New improved model was developed to calculate the absorption and refractive-index spectra in the band-edge region for all the important compound semiconductors. An accurate absorption model including Coulomb interaction and Urbach-broadened band edge has been demonstrated for direct bandgap semiconductors. We have developed a accurate model in which a piecewise linear approximation is used for the shape of the absorption spectrum. We also propose a steep-edged compound Lorentzian line-shape function (SCL-LSF) for modeling the Urbach tail, and the line broadening of exciton absorptions. The results of applying this fitting procedure to the absorption spectra of GaAs, InP and InAs are presented, and a consistent set of band parameters are extracted. The analytical absorption model is suitable for a complete closed-form Kramers-Kronig transform of the absorption spectrum to obtain the refractive index spectrum. A band-to-band Coulomb interaction model for the refractive index spectra is presented of AlxGa1-xAs for 0 < x < 0.412, and In0.53Ga0.47As ternary semiconductors at photon energies near and above the band gap. An accurate absorption model is used to calculate the contribution on the refractive index near band-edge region through a complete closed-form Kramers-Kronig transform. By including a single oscillator Sellmeier model for the high-energy absorption spectrum, closed-form expressions are obtained for the band-edge region refractive index. Both spectra are fully described in terms of a finite set of parameters that can be interpolated for all the important compound semiconductors. The refractive index spectra are extended beyond the band-gap energy and are in excellent agreement with the available experimental data. Our new model makes accurate modeling possible for devices such as electroabsorption and electrorefraction modulators.

Orientadores: Roberto Eugenio Lagos Monaco, Roberto Antonio Clemente / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T17:49:01Z (GMT). No. of bitstreams: 1 Yamaki_TaniaPatriciaSimoes_D.pdf: 15751882 bytes, checksum: 3bccb71a25a31c07f0e3e25ffb074896 (MD5) Previous issue date: 2010 / Resumo: Após apresentarmos uma revisão dos principais modelos teóricos para o movimento Browniano, consideramos em particular o caso de uma partícula Browniana carregada sob ação de campos elétrico e magnético. A obtenção de uma solução analítica para este caso, resolvendo a equação de Kramers para a distribuição de probabilidades de uma partícula no espaço de fase, foi sugerida em 1943 por Chandrasekhar, mas até os anos noventa do século passado, o problema foi raramente considerado na literatura. Obtivemos a solução fundamental exata deste problema, e analisamos algumas aplicações. Consideramos uma classe particular de soluções, aquelas com perfil inicial Gaussiano (no espaço de fase), sendo a solução uma convolução de Gaussianas (a solução fundamental ou propagador, e o perfil inicial). Calculamos algumas grandezas hidrodinâmicas e termodinâmicas a partir da expressão exata para a distribuição de probabilidades de uma partícula Browniana, a saber, a densidade de partículas, as densidades de fluxo de partículas, de energia, de fluxo de energia, de entropia e também a temperatura efetiva do gás Browniano, que pode ser obtida a partir das densidades de partícula e energia cinética. Publicamos em 2005 a solução fundamental exata e algumas aplicações no regime assintótico. / Abstract: After presenting a sketch of the several theoretical approaches to the Brownian motion model, we consider a charged Brownian particle under electric and magnetic fields. A path to solve analitically Kramers equation, for the particle distribution probability in phase space, was suggested in 1943 by Chandrasekhar, nevertheless until the nineties of last century, this problem was rarely considered. We present the exact fundamental solution and analyze some applications. We consider a particular class of solutions, namely, with a gaussian initial profile (in phase space), thus the resulting solution is a convolution of gaussians (both the fundamental solution or propagator, and the initial profile). Then we compute some hydrodinamical and thermodynamical densities from the exact expression for the probability distribution of a Brownian particle, for example, particle density, matter ux density, energy density, energy ux density, entropy density, among others, and some derived quantities suchs as the effective temperature of the Brownian gas. In 2005 we published part of these results, namely the fundamental solution and some application on the asymptotic regime / Doutorado / Física Estatistica e Termodinamica / Doutora em Ciências

Orientador: René Alfonso Nome Silva / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Química / Made available in DSpace on 2018-08-26T04:23:53Z (GMT). No. of bitstreams: 1 Zornio_BrunoFedosse_M.pdf: 1493558 bytes, checksum: 07565e7077eefa5f9f91f03dc9cc90d4 (MD5) Previous issue date: 2014 / Resumo: No final do século XIX Van¿tHoff empiricamente estabeleceu que a constante de velocidade de uma reação química é função exponencial da razão entre energia de ativação da reação pela energia térmica do ambiente (e portanto função da temperatura). Há uma variada ordem nas escalas de tempos reacionais, em especial, a constante de velocidade de reações lentas (por exemplo, reações bioquímicas não catalisadas) é difícil de determinar. Uma partícula difundindo em um meio viscoso que apresenta movimento aleatório ¿ com posição média (em um intervalo de tempo suficientemente grande) nula, e a variância da posição linearmente dependente em função do tempo ¿ é dita browniana, e quando submetida a um potencial bi quadrático é um bom modelo para descrição de reações químicas. A partir da dinâmica de Langevin (que serve para descrever a dinâmica de uma partícula browniana) é derivada a teoria de Kramers para meio viscosos - que relaciona o formato da curva potencial com a constante de taxa de reações químicas -. Experimentalmente pode-se recriar esse modelo utilizando pinças ópticas. Pinças ópticas são capazes de aprisionar partículas da ordem micrométricas em suspensão, pode-se recriar um potencial bi estávelutilizando uma pinça óptica dupla (com dois pontos de aprisionamento). Este estudo tem como objetivo avaliar a constante de taxa de um processo de transição entre poços de potencial de partículas brownianas teoricamente utilizando uma simulação de dinâmica de Langevin para sistemas em equilíbrio tanto quanto para sistemas antes de atingir o equilíbrio, assim como determinar experimentalmente utilizando microscopia ocoeficiente de difusão a partir da trajetória temporal de uma única partícula. Os resultados teóricos obtidos são bastante condizentes com os resultados experimentais descritos na literatura, assim como as predições da constante de taxa para tempos antes do equilíbrio apresentam correlação com o sistema em equilíbrio. Com relação à estimativa do coeficiente de difusão apresenta um erro sistemático associado ao tamanho da trajetória temporal de uma única partícula / Abstract: By the end of the XIX century, Van¿t¿ Hoff has empirically established that the rate constant of some chemical reaction is exponentially dependent by the ratio between the reaction activation energy and the environment thermal energy (and so on function of temperature). There is a wide variety in the reaction time scales, in particular, the rate constant of slow reactions (such as uncatalysed biochemical reactions) is difficult to determine. A diffusing particle in a viscous media which exhibit random motion ¿ with mean position (in a sufficiently large time series) is zero, and the position variance is linearly time dependent ¿ is called Brownian, and when is submitted in a biquadratic potential it¿s a good model to describe chemical reactions. By the Langevin dynamics (which serves to describe the Brownian particle motion) the Kramers theory for viscous media is derived ¿ that theory connects the potential energy shape with the chemical rate constant -. Experimentally it is possible to create this model using optical tweezes. Optical tweezers where capable to trap micrometrical beads in suspension, it can generate a bi-stable using a double optical tweezers (that is with two trapping points). The main objective of this essay is evaluate the rate constant a Brownian particles jumping between potential wells theoretically using Langevin dynamics simulations for the system at equilibrium and before reach the equilibrium, as determinate experimentally the diffusion coefficient of single particle time path using microscopy. The theoretical results is very consistent with experimental results described in literature, as well as the prediction of the rate constant for the system before reaches equilibrium are correlated with the rate constant for the system at equilibrium. For the diffusion coefficient estimative it was observed that there is a systematical source of errors, and its is related with the length of the time series of the single particle path / Mestrado / Físico-Química / Mestre em Química

This thesis describes a method developed to quickly measure the Rayleigh wave Q for a test material using a minimally invasive laser probe. The probe was donated to our lab by Dr. Alex Maznev at Phillips AMS in Natick, Ma. The machine was originally used to measure ultra thin film metal thicknesses; however we have utilized it to suit our needs. The optics head relies on a technique known as the transient grating method to generate a dispersion curve. This dispersion curve is then operated on by a local approximation for the Kramers-Kronig relations. The Kramers-Kronig relations for acoustic waves relate the real and imaginary parts of the dynamic compressibility to one another. The real part of the compressibility relates to the phase velocity of the wave and the imaginary part relates to the attenuation. Once the attenuation for the corresponding range of frequencies is determined the last step is to apply both the dispersion data and the attenuation data to the material Q equation to find Q over a range of frequencies. This thesis discusses the design of the machine, the theory behind the Kramers-Kronig relations and surface acoustic waves, the experimental procedure, and lastly results generated by the technique.

In this dissertation a class of stochastic differential equations is considered in the limit as mass tends to zero, called the Smoluchowski-Kramers limit. The Smoluchowski-Kramers approximation is useful in simplifying the dynamics of a system. For example, the problems of calculating of rates of chemical reactions, describing dynamics of complex systems with noise, and measuring ultra small forces, are simplified using the Smoluchowski-Kramers approximation. In this study, we prove strong convergence in the small mass limit for a multi-dimensional system with arbitrary state-dependent friction and noise coefficients. The main result is proved using a theory of convergence of stochastic integrals developed by Kurtz and Protter. The framework of the main theorem is sufficiently arbitrary to include systems of stochastic differential equations driven by both white and Ornstein-Uhlenbeck colored noises.

In this work the effect of elasticity on turbulent drag reduction due to polymers is investigated using a hybrid Direct Numerical Simulation (D.N.S) and Langevin dynamics approach. Simulations are run at a friction Reynolds number of Re_&tau = 560 for 960.000 dumbbells with Deborah numbers of De = 0, De = 1, and De = 10. The conclusions are that it is possible to simulate a drag reduced flow using hybrid D.N.S. with Langevin dynamics, that polymers, like other occurrences of drag reduction, reduce drag through streak stabilization, and that the essential property of polymers and fibers in having a drag reducing effect is their ability to exert a torqueon the solvent when they orientate in the boundary layer of the turbulent flow.

Cette thèse s'inscrit dans le cadre de la simulation de particules colloïdales. Plus précisément, nous nous intéressons aux particules dans un écoulement turbulent et modélisons leur dynamique par un processus lagrangien, leurs interactions comme des collisions parfaitement élastiques où l'influence de l'écoulement est modélisée par un terme de force sur la composante vitesse du système. En couplant les particules deux par deux et considérant leurs position et vitesse relatives, la collision parfaitement élastique devient une condition de réflexion spéculaire. Nous proposons un schéma de discrétisation en temps pour le système Lagrangien résultant avec des conditions aux bords spéculaires et prouvons que l'erreur faible diminue au plus linéairement dans le pas de discrétisation temporelle. La démonstration s’appuie sur des résultats de régularité de l'EDP Feynman-Kac et requiert une certaine régularité sur le terme de force. Nous expérimentons numériquement certaines conjectures, dont l’erreur faible diminuant linéairement pour des termes de force qui ne respectent pas les conditions du théorème. Nous testons le taux de convergence de l’erreur faible pour l’extrapolation de Romberg. Enfin, nous nous intéressons aux approximations Lagrangiennes/Browniennes en considérant un système Lagrangien où la composante vitesse se comporte comme un processus rapide. Nous contrôlons l'erreur faible entre la composante position du modèle Lagrangien et un processus de diffusion uniformément elliptique. Nous démontrons ensuite un contrôle similaire en introduisant une limite réfléchissante spéculaire sur le système Lagrangien et une réflexion appropriée sur la diffusion elliptique. / This thesis broadly concerns colloidal particle simulation which plays an important role in understanding two-phase flows. More specifically, we track the particles inside a turbulent flow and model their dynamics as a stochastic process, their interactions as perfectly elastic collisions where the influence of the flow is modelled by a drift on the velocity term. By coupling each particle and considering their relative position and velocity, the perfectly elastic collision becomes a specular reflection condition. We put forward a time discretisation scheme for the resulting Lagrange system with specular boundary conditions and prove that the convergence rate of the weak error decreases at most linearly in the time discretisation step. The evidence is based on regularity results of the Feynman-Kac PDE and requires some regularity on the drift. We numerically experiment a series of conjectures, amongst which the weak error linearly decreasing for drifts that do not comply with the theorem conditions. We test the weak error convergence rate for a Richardson Romberg extrapolation. We finally deal with Lagrangian/Brownian approximations by considering a Lagrangian system where the velocity component behaves as a fast process. We control the weak error between the position of the Lagrangian system and an appropriately chosen uniformly elliptic diffusion process and subsequently prove a similar control by introducing a specular reflecting boundary on the Lagrangian and an appropriate reflection on the elliptic diffusion.

Dans cette thèse, nous étudions le comportement asymptotique précis à basse température de l’événement de sortie d'un domaine métastable $Omegasubset mathbb R^d$ (point de sortie et temps de sortie) pour le processus de Langevin sur amorti. En pratique, le processus de Langevin sur amorti peut par exemple simuler l'évolution des positions des atomes d'une molécule ou la diffusion d'impuretés interstitielles dans un cristal. Nos résultats principaux concernent le comportement asymptotique précis de la distribution de la loi du point de sortie de $Omega$. Dans la limite d'une petite température, ces résultats permettent de justifier l'utilisation de la formule d'Eyring-Kramers pour modéliser les événements de sortie de $Omega$. La loi d'Eyring-Kramers est par exemple utilisée pour calculer les taux de transition entre les états d'un système dans un algorithme de Monte-Carlo cinétique afin de simuler efficacement les différents états visités par le système. L'analyse repose de manière essentielle sur la distribution quasi stationnaire associée au processus de Langevin sur amorti dans $Omega$. Nos preuves utilisent des outils d'analyse semi-classique. La thèse se décompose en trois chapitres indépendants. Le premier chapitre (rédigé en français) est une introduction aux résultats obtenus. Les deux autres chapitres (rédigées en anglais) sont consacrés aux énoncés mathématiques / This thesis is dedicated to the study of the sharp asymptotic behaviour in the low temperature regime of the exit event from a metastable domain $Omegasubset mathbb R^d$ (exit point and exit time) for the overdamped Langevin process. In practice, the overdamped Langevin dynamics can be used to describe for example the motion of the atoms of a molecule or the diffusion of interstitial impurities in a crystal. The obtention of sharp asymptotic approximations of the first exit point density in the small temperature regime is the main result of this thesis. These results justify the use of the Eyring-Kramers law to model the exit event. The Eyring-Kramers law is used for example to compute the transition rates between the states of a system in a kinetic Monte-Carlo algorithm in order to sample efficiently the state-to-state dynamics. The cornerstone of our analysis is the quasi stationary distribution associated with the overdamped Langevin dynamics in $Omega$. The proofs are based on tools from semi-classical analysis. This thesis is divided into three independent chapters. The first chapter (in French) is dedicated to an introduction to the mathematical results. The other two chapters (in English) are devoted to the precise statements and proofs

Cyclophilin A (CypA) is the well-studied member of a group of ubiquitous and evolutionarily conserved families of enzymes called peptidyl–prolyl isomerases (PPIases). These enzymes catalyze the cis-trans isomerization of peptidyl-prolyl bond in many proteins. The distinctive functional path triggered by each isomeric state of peptidyl-prolyl bond renders PPIase-catalyzed isomerization a molecular switching mechanism to be used on physiological demand. PPIase activity has been implicated in protein folding, signal transduction, and ion channel gating as well as pathological condition such as cancer, Alzheimer’s, and microbial infections. The more than five order of magnitude speed-up in the rate of peptidyl–prolyl cis–trans isomerization by CypA has been the target of intense research. Normal and accelerated molecular dynamic simulations were carried out to understand the catalytic mechanism of CypA in atomistic details. The results reaffirm transition state stabilization as the main factor in the astonishing enhancement in isomerization rate by enzyme. The ensuing intramolecular polarization, as a result of the loss of pseudo double bond character of the peptide bond at the transition state, was shown to contribute only about −1.0 kcal/mol to stabilizing the transition state. This relatively small contribution demonstrates that routinely used fixed charge classical force fields can reasonably describe these types of biological systems. The computational studies also revealed that the undemanding exchange of the free substrate between β- and α-helical regions is lost in the active site of the enzyme, where it is mainly in the β-region. The resultant relative change in conformational entropy favorably contributes to the free energy of stabilizing the transition state by CypA. The isomerization kinetics is strongly coupled to the enzyme motions while the chemical step and enzyme–substrate dynamics are in turn buckled to solvent fluctuations. The chemical step in the active site of the enzyme is therefore not separated from the fluctuations in the solvent. Of special interest is the nature of catalysis in a more realistic crowded environment, for example, the cell. Enzyme motions in such complicated medium are subjected to different viscosities and hydrodynamic properties, which could have implications for allosteric regulation and function.

En raison de leur capacité à absorber et diffuser la lumière, les aérosols jouent un rôle essentiel dans le bilan radiatif de la Terre. Cependant, la grande variabilité spatiale et temporelle de leur concentration et propriété physico-chimique rend délicate la quantification précise de leur impact sur le climat. Les mesures par télédétection sont des outils efficaces d’observation et d’analyse des aérosols de l’échelle locale à globale. Néanmoins, pour exploiter pleinement les capacités de ce type d’instruments, il est indispensable de mieux connaître les propriétés optiques des aérosols qui dépendent de leurs propriétés minéralogiques ou chimiques. Ces deux propriétés sont liées par l’Indice Complexe de Réfraction (ICR), qui représente une des principales sources d’incertitudes de l’étude des aérosols par télédétection. L’objectif de ce travail est donc de proposer et d’exploiter une méthode originale visant à mieux déterminer les ICR de particules. Pour cela, une nouvelle approche robuste et versatile a été développée et mise en œuvre. Ainsi, afin de déterminer précisément les capacités de cette dernière, la validation de chacune des étapes du processus d’obtention des ICR a été réalisée. L’approche complète a ensuite été appliquée pour des particules en suspension de SiO2 amorphe et cristalline, qui constituent notamment, la fraction majoritaire des aérosols volcaniques et désertiques.Enfin, les premiers résultats obtenus pour des aérosols prélevés lors de campagnes de mesures sont également présentés. Ceux-ci mettent en évidence le potentiel de l’approche proposée pour la détermination d’ICR, en vue d’améliorer l’exploitation de la mesure des aérosols par télédétection. / Due to their ability to absorb and scatter radiations, aerosols play an important role in the Earth’s radiative budget. However, quantitative estimations of their effects on climate are quite uncertain due to their large spatial and temporal variability in terms of concentration and physical properties. Measurements from remote sensing instruments are efficient tools to observe and investigate aerosol distributions from regional to global scales. Nevertheless, to fully exploit instrument capabilities, precise optical properties – dependent on chemical or mineralogical properties – are needed. These properties are linked by the Complex Refractive Index (CRI), which represents one of the main sources of uncertainty for studying aerosols from remote sensing instruments.The objective of this study is to propose and exploit a new methodology, aiming to determine precise CRI of particles. For this purpose, a new robust and versatile approach has been developed and implemented. Moreover, to determine capabilities of this approach, validation of each step in the procedure for CRI determination has been realized. The complete approach has been also applied for suspended particles of amorphous and crystalline SiO2, which are the major fraction of volcanic and mineral dust aerosols. Lastly, first results from collected samples from measurement campaigns are also presented. These results highlight the potential of the proposed approach to determine CRI, in order to improve the aerosol measurement exploitations by remote sensing instruments.