor definition of the reference frame given by the GPS observables themselves, since they are not sensitive to changes due to translations, rotation and are also scale invariant. So the information used to define the reference frame must be introduced by means of pseudo-observation equations called constraints. Several kinds of constraints can be imposed: some of them acting on the coordinates and velocities of the sites, others acting on the translation, rotation and scale parameters. CATREF is based on the second kind of constraints (the so-called minimum constraints). Offsets detected in the time series are treated through a piecewise approach: two sets of coordinates and velocities are estimated for the same site, using the data before and after the offset epoch and constraining the velocities (before and after) to the same value. The weighted RMS (WRMS) of the weekly solution versus the stacked solution is used to check the correctness of the constraints and outliers removal. Following A. Kenyeres http://www.epncb.oma.be/_organisation/projects/series_sp/cumulative_solution.php we can say that WRMS of or greater than 1 cm reveals the presence of outliers, and that a very small WRMS value (under 1 mm for the vertical residuals) reveals a wrong constraint removal. In our case we have WRMS_{EUREF}?[2.0,3.5] mm, WRMS_{UPA}?[2.0,4.5] mm and WRMS_{GP}?[2.0,5.0] mm. The WRMS of the vertical residuals is greater than 2 mm for the three multi-year solutions. We expected that WRMS of the UPA and GP stacking were greater than EUREF one because the raw data coming from UPA and GP are non checked as strictly as EUREF data. Moreover the plots of the Helmert parameters related to the UPA and GP neq's stacking reveal the inadequacy of reference frame definition, especially for the UPA neq's. However the weekly stacking of the EUREF, UPA and GP neq's seems to compensate this fact. The combined reference frame is aligned to ITRF05 by minimum constraints imposed on the following subset of sites: . BRUS A 13101M004 JOZE A 12204M001 POTS A 14106M003 TRAB A 20808M001 GLSV A 12356M001 MAS1 A 31303M002 ZIMM A 14001M004 TRO1 A 10302M006 GRAS A 10002M006 METS A 10503S011 RABT A 35001M002 VILL A 13406M001 HOFN A 10204M002 NOT1 A 12717M004 A further check of the correctess of the alignment of the combined frame to ITRF05 is performed by computing the residuals of the velocity on a subset of sites common to the combined frame and the ITRF05. The common sites are 29 and the averaged velocity residuals in East and North direction are: East [mm/yr] North [mm/yr] -0.11 0.07 The total number of sites contained in the EUREF, UPA ang GP multi-year solution is 247. ETRF velocities are computed using the transformation parameters reported in boucheraltamimi. Later we did the processing of 9 annual and bi-annual measurement campaigns related to the CEGRN network (time span 1994-2007), using reprocessed satellite orbits and EOPs files (see steigenberger). The related neq's, stacked with the corresponding neq's computed by the others analysis centres participating in the CEGRN project, were stacked with the EUREF, UPA and GP neq's, resulting a multi-year solution wich contains 296 sites. From this velocity field we can infer that the central European area is rigid (it shows horizontal ETRF velocity values smaller than 1 mm/yr) and that the Mediterranean area is characterized by ETRF velocity values greater than 2 mm/yr. Moreover we verified that the effect of the annual term, for a time span greater than 2.5 years, is negligible (see blewittlavalle). The averaged effect is 0.01 mm/yr and 0.06 mm/yr for the East and North components of the horizontal velocity. The stacking strategy (with CATREF ) is fully explained in chapter 9. Offsets tables, Helmert parameters and WRMS plots are given. The velocity field was used to infer the strain rate. The horizontal strain rate tensor can be expressed as a linear combination of the partials of the velocity field, computed with respect to the East and North directions: ?_{ee} = ((?v^{e})/(?e)), ?_{en} = (1/2)(((?v?)/(?e))+((?v^{e})/(?n))), ?_{nn} = ((?v?)/(?n)). The horizontal velocity field can be approximated analitically by means of least squares collocation. The least squares collocation is based on a knowledege of the statistical properties of the field. The interpolation formula can be written as (see moritz): s=C_{st}(C_{tt}+C_{nn})?¹l where s is the values of the field in the interpolation grid, l is the vector of the observed (centered) values of the field, C_{nn} is the noise covariance matrix (multipled by a factor 10 to compensate for the effects of random and flicker noise) of the measurements, C_{tt} is the covariance matrix of the observed values of the field and C_{st} is the cross-covariance matrix between the interpolation points and the oservation points. If we suppose the velocity field is isotropic and homogeneus, the elements of the covariance and cross-covariance matrices can be represented by the Cauchy function: C_{ij}^{e_{n}n}=((w_{e_{n}n})/(1+(((d_{ij})/(d?)))²)) where d_{ij} is the spherical distance between i and j sites, w_{e_{n}n} are the variances of the East and North components of the velocity field and d? is the correlation length. The w_{e_{n}n} values were computed through the empirical variance formula, and the d? value was estimating by fitting the (normalized) Cauchy function to the empirical correlogram. We found d?=105 Km. This values is (1/3) smaller than the values reported by altamimilegrand, kahlestraub, kahlecocard1 e kahlecocard2. The strain-rate tensor is built using the partials of the analitical approximation given by the least squares collocation formula, computed with respect to East and North direction. To check the correctness of the algorithm we compare our strain-rate values with those estimated by serpe1. South-Eastern Alps are characterized by a deformation rate of 10÷15 nstrain/yr, Central Italy shows an extension rate of 25 nstrain/yr. Sardinia and Corsica do not show significant deformation rates. The agreement between or results and serpe1 is better where our velocity field is more dense. This agreement is important because our processing and stacking software, our GPS network configuration and our strain-rate computation algorithm is different from serpe1. Finally this agreeent suggests that the value of the correlation length we found is correct. Since we had not the strain-rate computation software, we coded the least squares collocation algorithm into a python module (see appendix A.8).

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Financiadora de Estudos e Projetos
One of the distributions used to model extremal events is the type I extremevalue distribution (Gumbel distribution). The usual extreme-value regression model requires independent observations. In this work, using generalized linear model (Mc-Cullagh e Nelder, 1989) and generalized estimating equations (Liang e Zeger, 1986), we developed the extreme-value regression model when there are independent clusters formed by dependent variables. The behavior of parameter estimators of the proposed model is studied through Monte Carlo simulations.
A distribuição valor extremo tipo I, também conhecida como distribuição Gumbel, é uma das distribuições utilizadas para a modelagem de eventos extremos. Os modelos existentes de regressão valor extremo supõem que as observações sejam independentes, inviabilizando o uso desses modelos quando existe dependência entre as observações. Nesta dissertação, utilizando modelos lineares generalizados (McCullagh e Nelder, 1989) e equações de estimação generalizadas (Liang e Zeger, 1986), desenvolvemos o modelo de regress~ao valor extremo para o caso em que h a grupos independentes formados por respostas dependentes. O comportamento dos estimadoresdos parâmetros do modelo proposto é avaliada através de simulações Monte Carlo.

Full Waveform Inversion has become an important research field in the context of seismic exploration, due to the possibility to estimate a high-resolution model of the subsurface in terms of acoustic and elastic parameters. To this aim, issues such as an efficient implementation of wave equation solution for the forward problem, and optimization algorithms, both local and global, for this high non-linear inverse problem must be tackled. In this thesis, in the framework of 2D acoustic approximation, I implemented an efficient numerical solution of the wave equation based on a local order of approximation of the spatial derivatives to reduce the computational time and the approximation error. Moreover, for what concerns the inversion, I studied two different global optimization algorithms (Simulated Annealing and Genetic Algorithms) on analytic functions that represent different possible scenarios of the misfit function to estimate an initial model for local optimization algorithm in the basin of attraction of the global minimum. Due to the high number of unknowns in seismic exploration context, of the order of some thousands or more, different strategies based on the adjoint method must be used to compute the gradient of the misfit function. By this procedure, only three wave equation solutions are required to compute the gradient instead of a number of solutions proportional to the unknown parameters. The FWI approach developed in this thesis has been applied first on a synthetic inverse problem on the Marmousi model to validate the whole procedure, then on two real seismic datasets. The first is a land profile with two expanding spread experiments and is characterized by a low S/N ratio. In this case, the main variations of the estimated P-wave velocity model well correspond to the shallow events observed on the post-stack depth migrated section. The second is a marine profile extracted from a 3D volume where the local optimization, based on the adjoint method, allows to estimate a high-resolution velocity model whose reliability has been checked by the alignment of the CIGs computed by pre-stack depth migration.

Ca2+ acts as a fundamental signal transduction element in the inner ear, delivering information about sound acceleration and gravity through a small number of mechano-transduction channels in the hair cell stereocilia as far as to the ribbon synapse, where it drives neurotransmission. The genetic approach is proving fundamental in unravelling the molecular basis of Ca2+ function in the control of these key cellular processes. Ablation or missense mutations of the PMCA2 Ca2+-pump of stereocilia cause deafness and loss of balance. To investigate the physiological significance of these genetic defects, we studied PMCA2 Ca2+-extrusion in hair cells of utricle organotypic cultures from neonatal mice inner ear. Confocal Ca2+ imaging showed that the dissipation of stereociliary Ca2+ transients, induced by cytosolic photoliberation, was compromised by various degrees in PMCA2 knockout mice as well as in the mutant deafwaddler and Oblivion mice. Alteration of the intracellular Ca2+ concentration ( ) can trouble the finely tuned control mechanisms of signal transduction, thus resulting as a fundamental physiological parameter to be investigated in the comprehension of deafness mechanisms. By comparing our experimental fluorescence data with those derived from Monte Carlo numerical simulations, we provided a novel method to effectively deconvolve within cytoplasmic microdomains that would otherwise remain inaccessible to direct observation. Data analysis performed within this environment indicates that changes of hair cell basolateral during synaptic transmission are primarily controlled by the endogenous Ca2+ buffers at both short (< 1 micron) and long (tens of microns) distances from the presynaptic active zones. Furthermore, we provided quantitative estimates of concentration and kinetics of the endogenous Ca2+-buffers and Ca2+-ATPases in frog vestibular hair cells. We successfully applied mathematical models also in the study of channel permeability to second messengers of gap junctions, intercellular channels connecting supporting cells of the organ of Corti. In particular, it's known that defective permeation of cAMP or inositol 1,4,5-trisphosphate through gap junction channels is associated with peripheral neuropathies and deafness, respectively. Our model permits quantification of defects of metabolic coupling and can be used to investigate interdependence of intercellular diffusion and cross-talk between diverse signaling pathways.

Infimalfolgen nichtkonvexer Variationsprobleme haben aufgrund feiner Oszillationen häufig keinen starken Grenzwert in Sobolevräumen. Diese Oszillationen haben eine physikalische Bedeutung; Finite-Element-Approximationen können sie jedoch im Allgemeinen nicht auflösen. Relaxationsmethoden ersetzen die nichtkonvexe Energie durch ihre (semi)konvexe Hülle. Das entstehende makroskopische Modell ist degeneriert: es ist nicht strikt konvex und hat eventuell mehrere Minimalstellen. Die fehlende Kontrolle der primalen Variablen führt zu Schwierigkeiten bei der a priori und a posteriori Fehlerschätzung, wie der Zuverlässigkeits- Effizienz-Lücke und fehlender starker Konvergenz. Zur Überwindung dieser Schwierigkeiten erweitern Stabilisierungstechniken die relaxierte Energie um einen diskreten, positiv definiten Term. Bartels et al. (IFB, 2004) wenden Stabilisierung auf zweidimensionale Probleme an und beweisen dabei starke Konvergenz der Gradienten. Dieses Ergebnis ist auf glatte Lösungen und quasi-uniforme Netze beschränkt, was adaptive Netzverfeinerungen ausschließt. Die vorliegende Arbeit behandelt einen modifizierten Stabilisierungsterm und beweist auf unstrukturierten Netzen sowohl Konvergenz der Spannungstensoren, als auch starke Konvergenz der Gradienten für glatte Lösungen. Ferner wird der sogenannte Fluss-Fehlerschätzer hergeleitet und dessen Zuverlässigkeit und Effizienz gezeigt. Für Interface-Probleme mit stückweise glatter Lösung wird eine Verfeinerung des Fehlerschätzers entwickelt, die den Fehler der primalen Variablen und ihres Gradienten beschränkt und so starke Konvergenz der Gradienten sichert. Der verfeinerte Fehlerschätzer konvergiert schneller als der Fluss- Fehlerschätzer, und verringert so die Zuverlässigkeits-Effizienz-Lücke. Numerische Experimente mit fünf Benchmark-Tests der Mikrostruktursimulation und Topologieoptimierung ergänzen und bestätigen die theoretischen Ergebnisse.
Infimising sequences of nonconvex variational problems often do not converge strongly in Sobolev spaces due to fine oscillations. These oscillations are physically meaningful; finite element approximations, however, fail to resolve them in general. Relaxation methods replace the nonconvex energy with its (semi)convex hull. This leads to a macroscopic model which is degenerate in the sense that it is not strictly convex and possibly admits multiple minimisers. The lack of control on the primal variable leads to difficulties in the a priori and a posteriori finite element error analysis, such as the reliability-efficiency gap and no strong convergence. To overcome these difficulties, stabilisation techniques add a discrete positive definite term to the relaxed energy. Bartels et al. (IFB, 2004) apply stabilisation to two-dimensional problems and thereby prove strong convergence of gradients. This result is restricted to smooth solutions and quasi-uniform meshes, which prohibit adaptive mesh refinements. This thesis concerns a modified stabilisation term and proves convergence of the stress and, for smooth solutions, strong convergence of gradients, even on unstructured meshes. Furthermore, the thesis derives the so-called flux error estimator and proves its reliability and efficiency. For interface problems with piecewise smooth solutions, a refined version of this error estimator is developed, which provides control of the error of the primal variable and its gradient and thus yields strong convergence of gradients. The refined error estimator converges faster than the flux error estimator and therefore narrows the reliability-efficiency gap. Numerical experiments with five benchmark examples from computational microstructure and topology optimisation complement and confirm the theoretical results.

Le présent travail de thèse fait suite à une première étude où une stratégie d’identification des paramètres et formes des lois de zones cohésives a été élaborée pour des matériaux homogènes. L’extension au cas de matériaux présentant des hétérogénéités nécessite d’accéder localement aux champs de contraintes.Ainsi, l’objectif principal de cette étude est de mettre au point une méthode de caractérisation locale des propriétés mécaniques et des contraintes. Cette méthode est basée sur l’erreur en relation de comportement combinée à l’exploitation de la richesse des mesures de champs cinématiques planes et plus particulièrement des champs de déformations, obtenus par dérivation numérique des champs de déplacements. Cette mesure cinématique est réalisée par une technique de corrélation d’images numériques enrichie.La méthode d’identification est basée sur la minimisation itérative d’une norme énergétique faisant intervenir le tenseur élastoplastique sécant. Différentes simulations numériques ont illustré la capacité de la procédure à identifier localement des champs de propriétés hétérogènes et sa robustesse et sa stabilité vis-à-vis du bruit de mesure, du choix du jeu de paramètres d’initialisation de l’algorithme et de la finesse du maillage.Pour finir, des essais plans avec différentes géométries d’éprouvettes ont été effectués et un essai a été mis au point pour obtenir de manière maîtrisée un état initial très hétérogène. Les résultats d’identification élastoplastique multilinéaire ont montré la capacité de la méthode à identifier les lois de comportements locales sur ce matériau hétérogène
The present work follows a first approach where a strategy for identifying the shape and the parameters of cohesive-zone laws has been developed for homogeneous materials. The extension of this method to heterogeneous material requires the knowledge of the local stress state.The study aims at developing a local characterization method for mechanical properties and stresses. This method is based on the constitutive equation gap principles and relies on the knowledge of mechanical kinematic fields and particularly of the strain fields. These fields are obtained by the numerical differentiation of displacement fields measured by digital image correlation.This identification method is based on the iterative minimization of an energy norm involving the secant elastoplastic tensor. Various numerical simulations were used to illustrate the performance of the procedure for locally identifying heterogeneous property fields, and to characterize its robustness and its stability with respect to noise to the values of the algorithm initialization parameter and to the mesh refinement.Finally, various experimental tests with different specimen geometries were performed and a test has been developed to obtain a controlled heterogeneous initial state. The multilinear elastoplastic identification results showed the ability of the method to identify the local behavior properties on heterogeneous materials

Les développements asymptotiques topologiques n'ont pas encore été étudiés pour les équations elliptiques quasilinéaires. Cette question apparaît dans la perspective d'appliquer les méthodes d'asymptotique topologique en optimisation de forme aux équations non linéaires de l'élasticité comme en imagerie pour la détection d'ensembles de codimension $\geq 2$ (points en 2D ou courbes en 3D). Dans la Partie I, notre principal résultat réside dans l'obtention du développement asymptotique topologique pour une classe d'équations elliptiques quasilinéaires, perturbées dans des sous-domaines non vides. Le gradient topologique peut être décomposé en un terme linéaire classique et en un terme nouveau, qui rend compte de la non linéarité. L'étude des difficultés spécifiques qui apparaissent avec l'équation de p-Laplace, par comparaison avec l'équation de Laplace, montre qu'un point central réside dans la possibilité de définir la variation de l'état direct à l'échelle 1 dans R^N. Nous étudions en conséquence des espaces de Sobolev à poids et quotientés, dont la semi-norme est la somme des normes L^p et L^2 du gradient dans R^N. Puis nous construisons une classe d'équations elliptiques quasilinéaires, telle que le problème définissant l'état direct à l'échelle 1 vérifie une double propriété de p- et 2- ellipticité. La méthode se poursuit par l'étude du comportement asymptotique de la solution du problème d'interface non linéaire dans R^N et par une mise en dualité appropriée des états directs et adjoints aux différentes étapes d'approximation pour les variations de l'état direct. La Partie II traite d'estimations et de développements asymptotiques de p-capacités de condensateurs, dont l'obstacle est d'intérieur vide et de codimension $\geq 2$. Après quelques résultats préliminaires, nous introduisons les condensateurs équidistants pour étudier le cas des segments. L'effet anisotrope engendré par un segment dans l'équation de p-Laplace est tel que l'inégalité de réarrangement de Pólya-Szegö pour les intégrales de type Dirichlet fournit un minorant trivial. De plus, quand p > N, on ne peut construire par extension une solution admissible pour le segment, aussi petite sa longueur soit-elle, à partir du cas du point. Nous établissons une minoration de la p-capacité N-dimensionnelle d'un segment, qui fait intervenir les p-capacités d'un point, respectivement en dimensions N et (N−1). Les cas de positivité de la p-capacité s'en déduisent. Notre méthode peut être étendue à des obstacles de dimensions supérieures et de codimension $\geq 2$. Introduisant les condensateurs elliptiques, nous montrons que le gradient topologique de la 2-capacité n'est pas un outil approprié pour distinguer les courbes et les obstacles d'intérieur non vide en 2D. Une solution pourrait être de choisir différentes valeurs de p ou bien de considérer le développement asymptotique à l'ordre 2, i.e. la hessienne topologique.

Dans cette thèse nous regardons plusieurs modèles de populations structurés s’écrivant à l’aide d’équations de transport. Le caractère bien posé ainsi que la positivité des solutions sont montrés de manière systématique au sens des sémiologues dans un cadre L1. Un premier travail est consacré à un système de type proie prédateur structuré en âge. Une étude de stabilité des équilibres nous permet de formuler explicitement un seuil un seuil d’extinction ainsi qu’in seuil pouvant amener à l’explosion des populations. On obtient numériquement la possibilité d’un cycle limite ainsi que la convergence vers un équilibre de coexistence des populations. Dans un cas particulier, ce modèle se réécrit comme un système différentiel à retard. A l’aide de fonctionnelle de Lyapunov, on montre la stabilité globale de cet équilibre sous certaines conditions. On étudie également 2 modèles structuré en taille, issus de la dynamique cellulaire. L’un est composé de deux équations de transport où la cellule peut être soit prolifèrent soit quiescente ; et le deuxième est une équation de type transport/ diffusion avec des conditions aux bords FELLER. On vérifie à chaque fois l’irréductibilité du semi groupe puis des arguments de faibles capacité L1 nous donne l’existence d’un « gap spectral » sous certaines conditions. On démontre ainsi dans certains cas la croissance exponentielle asynchrone du semi groupe
This thesis is dedicated to some structured populations models described with transport or transport-diffusion equations. The well-posedness, in the semigroupes setting in L1 and the positivity of the solutions are systematically shown. A first work is dedicated to an age-structured predator/prey system. A stability study of the equilibria allow us to give explicit formulations of an extinction threshold and an threshold which can lead to explosion of solutions. We numerically obtain the possibility to get a limit cycle and the convergence to a coexistence equilibrium of the populations. In a specific case, this model rewrites as a delay differential system. Using Lyapunov functional, we show the global stability of this equilibrium under some assumptions. We also study two size-structured models that come from cellular dynamics. The first one consists on two transport equations, where the cell can either proliferate or be quiescent, and the second one is a transport-diffusion equation with Feller boundary conditions. The irreducibility of the semigroup governing this latter model is always satisfied using the Hopf maximum principle. However, the irreducibility for the first model is true only under a necessary and sufficient condition that we give. We also show for these two models, using some weak compactness arguments in L1, the existence of a `spectral gap' (essential type strictly less than the type) ensuring the asynchronous exponential growth of the semigroup

In this thesis, we study mathematical models that describe the morphology of a generalized biological cell in equilibrium or under the influence of external forces. Within these models, the cell is considered as a thermodynamic system, where streaming effects in the cell bulk and the surrounding are coupled with a Helfrich-type model for the cell membrane. The governing evolution equations for the cell given in a continuum formulation are derived using an energy variation approach. Such two-phase flow problems that combine streaming effects with a free boundary problem that accounts for bending and surface tension can be described effectively by a diffuse interface approach. An advantage of the diffuse interface approach is that models for e.g. different biophysical processes can easily be combined. That makes this method suitable to describe complex phenomena such as cell motility and multi-cell dynamics. Within the first model for cell motility, we combine a biological network for GTPases with the hydrodynamic Helfrich-type model. This model allows to account for cell motility driven by membrane protrusion as a result of actin polymerization. Within the second model, we moreover extend the Helfrich-type model by an active gel theory to account for the actin filaments in the cell bulk. Caused by contractile stress within the actin-myosin solution, a spontaneous symmetry breaking event occurs that lead to cell motility. In this thesis, we further study the dynamics of multiple cells which is of wide interest since it reveals rich non-linear behavior. To apply the diffuse interface framework, we introduce several phase field variables to account for several cells that are coupled by a local interaction potential. In a first application, we study white blood cell margination, a biological phenomenon that results from the complex relation between collisions, different mechanical properties and lift forces of red blood cells and white blood cells within the vascular system. Here, it is shown that inertial effects, which can become of relevance in various parts of the cardiovascular system, lead to a decreasing tendency for margination with increasing Reynolds number. Finally, we combine the active polar gel theory and the multi-cell approach that is capable of studying collective migration of cells. This hydrodynamic approach predicts that collective migration emerges spontaneously forming coherently-moving clusters as a result of the mutual alignment of the velocity vectors during inelastic collisions. We further observe that hydrodynamics heavily influence those systems. However, a complete suppression of the onset of collective migration cannot be confirmed. Moreover, we give a brief insight how such highly coupled systems can be treated numerically using finite elements and how the numerical costs can be limited using operator splitting approaches and problem parallelization with OPENMP
Diese Dissertation beschäftigt sich mit mathematischen Modellen zur Beschreibung von Gleichgewichts- und dynamischen Zuständen von verallgemeinerten biologischen Zellen. Die Zellen werden dabei als thermodynamisches System aufgefasst, bei dem Strömungseffekte innerhalb und außerhalb der Zelle zusammen mit einem Helfrich-Modell für Zellmembranen kombiniert werden. Schließlich werden durch einen Energie-Variations-Ansatz die Evolutionsgleichungen für die Zelle hergeleitet. Es ergeben sie dabei Mehrphasen-Systeme, die Strömungseffekte mit einem freien Randwertproblem, das zusätzlich physikalischen Einflüssen wie Biegung und Oberflächenspannung unterliegt, vereinen. Um solche Probleme effizient zu lösen, wird in dieser Arbeit die Diffuse-Interface-Methode verwendet. Ein Vorteil dieser Methode ist, dass es sehr einfach möglich ist, Modelle, die verschiedenste Prozesse beschreiben, miteinander zu vereinen. Dies erlaubt es, komplexe biologische Phänomene, wie zum Beispiel Zellmotilität oder auch die kollektive Bewegung von Zellen, zu beschreiben. In den Modellen für Zellmotilität wird ein biologisches Netzwerk-Modell für GTPasen oder auch ein Active-Polar-Gel-Modell, das die Aktinfilamente im Inneren der Zellen als Flüssigkristall auffasst, mit dem Multi-Phasen-Modell kombiniert. Beide Modelle erlauben es, komplexe Vorgänge bei der selbst hervorgerufenen Bewegung von Zellen, wie das Vorantreiben der Zellmembran durch Aktinpolymerisierung oder auch die Kontraktionsbewegung des Zellkörpers durch kontraktile Spannungen innerhalb des Zytoskelets der Zelle, zu verstehen. Weiterhin ist die kollektive Bewegung von vielen Zellen von großem Interesse, da sich hier viele nichtlineare Phänomene zeigen. Um das Diffuse-Interface-Modell für eine Zelle auf die Beschreibung mehrerer Zellen zu übertragen, werden mehrere Phasenfelder eingeführt, die die Zellen jeweils kennzeichnen. Schließlich werden die Zellen durch ein lokales Abstoßungspotential gekoppelt. Das Modell wird angewendet, um White blood cell margination, das die Annäherung von Leukozyten an die Blutgefäßwand bezeichnet, zu verstehen. Dieser Prozess wird dabei bestimmt durch den komplexen Zusammenhang zwischen Kollisionen, den jeweiligen mechanischen Eigenschaften der Zellen, sowie deren Auftriebskraft innerhalb der Adern. Die Simulationen zeigen, dass diese Annäherung sich in bestimmten Gebieten des kardiovaskulären Systems stark vermindert, in denen die Blutströmung das Stokes-Regime verlässt. Schließlich wird das Active-Polar-Gel-Modell mit dem Modell für die kollektive Bewegung vom Zellen kombiniert. Dies macht es möglich, die kollektive Bewegung der Zellen und den Einfluss von Hydrodynamik auf diese Bewegung zu untersuchen. Es zeigt sich dabei, dass der Zustand der kollektiven gerichteten Bewegung sich spontan aus der Neuausrichtung der jeweiligen Zellen durch inelastische Kollisionen ergibt. Obwohl die Hydrodynamik einen großen Einfluss auf solche Systeme hat, deuten die Simulationen nicht daraufhin, dass Hydrodynamik die kollektive Bewegung vollständig unterdrückt. Weiterhin wird in dieser Arbeit gezeigt, wie die stark gekoppelten Systeme numerisch gelöst werden können mit Hilfe der Finiten-Elemente-Methode und wie die Effizienz der Methode gesteigert werden kann durch die Anwendung von Operator-Splitting-Techniken und Problemparallelisierung mittels OPENMP

Nous nous intéressons dans cette thèse à la théorie cinétique et aux systèmes de particules dans le cadre des équations de Boltzmann et Landau. Premièrement, nous étudions la dérivation des équations cinétiques comme des limites de champ moyen des systèmes de particules, en utilisant le concept de propagation du chaos. Plus précisément, nous étudions les probabilités chaotiques sur l'espace de phase de ces systèmes de particules : la sphère de Boltzmann, qui correspond à l'espace de phase d'un système de particules qui évolue conservant le moment et l'énergie ; et la sphère de Kac, correspondant à un système de particules qui conserve seulement l'énergie. Ensuite, nous nous intéressons à la propagation du chaos, avec des estimations quantitatives et uniforme en temps, pour les équations de Boltzmann et Landau. Deuxièmement, nous étudions le comportement asymptotique en temps grand des solutions de l'équation de Landau.

On s'intéresse dans cette thèse à l'étude des solutions des équations de Boltzmann (élastiques et inélastiques) et Landau. Les axes de cette étude sont la régularité des solutions et leur comportement asymptotique, et nous nous attachons systématiquement à quantifier les résultats obtenus. Dans la première partie, d'une part nous considérons les solutions spatialement homogènes de l'équation de Boltzmann, pour lesquelles nous montrons la propagation de la régularité et la décroissance des singularités pour des interactions à courte portée, et la propagation de bornes
d'intégrabilité pour des interactions à longue portée. D'autre part, nous quantifions la positivité des solutions spatialement
inhomogènes, sous des hypothèses de régularité. Dans la deuxième partie, nous donnons des estimations de trou spectral et de coercivité sur les opérateurs de Boltzmann et Landau linéarisés, puis nous prouvons la convergence exponentielle vers l'équilibre avec taux explicite pour un gaz de sphères dures spatialement homogènes. Dans la troisième partie, nous considérons l'équation de Boltzmann spatialement homogène pour les gaz granulaires, pour laquelle nous construisons des solutions pour des modèles d'inélasticité réalistes (mais fortement non-linéaires) et discutons la possibilité de « gel » en temps fini ou asymptotiquement. Puis nous montrons l'existence de profils auto-similaires et étudions le comportement de la solution pour les grandes vitesses. Dans la quatrième partie, nous utilisons une semi-discrétisation de l'opérateur de Boltzmann pour proposer
des schémas numériques rapides basés sur les méthodes spectrales ou les méthodes par discrétisation des vitesses.

Mit dem Begriff Wellenleiterquantenelektrodynamik (WQED) wird gemeinhin die Physik des quantisierten und in eindimensionalen Wellenleitern geführten Lichtes in Wechselwirkung mit einzelnen Emittern bezeichnet. In dieser Arbeit untersuche ich Effekte der WQED für einzelne Dreiniveausysteme (3NS) bzw. Paare von Zweiniveausystemen (2NS), die in den Wellenleiter eingebettet sind. Hierzu bediene ich mich hauptsächlich numerischer Methoden und betrachte die Modellsysteme im Rahmen der Drehwellennäherung. Ich untersuche die Dynamik der Streuung einzelner Photonen an einzelnen, in den Wellenleiter eingebetteten 3NS. Dabei analysiere ich den Einfluss dunkler bzw. nahezu dunkler Zustände der 3NS auf die Streuung und zeige, wie sich mit Hilfe stationärer elektrischer Treibfelder gezielt auf die Streuung einwirken lässt. Ich quantifiziere Verschränkung zwischen dem Lichtfeld im Wellenleiter und den Emittern mit Hilfe der Schmidt-Zerlegung und untersuche den Einfluss der Form der Einhüllenden eines Einzelphotonpulses auf die Ausbeute der Verschränkungserzeugung bei der Streuung des Photons an einem einzelnen Lambda-System im Wellenleiter. Hier zeigt sich, dass die Breite der Einhüllenden im k-Raum und die Emissionszeiten der beiden Übergänge des 3NS die maßgeblichen Parameter darstellen. Abschließend ergründe ich die Emissionsdynamik zweier im Abstand L in den Wellenleiter eingebetteter 2NS. Diese Dynamik wird insbesondere durch kavitätsartige und polaritonische Zustände des Systems aus Wellenleiter und Emitter ausschlaggebend beeinflusst. Bei der kollektiven Emission der 2NS treten - abhängig vom Abstand L - Sub- bzw. Superradianz auf. Dabei nimmt die Intensität dieser Effekte mit längerem Abstand L zu. Diese Eigenart lässt sich auf die Eindimensionalität des Wellenleiters zurückführen.
The field of waveguide quantum electrodynamics (WQED) deals with the physics of quantised light in one-dimensional (1D) waveguides coupled to single emitters. In this thesis, I investigate WQED effects for single three-level systems (3LS) and pairs of two-level systems (2LS), respectively, which are embedded in the waveguide. To this end, I utilise numerical techniques and consider all model systems within the rotating wave approximation. I investigate the dynamics of single-photon scattering by single, embedded 3LS. In doing so, I analyse the influence of dark and almost-dark states of the 3LS on the scattering dynamics. I also show, how stationary electrical driving fields can control the outcome of the scattering. I quantify entanglement between the waveguide''s light field and single emitters by utilising the Schmidt decomposition. I apply this formalism to a lambda-system embedded in a 1D waveguide and study the generation of entanglement by scattering single-photon pulses with different envelopes on the emitter. I show that this entanglement generation is mainly determined by the photon''s width in k-space and the 3LS''s emission times. Finally, I explore the emission dynamics of a pair of 2LS embedded by a distance L into the waveguide. These dynamics are primarily governed by bound states in the continuum and by polaritonic atom-photon bound-states. For collective emission processes of the two 2LS, sub- and superradiance appear and depend strongly on the 2LS''s distance: the effects increase for larger L. This is an exclusive property of the 1D nature of the waveguide.

Dans cette thèse, nous étudions l'ensemble des solutions d'équations aux dérivées partielles résultant de modèles d'astrophysique et de biologie. Nous répondons aux questions de l'existence, mais aussi nous essayons de décrire le comportement de certaines familles de solutions lorsque les paramètres varient. Tout d'abord, nous étudions deux problèmes issus de l'astrophysique, pour lesquels nous montrons l'existence d'ensembles particuliers de solutions dépendant d'un paramètre à l'aide de la méthode de réduction de Lyapunov-Schmidt. Ensuite un argument de perturbation et le théorème du Point xe de Banach réduisent le problème original à un problème de dimension finie, et qui peut être résolu, habituellement, par des techniques variationnelles. Le reste de la thèse est consacré à l'étude du modèle Keller-Segel, qui décrit le mouvement d'amibes unicellulaires. Dans sa version plus simple, le modèle de Keller-Segel est un système parabolique-elliptique qui partage avec certains modèles gravitationnels la propriété que l'interaction est calculée au moyen d'une équation de Poisson / Newton attractive. Une différence majeure réside dans le fait que le modèle est défini dans un espace bidimensionnel, qui est expérimentalement consistant, tandis que les modèles de gravitationnels sont ordinairement posés en trois dimensions. Pour ce problème, les questions de l'existence sont bien connues, mais le comportement des solutions au cours de l'évolution dans le temps est encore un domaine actif de recherche. Ici nous étendre les propriétés déjà connues dans des régimes particuliers à un intervalle plus large du paramètre de masse, et nous donnons une estimation précise de la vitesse de convergence de la solution vers un profil donné quand le temps tend vers l'infini. Ce résultat est obtenu à l'aide de divers outils tels que des techniques de symétrisation et des inégalités fonctionnelles optimales. Les derniers chapitres traitent de résultats numériques et de calculs formels liés au modèle Keller-Segel

Scour is caused by the erosive action of flow of water, which erodes and takes away sediments from the river bed, as well as from the area of bridge piers and abutments. This process of scour is well-known for its complicated behaviour, and this process becomes more complex for the group of piers. As per the literature available, scour is a major contributor for the collapse of the bridge structures. Hence it becomes essential for the researches to predict the scour depth accurately. To fulfill this necessity, the deep understanding of the flow-field around the piers and factors affecting the scour depth is important. Numerous studies are available in the literature on the flow-field and local scour, but majority of them are focused only on single pier. However, multiple piers are more common in the bridge designing due to economical and geotechnical considerations. Engineers across the world are predominately considering single pier characterization for the group of piers, although all bridge structures are laid on the group of piers. The design considerations developed for a single pier mostly ignores the most significant group effects for multiple piers such as: pier sheltering, pier spacing and mutual interference effect. It is demonstrated by the fact that inadequate research and development for the multiple piers have been observed. Therefore, it is utmost important to investigate the factors affecting the multiple piers and develop an equation by considering all the variables for accurate prediction of scour depth. The primary aim of this research is to investigate the effect of the pier spacing (Ps) between the piers and temporal scour development on scour depth and propose a new equation for scour depth estimation. In order to meet the objectives of this research, detailed experimental study has been conducted for, single pier, two piers, and three piers. In total, 232 experiments have been carried out for various pier spacing and pier arrangements on uniformly graded sediment in the Hydraulic Engineering Laboratory of Delhi Technological University, Delhi, India. Pier arrangements studied in this research are: single pier, two piers in tandem arrangement, two piers in side-by-side arrangement, two piers at an angle of 15 and 30 degrees to the direction of flow, three piers in tandem arrangement, three piers in side-by-side arrangement and three piers in staggered viii arrangement. The instantaneous 3-D velocity measurement is conducted by utilizing SonTek 16-MHz Micro-ADV (Acoustic Doppler Velocimeter) has been used. For profoundly understanding and continuous monitoring of scour evolution SeaTek Ultrasonic ranging system have been used. The Experimental observations for the temporal scour evolutions and scour hole development pattern for all the pier arrangements under various pier spacing has been presented in the graphical and pictorial form. The findings of this research shed light on the factors that causes scour: pier spacing, flow depth, Froude number, and scour development pattern. These are all important variables, which needs to consider in order to accurately predict the maximum scour depth. Results shows that, the flow-field around the group of piers is much more complex than single pier and pier spacing plays a major role in the scour depth estimation. The results also exemplify that non-dimensional scour depth increases with the increase in the Froude number and velocity of flow. The effect of pier spacing shows that the scour depth increases as the pier spacing increases at a certain Ps range, then it decreases. Furthermore, two semi empirical equations has been proposed for the tandem and side-by-side arrangements by using GEP, and the comparison of the proposed GEP equation with the well-known equation and experimental results shows that the GEP is better prediction tool for scour depth. Lastly, to evaluate the influence of various parameters on the scour depth sensitivity analysis has been conducted, and concluded that pier spacing plays an important role in scour estimation. The findings of this study can be further used for the evaluation of the research data.

Indiana University-Purdue University Indianapolis (IUPUI)
Joint models for longitudinal and time-to-event data has been introduced to study the association between repeatedly measured exposures and the risk of an event. The use of joint models allows a survival outcome to depend on some characteristic functions from the longitudinal measures. Current estimation methods include a two-stage approach, Bayesian and maximum likelihood estimation (MLEs) methods. The twostage method is computationally straightforward but often yields biased estimates. Bayesian and MLE methods rely on the joint likelihood of longitudinal and survival outcomes and can be computationally intensive. In this work, we propose a joint generalized estimating equation framework using an inverse intensity weighting approach for parameter estimation from joint models. The proposed method can be used to longitudinal outcomes from the exponential family of distributions and is computationally e cient. The performance of the proposed method is evaluated in simulation studies. The proposed method is used in an aging cohort to determine the relationship between longitudinal biomarkers and the risk of coronary artery disease.

Leader member exchange (LMX) has been a widely researched topic in leadership literature. Despite the amount of research done there have been few articles addressing the agreement levels of LMX perceptions. This investigation examined the influence of dispositional affect and trust as moderators of the relation between LMX agreement and Job Attitudes (i.e. job satisfaction, organizational commitment. A partial least squares structural equation model was used to analyze these moderations over a sample of 70 subordinates and leadersThe findings indicate that dispositional affect and trust do moderate the aforementioned relation in non-linear patterns, and highlight the importance of exploring LMX agreement
As trocas entre líderes e membros (LMX) têm sido um tópico bastante abordado na literatura em liderança. Apesar do volume the investigações feitas, têm existido poucos artigos a abordar os níveis de concordância das percepções de LMX. Esta investigação examinou a influência de fatores de disposição afetiva e de confiança como moderadores da relação entre a concordância de LMX e atitudes organizacionais (i.e. satisfação com o trabalho, compromisso organizacional) Um modelo de equação estrutural de partial least squares foi utilizado para analisar estas moderações sobre uma amostra de 70 subordinados e chefias. Os resultados indicam que a disposição afetiva e a confiança moderam a relação previamente mencionada em padrões não-lineares, e sublinham a importância de explorar a concordância de LMX mais profundamente

碩士
國立成功大學
資源工程學系碩博士班
100
The purpose of this study was to analyze the frontal advance equations of aqueous and ionized CO2 when CO2 is injected and stored in a deep saline aquifer, and to estimate the migration distances and velocities of the different phases of CO2. The flow behaviors of three mobile phases of CO2—supercritical, aqueous, and ionized—were studied. The numerical simulation method was used in this study to derive the frontal advance equations of aqueous and ionized CO2, and to study the effects of dissolution and geochemical reactions on the velocity of supercritical phase CO2. The analytical solution of velocity of supercritical phase CO2 derived from Noh’s theory was used to verify the numerical simulation results. The major results and conclusions obtained from this study are：(1) The frontal advance equations of aqueous and ionized CO2 were derived. The migration distances of aqueous and ionized CO2, as well as the velocity of supercritical phase CO2, can be estimated from the derived equations. (2) The migration distance after the CO2 was injected into a saline aquifer, from far to near, were aqueous, ionized, and supercritical phases. There are fixed distances between the front of aqueous phase CO2 and supercritical phase CO2, and between the front of ionized phase CO2 and supercritical phase CO2. (3) Dissolution and geochemical reactions will decrease the velocity of supercritical phase CO2. The retardation factor can be used to estimate the affected velocity of supercritical phase CO2 when the analytical method or the graphical method is adopted. (4) The dissolution effect has a great effect on the velocity of supercritical phase CO2 than do geochemical effects. In other words, the decrease of velocity of supercritical phase CO2 was caused primarily by the dissolution effect.