Após a excitação de uma amostra semicondutora por um pulso ultracurto, os fotoporadores interagem com a rede excitando modos longitudinais ópticos. Essa interação provoca variações no índice de refração do material, produzindo modulações na resposta óptica do meio (efeito eletro-óptico). Por outro lado, esta dinâmica origina polarizações dependentes do tempo o que gera emissão de radiação terahertz. Experimentos recentes (pump-probe) observaram modulações do campo através de medidas da refletividade resolvidas no tempo. A refletividade e o campo estão relacionados segundo o efeito eletro-óptico. Também se resolve temporalmente o campo irradiado pela amostra, através de antenas que operam na faixa de terahertz. Tanto as medidas eletro-ópticas quanto de emissão terahertz fornecem informações sobre a interação dinâmica do plasma com a rede após a excitação óptica. Nesse trabalho simulamos a interação dinâmica de plasma e fônons em n-GaAs e Telúrio (\"bulk\") após estes serem excitados por um pulso ultracurto. Utilizamos equações hidrodinâmicas para descrever transporte de cargas e uma equação fenomenológica de oscilador harmônico forçado, para descrever oscilações longitudinais ópticas da rede. Complementando nossa descrição temos a equação de Poisson, com a qual calculamos o campo gerado pelo plasma e pela polarização da rede semicondutora. Essas equações constituem um sistema de seis equações diferencias (quatro parciais) acopladas. Para resolvê-las utilizamos o método das diferenças finitas. Do cálculo numérico obtemos a evolução temporal do campo elétrico no interior do material. Com esse campo determinamos as freqüências de oscilação do sistema e calculamos o campo irradiado. Nossos resultados apresentam acordo qualitativo com os experimentos / Above-band-gap optical excitation of semiconductors generates highly non-equilibrium photocarriers which interact with phonons thus exciting vibrational modes in the system. This interaction induces refractive-index changes via the electro-optic effect. Moreover it gives rise to electromagnetic radiation at characteristic frequencies (terahertz). Both effects have been measured by time-resolved ultra fast spectroscopy. Recent pump-probe experiments have found strong modulations of the internal electric field through electro-optic measurements. The emitted electromagnetic radiation has also been detected by a terahertz dipole antenna. Both electro-optic and terahertz emission measurements provide information about the coupled dynamics of photocarriers and phonons. In this work we simulate the dynamics of plasmon-phonon coupled modes in n-GaAs and Tellurium (bulk) following ultrafast laser excitation. The time evolution of the photocarrier densities and currents is described semi classically in terms of the moments of the Boltzmann equation. Phonon effects are accounted for by considering a phenomenological driven-harmonic-oscillator equation, which is coupled to the electron-hole plasma via Poisson\'s equation. These equations constitute a coupled set of differential equations. We use finite differencing to solve these equations. From the numerical results for the evolution of internal fields we can calculate both the characteristic frequencies of system and its terahertz radiation spectrum. Our results are consistent with recent experimental data

Made available in DSpace on 2014-10-09T12:29:01Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:02:24Z (GMT). No. of bitstreams: 1 00965.pdf: 1750630 bytes, checksum: e69ee5985ba23aa96db338a0d9813c17 (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:23:13Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:03:49Z (GMT). No. of bitstreams: 1 00175.pdf: 1908417 bytes, checksum: c87cee4e2e713d08f78b85e9f40bade2 (MD5) / Dissertacao (Mestrado) / IEA/D / Instituto de Fisica, Universidade de Sao Paulo - IF/USP

Made available in DSpace on 2014-10-09T12:53:20Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:09:35Z (GMT). No. of bitstreams: 0 / No presente trabalho foi realizada uma análise de dois padrões de aço inoxidável ferrítico submetidos à ação de lasers pulsados, um no regime de nanosegundos e outro no regime de femtosegundos. Foram determinadas as temperaturas e densidades do plasma formado a partir da análise espectroscópica da radiação emitida em diferentes faixas espectrais, por diferentes espécies e em diferentes janelas de integração no tempo. As temperaturas foram obtidas de duas formas, pelo método do gráfico de Boltzmann e pela razão entre duas linhas. Os resultados foram comparados com o intuito de verificar se o método da razão conseguia recuperar os resultados obtidos pela abordagem do gráfico de Boltzmann. Foi observada uma grande concordância entre os dois métodos no regime de femtosegundos, ao passo que no regime de nanosegundos a recuperação das temperaturas não foi tão satisfatória. A densidade eletrônica do plasma foi determinada a partir do alargamento Stark e verificou-se que o plasma gerado pelo laser de nanosegundos era mais denso que aquele gerado no regime de femtosegundos. As densidades determinadas sob diferentes janelas de integração do sinal no tempo foram também comparadas sendo que aquelas relativas aos estágios iniciais do plasma eram maiores que aquelas de estágios finais. Com a obtenção das temperaturas e das densidades foi possível caracterizar totalmente o plasma e compará-lo com outros plasmas naturais e artificiais. / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP

The cosmic microwave background (CMB) provides unprecedented details about the history of our universe and helps to establish the standard model in modern cosmology. With the ongoing and future CMB observations, higher precision can be achieved and novel windows will be opened for studying different phenomena. Non-Gaussianity is one of the most exciting effects which fascinate many cosmologists. While numerous alternative inflationary models predict detectable primordial non-Gaussianities generated during inflation, the single-field slow-roll inflation of the standard model is known to produce negligible non-Gaussianities. However, post-inflationary processes guarantee the generation of non-Gaussianities through the nonlinear evolution of our universe after inflation, regardless of the underlying inflationary theory. These non-Gaussianities not only may contaminate the potential primordial non-Gaussian signals, but also may offer independent tests for late-time physics (such as General Relativity). Therefore, it is of great interest to study them quantitatively. In this thesis, we will study the post-inflationary non-Gaussianities in two main aspects. First, we calculate the CMB bispectrum imprinted by the 2nd-order perturbations during recombination. We carry out a numerical calculation including all the dominant effects at recombination and separate them consistently from the late-time effects. We find that the recombination bispectrum is subdominant compared to the ISW-lensing bispectrum. Although the effect will not be detectable for the Planck mission, its signal-to-noise is large enough that they present themselves as systematics. Thus, it has to be taken into account in future experiments. Second, we formulate the lensing, redshift and time-delay effects through the Boltzmann equation. The new formalism allows us to explicitly list out all the approximations implied in the canonical remapping approach. In particular, we quantify the correction of the CMB temperature power spectrum from the lens-lens couplings and confirm that the correction is small.

Ce manuscrit présente des résultats d’analyse mathématique autour de deux exemples de problèmes singuliers d’équations aux dérivées partielles issus de la modélisation. I. Diffusion croisée en dynamique des populations. En dynamique des populations, les systèmes de réaction –diffusion croisée modélisent l’évolution de populations d’espèces en compétition avec un effet répulsif entre les individus. Pour ces systèmes fortement couplés, souvent non linéaires, une question aussi fondamentale que l’existence de solutions se révèle extrêmement complexe. Dans ce manuscrit, on introduit une approche basée sur des extensions récentes de lemmes de dualité et sur des méthodes d’entropie. On démontre l’existence de solutions faibles dans un cadre général de systèmes de réaction-diffusion croisée, ainsi que certaines propriétés qualitatives des solutions. II. Équation de Boltzmann en domaine borné. L’équation de Boltzmann, introduite en 1872, modélise la dynamique des gaz raréfiés hors équilibre. Malgré les nombreux résultats autour de la question de l’existence de solutions fortes proches de l’équilibre, très peu concernent le cas d’un domaine borné, situation pourtant fréquente dans les applications. Une raison de la difficulté du problème est l’irruption des singularités le long des trajectoires rasant le bord du domaine. Dans ce manuscrit, on présente une théorie de la régulation de l’équation de Boltzmann en domaine borné. Grâce à l’introduction d’une distance cinétique qui compense les singularités au bord, on montre des résultats de propagation de normes de Sobolev et de propagation C^1 en domaine convexe. En domaine non convexe, on montre un résultat de propagation de régularité BV. / This manuscript presents results of mathematical analysis concerning two singular problems of partial differential equations coming from the modeling. I. Cross-diffusion in Population dynamics. In Population dynamics, reaction-cross diffusion systems model the evolution of the populations of competing species with a repulsive effect between individuals. For these strongly coupled, often non linear systems, a question as basic as the existence of solutions appears to be extremely complex. In this manuscript, we introduce an approach based on the most recent extensions of duality lemmas and on entropy methods. We prove the existence of weak solutions in a general setting of reaction-cross diffusion systems, as well as some qualitative properties of the solutions. II. Boltzmann equation in bounded domains The Boltzmann equation, introduced in 1872, model the evolution of a rarefied gas out of equilibrium. Despite the numerous results concerning the existence of strong solutions close to equilibrium, very few concern the case of bounded domain, though this situation is very useful in applications. A crucial reason of the difficulty of this problem is the formation of a singularity on the trajectories grazing the boundary. In this manuscript, we present a theory of the regularity of the Boltzmann equation in bounded domains. Thanks to the introduction of a kinetic distance which balances the singularity, we obtain results of propagation of Sobolev norms and C^1 propagation in convex domains. In non convex domains, we obtain the propagation of BV regularity.

This thesis is concerned with the new formulation of a finite-volume lattice Boltzmann equation method and its implementation on unstructured meshes. The finite-volume discretization with a cell-centered tessellation is employed. The new formulation effectively adopts a total variation diminishing concept. The formulation is analyzed for the modified partial differential equation and the apparent viscosity of the model. Further, the high-order extension of the present formulation is laid out. Parallel simulations of a variety of two-dimensional benchmark flows are carried out to validate the formulation. In Chapter 1, the important notions of the kinetic theory and the most celebrated equation in the kinetic theory, ‘the Boltzmann equation’ are given. The historical developments and the theory of a discrete form of Boltzmann equation are briefly discussed. Various off-lattice schemes are introduced. Various methodologies adopted in the past for the solution of the lattice Boltzmann equation on finite-volume discretization are reviewed. The basic objectives of this thesis are stated. In Chapter2,the basic formulations of lattice Boltzmann equation method with a rational behind different boundary condition implementations are discussed. The benchmark flows are studied for various flow phenomenon with the parallel code developed in-house. In particular, the new benchmark solution is given for the flow induced inside a rectangular, deep cavity. In Chapter 3, the need for off-lattice schemes and a general introduction to the finite-volume approach and unstructured mesh technology are given. A new mathematical formulation of the off-lattice finite-volume lattice Boltzmann equation procedure on a cell-centered, arbitrary triangular tessellation is laid out. This formulation employs the total variation diminishing procedure to treat the advection terms. The implementation of the boundary condition is given with an outline of the numerical implementation. The Chapman-Enskog (CE) expansion is performed to derive the conservation equations and an expression for the apparent viscosity from the finite-volume lattice Boltzmann equation formulation in Chapter 4. Further, the numerical investigations are performed to analyze the apparent viscosity variation with respect to the grid resolution. In Chapter 5, an extensive validation of the newly formulated finite-volume scheme is presented. The benchmark flows considered are of increasing complexity and are namely (1) Posieuille flow, (2) unsteady Couette flow, (3) lid-driven cavity flow, (4) flow past a backward step and (5) steady flow past a circular cylinder. Further, a sensitivity study to the various limiter functions has also been carried out. The main objective of Chapter6is to enhance the order of accuracy of spatio-temporal calculations in the newly presented finite-volume lattice Boltzmann equation formulation. Further, efficient implementation of the formulation for parallel processing is carried out. An appropriate decomposition of the computational domain is performed using a graph partitioning tool. The order-of-accuracy has been verified by simulating a flow past a curved surface. The extended formulation is employed to study more complex unsteady flows past circular cylinders. In Chapter 7, the main conclusions of this thesis are summarized. Possible issues to be examined for further improvements in the formulation are identified. Further, the potential applications of the present formulation are discussed.

<div>The Boltzmann equation, an integro-differential equation for the molecular distribution function in the physical and velocity phase space, governs the fluid flow behavior at a wide range of physical conditions, including compressible, turbulent, as well as flows involving further physics such as non-equilibrium internal energy exchange and chemical reactions. Despite its wide applicability, deterministic solutions of the Boltzmann equation present a huge computational challenge, and often the collision operator is simplified for practical reasons, hereby, referred to as linear kinetic models. These models utilize the moment of the underlying probability distribution to mimic some properties of the original collision operator. But, just because we know the moments of a distribution, doesn't mean we know the actual distribution. The approximation of reality can never supersede the reality itself. Because, all the facts (moments) about the world (distribution) cannot explain the world. The premise lies not in the fact that a certain flow behavior can be correctly predicted; but rather that the Boltzmann equation can reveal and explain previously unsuspected aspects of reality.</div><div><br></div><div>Therefore, in this work, we introduce accurate, efficient, and robust numerical schemes for solving the multi-species Boltzmann equation which can model general repulsive interactions. These schemes are high order spatially and temporally accurate, spectrally accurate in molecular velocity space, exhibit nearly linear parallel efficiency on the current generation of processors; and can model a wide-range of rarefied flows including flows involving momentum, heat, and diffusive transport. The single-species variant formed the basis of author's Masters' thesis.</div><div><br></div><div>While the first part of the dissertation is targeted towards multi-species flows that exhibit rich non-equilibrium phenomenon; the second part focuses on single-species flows that do not depart significantly from equilibrium. This is the case, for example, in micro-nozzles, where a portion of flow can be highly rarefied, whereas others can be in near-continuum regime. However, when the flow is in near-continuum regime, the traditional deterministic numerical schemes for kinetic equations encounter two difficulties: a) since the near-continuum is essentially an effect of large number of particles in an infinitesimal volume, the average time between successive collisions decrease, and therefore the discrete simulation timestep has to be made smaller; b) since the number of molecular collisions increase, the flow acquires steady state slowly, and therefore one needs to carry out time integration for large number of time steps. Numerically, the underlying issue stems from stiffness of the discretized ordinary differential equation system. This situation is analogous to low Reynolds number scenario in traditional compressible Navier-Stokes simulations. To circumvent these issues, we introduce a class of high order spatially and temporally accurate implicit-explicit schemes for single-species Boltzmann equation and related kinetic models with the following properties: a) since the Navier-Stokes can be derived from the asymptotics of the Boltzmann equation (using Chapman-Enskog expansion~\cite{cercignani2000rarefied}) in the limit of vanishing rarefaction, these schemes preserve the transition from Boltzmann to Navier-Stokes; b) the timestep is independent of the rarefaction and therefore the scheme can handle both rarefied and near-continuum flows or combinations thereof; c) these schemes do not require iterations and therefore are easy to scale to large problem sizes beyond thousands of processors (because parallel efficiency of Krylov space iterative solvers deteriorate rapidly with increase in processor count); d) with use of high order multi-stage time-splitting, the time integration over sufficiently long number of timesteps can be carried out more accurately. The extension of the present methodology to the multi-species case can be considered in the future. </div><div><br></div><div>A series of numerical tests are performed to illustrate the efficiency and accuracy of the proposed methods. Various benchmarks highlighting different scattering models, different mass ratios, momentum transport, heat transfer, and diffusive transport have been studied. The results are directly compared with the direct simulation Monte Carlo (DSMC) method. As an engineering use-case, the developed methodology is applied for the study of thermal processes in micro-systems, such as heat transfer in electronic-chips; and primarily, the ingeniously Purdue-developed, Microscale In-Plane Knudsen Radiometric Actuator (MIKRA) sensor, which can be used for flow actuation and measurement.</div>

Semiconductor nanostructures are currently an active area of research, especially in the field of photovoltaics as they will play a major role in next generation solar devices that break the current theoretical limit for light-to-current conversion. For instance, the efficiency of the nanostructure-based solar cells can be increased due to carrier multiplication, or multiple exciton generation (MEG) process, where absorption of a single energetic photon results in the generation of several charge carriers. In order to design nanostructures with the desired properties, a detailed theoretical approach for studying photoexcited state processes is necessary. The approach developed in this work is based on many-body perturbation theory (MBPT) and the Boltzmann transport equation (BE) in combination with density functional theory (DFT) in order to compute quantum efficiency (QE). Conclusions about QE are made after studying all the major relaxation channels in a photoexcited system, such as exciton-to-biexciton decays, biexciton recombination and phonon-mediated exciton relaxation. In all calculations, excitonic effects have been included by solving the Bethe-Salpeter equation (BSE). Then, by including excitons in the MBPT calculations, the exciton-to- biexciton rates R1→2 as well as the biexciton-to-exciton rates R2→1 are computed by taking into account the singlet fission (SF) process. The methods developed here have been applied to various semiconductor nanostructures such as pristine chiral (6,2), (6,5) and (10,5) and functionalized (6,2) SWCNTs. We predict efficient MEG in the (6,2) and (6,5) SWCNTs within the solar spectrum range starting at the 2Eg energy threshold and with QE reaching ~ 1:6 at about 3Eg, where Eg is the electronic gap. Also, methods for MEG rates calculations have been improved by taking into account exciton-exciton interactions in the intermediate biexciton state, where results show a small (~ 40 meV) red-shift in the biexciton density of states. Finally, the MEG-BE technique is applied in studying charge transfer. Charge transfer has been studied in a doped silicon quantum dot (QD) - functionalized SWCNT system where it was found that an initial excitation localized on either the QD or CNT evolves into a transient CT state. / National Science Foundation (NSF CHE-1413614)

The content of Chapter 1 is an author produced version of a paper published in Physics of Fluids. The final publication is available at AIP via http://dx.doi.org/10.1063/1.3691262. The content of Chapters 2 and 4 is an author produced version of papers published in Journal of Statistical Physics. The final publications are available at Springer via http://dx.doi.org/10.1007/s10955-012-0512-z and http://dx.doi.org/10.1007/s10955-015-1364-0, respectively. / 京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第19682号 / 工博第4137号 / 新制||工||1638(附属図書館) / 32718 / 京都大学大学院工学研究科機械理工学専攻 / (主査)教授 青木 一生, 教授 髙田 滋, 教授 稲室 隆二 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM