Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho estabeleceremos as definiÃÃes das funÃÃes de Green em mecÃnica estatÃstica e suas propriedades bÃsicas. Estas funÃÃes dependem duplamente do tempo e da temperatura. Isto pode ser observado por meio de suas definiÃÃes, onde aparecem os valores mÃdios dos produtos de operadores. Neste caso a mÃdia à feita sobre o ensemble grÃo-canÃnico. Os operadores envolvidos nestas funÃÃes satisfazem a equaÃÃo de movimento de Heisenberg, o que nos permite descrever as equaÃÃes de evoluÃÃo para as funÃÃes de Green. Por meio da representaÃÃo espectral das funÃÃes de correlaÃÃo temporal, que à feita atravÃs da introduÃÃo de uma transformada de Fourier para mudar o sistema do espaÃo dos tempos para o espaÃo das frequÃncias, podemos obter as representaÃÃes espectrais para as funÃÃes de Green retardada, avanÃada e causal. Por Ãltimo, faremos o uso da funÃÃo de Green retardada para descrever a condutividade elÃtrica de um sistema de elÃtrons submetido a um campo elÃtrico externo dependente de tempo, em outras palavras, descreveremos o tensor de condutividade elÃtrica em termos da funÃÃo de Green retardada e, por Ãltimo, calcularemos a condutividade elÃtrica de um sistema de elÃtrons e fÃnons.

No presente trabalho descrevemos nossos resultados relativos à investigação da dinâmica de solvatação mecânica por meio de simulações por dinâmica molecular, respeitando o regime da resposta linear, em sistemas-modelo de argônio líquido com um soluto monoatômico ou diatômico dissolvido. Estudamos sistematicamente a influência dos parâmetros moleculares dos solutos (tamanho, polarizabilidade) e da densidade frente a vários modelos de solvatação. Funções de Correlação Temporal da Energia de Solvatação foram calculadas com relação à correlações de n-corpos (n = 2; 3) distinguindo interações repulsivas e atrativas para ambos os sistemas líquidos. Também obtivemos segundas derivadas temporais dessas funções referindo-se à parcelas translacionais, rotacionais e roto-translacionais na solução do diatômico. Encontramos que funções de correlação temporal coletivas podem ser razoavelmente bem aproximadas por correlações binárias a densidades baixas e, a densidades altas, correlações ternárias tornam-se mais importantes produzindo um descorrelacionamento mais rápido das funções coletivas devido a efeitos de cancelamento parciais. As funções de correlação para interações repulsivas e atrativas exibem comportamentos dinâmicos independentes do modelo de solvatação devido a fatores de escalonamento linear que afetam apenas as amplitudes das dessas funções de correlação temporal. Em geral, os sistemas com grau de liberdade rotacional apresentam tempos de correlação mais curtos para a dinâmica coletiva e tempos de correlação mais longos para as funções binárias e ternárias. Finalmente, esse estudo mostra que os sistemas contendo o diatômico relaxam-se predominantemente por mecanismos translacionais binários em modelos de solvatação envolvendo alterações apenas na polarizabilidade do soluto, e por mecanismos rotacionais atrativos binários em modelos envolvendo alterações no comprimento de ligação. / In the present work, we describe our results concerning our molecular dynamics investigation of the mechanical solvation dynamics within the linear response regime in model systems composed by liquid argon with a monoatomic or diatomic solute. The effect of molecular parameters (size, polarizability) and density has been elucidated for various solvation models. Time Correlation Functions for the solvation energy were calculated and separated into n-body (n = 2; 3) contributions distinguishing repulsive and attractive interactions in both liquid systems. In addition, we computed second time derivatives of these functions in order to describe translational, rotational, and roto-translational portions in the solutions containing the diatomics. We found that collective time correlation functions are well described by binary correlations at low liquid densities and, at high densities, ternary correlations become more important producing faster decaying collective time correlation functions due to partial cancellation effects. The repulsive and attractive time correlation functions exhibit a dynamic behavior that is independent on the solvation model due to linear scaling factors that only affect the absolute amplitudes of these functions. In general, the systems involving a rotational degree of freedom furnish smaller correlation times for the collective solvation dynamics, but stronger correlated two-body and three-body terms. Finally, this study shows that the solvation dynamics for the solution containing the diatomics relaxes predominatly by binary translational mechanisms when solvation models involving changes only in the polarizability parameter are considered. Binary attractive rotational mechanism become important in models with changes in the bond length.

No description available.

This paper is devoted to the computation of statistical characteristics of the response of discrete vibration systems with a random external excitation. The excitation can act at multiple points and is modeled by a time-shifted random process and its derivatives up to the second order. Statistical characteristics of the response are given by expansions as to the correlation length of a weakly correlated random process which is used in the excitation model. As the main result analytic expressions of some integrals involved in the expansion terms are derived.

The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as with their representations and the computation of their moment functions. Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of the stationary solution still can be computed explicitly. This allows the assessment of the goodness of the approximations found from the derived asymptotic expansions.

This thesis is an attempt at studying quantum coherence effects coupled via plasmons. After introducing the quantum coherence in atomic systems in Chapter 1, we utilize it in Chapter 2 to demonstrate a new technique of detection of motion of single atoms or irons inside an optical cavity. By taking into account the interaction of coherences with surface plasmonic waves excited in metal nanoparticles, we provide a theoretical model along with experimental data in Chapter 3 to describe the modification of Raman spectra near metal nanoparticles. We show in chapter 4 that starting from two emitters, coupled via a plasmonic field, the symmetry breaking occurs, making detectable the simultaneous existence of the fast super-radiance and the slow sub-radiance emission of dye fluorescence near a plasmonic surface. In Chapter 5, we study the photon statistics of a group of emitters coupled via plasmons and by the use of quantum regression theorem, we provide a theoretical model to fully investigate the dependence of photon bunching and anti-bunching effects to the interaction between atoms, fields and surrounding mediums.

We present a self-consistent calculation of the mono vacancy formation energy for seven simple metals Li, Na, K, Rb, Cs (all bcc), Al (fcc) and Mg (hcp) using both model and ab initio pseudopotential used in earlier unified studies. The local model pseudopotential calculations show small variations with respect to different exchange-correlation functions and the results are in fair agreement with other similar calculations and the available experimental data. The comparisons show that reliable model (pseudo) potential for simple metals can indeed be obtained for explaining a host of properties. Also, considering the importance of third order term in ab initio calculations, the results of our second order calculation appear fairly reasonable and are comparable with other first principle calculations. The perturbation series being an oscillating one, we hope to improve the calculational results using suitable series convergence acceleration method in the next part of our study.

<p>A first-principles theory of plasticity in metals currently does not exist. While many plasticity models make reference to rules based on heuristic arguments regarding dislocations (the fundamental mediators of plastic deformation in crystals), the scientific community still does not have a theory of dislocation dynamics which can recover even basic features of plasticity theory. Discrete dislocation dynamics, though a valuable tool for understanding fundamentals topics in dislocation plasticity, becomes unusable beyond ~1.5\% strain due to the line length multiplication inherent in deformation. As a result, it is necessary to develop continuum theories of dislocation dynamics which treat dislocation densities rather than individual dislocations. This thesis examines the foundations of one such continuum theory: line bundle continuum dislocation dynamics, which assumes that dislocations are roughly parallel at every point. First, this assumption is given definite meaning and it is shown from discrete dislocation dynamics data that to be appropriate when modelling dislocation densities on fine length scales (resolving densities on lengths less than 100 nm). Second, it is found that an additional driving force, the correlation stress, emerges from coarse-graining the line bundle dynamics. This correction to the dislocation interactions is dependent on tensorial dislocation correlation functions describing the short-range errors in the products of dislocation densities lying on two slip systems. The full set of these dislocation correlation functions are evaluated from discrete density data with the aid of a novel left-and-right handed classification of slip system interactions in FCC crystals. Lastly, a study of the correlation stress in a representative dislocation system suggests that these stresses are roughly one tenth the magnitude of the mean-field dislocation interaction stress. Taken together, this thesis bridges discrete and continuum models of dislocation dynamics and provides a foundation for future work on a first-principles theory of metal plasticity. </p>

Made available in DSpace on 2016-06-02T20:06:01Z (GMT). No. of bitstreams: 1 2117.pdf: 990773 bytes, checksum: a7b62936541ab91d8ae3424f62aa0f40 (MD5) Previous issue date: 2008-08-22 / In the financial market usually notices are taken of the shares sequentially over the time in order to characterize them a time series. However, the major interest is to forecast the behavior of these shares. Motivated by this fact, a lot of models were created based on the past information considering constant averages and variance over time. Although, in financial series a feature often presented is called volatility, which can be noticed by the variance to vary in time. In order to catch this characteristic were developed the models of the family GARCH, that model the conditional variance through known information. These models were well used and have passed by many formulation modifications to be able to catch different effects, such as the effect leverage EGARCH. Thus, the goal is to estimate volatility patterns obeying the specifications of the family GARCH verifying which ones of them describe better the data inside and outside the sample. / No mercado financeiro costuma-se fazer observações sobre as carteiras sequencialmente ao longo do tempo, caracterizando uma série temporal. Contudo, o maior interesse está em prever o comportamento destas carteiras. Motivado por este fato, foram criados muitos modelos de previsão baseando-se em observações passadas considerando a média e variância constantes no tempo. Porém, nas séries financeiras uma característica muito presente é a chamada volatilidade, que pode ser observada pela variância não constante no tempo. A fim de captar esta característica, desenvolveram-se os modelos da família GARCH, que modelam a variância condicional através de informações passadas. Estes modelos foram muito utilizados e sofreram muitas modificações nas formulações para poderem captar diferentes efeitos, como o efeito de leverage (EGARCH). Assim, deseja-se estimar modelos de volatilidade obedecendo às especificações da família GARCH, verificando quais deles descrevem melhor os dados dentro e fora da amostra.

Tato práce popisuje metodu analýzy translačního pohybu užitím křížové korelace. Ukazujeme, jakým způsobem se chová funkce křížové korelace obrazů s navzájem posunutými objekty, a jak nám to umožňuje nacházet jejich vektory posunu. Pro následnou implementaci je nalezena efektivní metoda pro hledání pouze požadovaného počtu lokálních maxim funkce.