We analyze ground state properties of few-nucleons systems and $^{16}$O using \eftnopi (Pionless Effective Field Theory) at \ac{LO}. This is the first time the theory is extended to many-body nuclear systems. The free constants of the interaction are fitted using both experimental data and \ac{LQCD} results. The nuclear many-body Schr\"odinger equation is solved by means of the Auxiliary Field Diffusion Monte Carlo method. A linear optimization procedure has been used to recover the correct structure of the ground state wavefunction. {\eftnopi} as revealed to be an appropriate theory to describe light nuclei both in nature, and in the case where heavier quarks are used in order to make \ac{LQCD} calculation feasible. Our results are in good agreement with experiments and \ac{LQCD} predictions. In our \ac{LO} calculation, $^{16}$O appears to be unstable against breakup into four $^4$He for the quark masses considered.

The dynamics of systems out of equilibrium, such as the phase transition process, are very rich, and related to largely scalable problems, from very small ultracold gases to large expanding galaxies. Quantum low-dimensional systems show interesting features, notably different from the canonical three-dimensional case. Bose-Einstein condensates are very good platforms to study macroscopic quantum phenomena. These three points describe well the motivation behind the study presented in this work. In this thesis, some dynamical problems of trapped and uniform condensates are studied, both at zero and finite temperature. In particular, we focus on the analysis of the propagation of linear and nonlinear excitations in a quasi-1D and in quasi-2D systems. In the first case, we are able to correctly describe the dynamics of a solitonic vortex in an elongated condensate, as measured by Serafini et al. [Phys. Rev. Lett. 115, 170402 (2015)]. In the second case, we reproduce the decay rate of a phase-imprinted soliton (collaboration with Birmingham), and assess its dependence on the temperature. We also replicate the propagation speed of sound waves over a wide range of temperatures as in Ville et al. [arXiv:1804.04037] (collaboration with Collà ̈ge de France). The result of this analysis is included in Ota et al. [arXiv:1804.04032], which is currently under revision. In uniform low-dimensional systems Bose-Einstein condensation is technically not possible, and in two dimensions it is replaced by the Berezinskii-Kosterlitz-Thouless superfluid phase transition. We study its critical properties by analysing the spontaneous generation of vortices during a quench, produced via the Kibble-Zurek mechanism. This procedure predicts, for any dimension, the scaling for the density of defects formed during a fast transition, when the system is not adiabatically following the control parameter, and regions of phase inhomogeneity are formed. We address the role of reduced dimensionality on this process. All finite temperature simulations are performed by means of the stochastic (projected) Gross-Pitaevskii equation, a model fully incorporating density and phase fluctuations for weakly interacting Bose gases.

Made available in DSpace on 2015-03-04T18:50:31Z (GMT). No. of bitstreams: 1 Edgar.pdf: 1094234 bytes, checksum: 7aa0fe5a29dfc6d6a8b9f215c97da0da (MD5) Previous issue date: 2010-09-29 / In this work, we study the modell of a system of N beams interconnected with each other, where one of its ends is clamped and the other is submitted to a dissipative mechanism of frictional type. We show that model is well posed, using the semigroup theory, and using energy method, we prove that the system is exponentially stable. Finally, through numerical methods, we con_rm these properties for the corresponding discrete model. We obtain the numerical modeling and graphics showing the evolution of the modell solution. / Neste trabalho, estudamos a modelagem de um sistema de N vigas interconectadas entre si, onde um de seus extremos está engastado e o outro está submetido a um mecanismo dissipativo do tipo friccional. Mostramos a boa colocação do modelo, usando a teoria de semigrupos; e usando o método de energia, provamos que o sistema é exponencialmente estável. Finalmente, através dos métodos numéricos, confirmamos estas propriedades para o correspondente modelo discreto. Fazemos a modelagem numérica e obtemos gráficos que mostram a evolução da solução do modelo.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-01-03T13:03:15Z No. of bitstreams: 1 DissPRS.pdf: 2244710 bytes, checksum: d11e0b755d5503e93a47a8a6dc113814 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2017-01-16T16:23:49Z (GMT) No. of bitstreams: 1 DissPRS.pdf: 2244710 bytes, checksum: d11e0b755d5503e93a47a8a6dc113814 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2017-01-16T16:23:57Z (GMT) No. of bitstreams: 1 DissPRS.pdf: 2244710 bytes, checksum: d11e0b755d5503e93a47a8a6dc113814 (MD5) / Made available in DSpace on 2017-01-16T16:24:06Z (GMT). No. of bitstreams: 1 DissPRS.pdf: 2244710 bytes, checksum: d11e0b755d5503e93a47a8a6dc113814 (MD5) Previous issue date: 2016-10-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Titanium dioxide nanoparticles (TiO2-NP) are commonly used in many industrial activities. Consequently, the daily consumption by humans is estimated in 5.4 mg day, with an input in the environment of 4.2 mg day per person, receiving or not appropriated treatment before disposure. The cytotoxicity, genotoxicity and mutagenicity of TiO2-NP were investigated using the established fish cell line derived from zebrafish (Danio rerio) liver (i. e. ZF-L cells). Prior to the evaluation of nanoparticle’s toxic potential, a careful characterization was realized in culture medium in the presence or not of fetal bovine serum (FBS). Regarding to the characterization in terms of size was accessed using a transmission electron microscope (TEM), the agglomeration potential and surface charge were accessed by diameter light scattering (DLS) and zeta potential measurements, respectively, using a spectrophotometer. TiO2-NP in environmentally relevant concentrations were tested for cytotoxicity, genotoxicity and mutagenicity. Cell viability was accessed by four different tests, the trypan blue assay (membrane integrity), MTT reduction assay (mitochondria), neutral red retention assay (lysosomes) and finally, induction of apoptosis and necrosis. Genotoxicity was determined by observing the fragmentation of DNA by the comet assay, while mutagenicity was determined by Cytokinesis-block micronucleus technique. The characterization showed that the FBS was effective in dispersing the nanoparticles and prevent the formation of large agglomerates allowing robust responses on the real toxicity of NP. After 24 hours of treatment, there was cell membranes rupture, decreasing cell viability to 35.33%, at the highest concentration (1.0 μg mL-1). Mitochondrial metabolic activity remained unchanged, but it was possible to detect the proliferation of lysosomes, which was mainly attributed to the NP endocytosis. The induction of apoptosis was 50.4%, and necrosis was 13.9%, both in the concentration 1.0 μg mL-1 TiO2-NP. In the case of necrosis, a result 10 times greater than that presented by the negative control. Added necrosis and apoptosis indicated a decrease in cell viability to 35.7%. The comet test showed the fragmentation of the DNA, it was also possible to observe the formation of micronuclei, bridges and shoots demonstrated by the micronucleus assay. In general, this study demonstrated that TiO2-NP, after 24 hours of exposure, significantly affect cell viability and cause DNA damage, which may become irreversible. In conclusion, this study showed the cytotoxic, genotoxic and mutagenic potential of TiO2-NP for ZF-L cells. Mitochondrial and lysosome responses require further studies on the effect of TiO2-NP on these organelles. / Nanopartículas de dióxido de titânio (NP-TiO2) são comumente usadas em muitos produtos industriais. Por conseguinte, seu consumo diário por seres humanos é estimado em 5,4 mg dia-1, o que acarreta em um aporte no ambiente de 4,2 mg dia-1 por pessoa, podendo ou não receber um tratamento apropriado antes do seu despejo. Foram avaliadas a citotoxicidade, genotoxicidade e mutagenicidade de NPTiO2 para a linhagem permanente derivada de fígado de peixe-zebra (Danio rerio) (células ZF-L). Antes da avaliação do potencial tóxico das nanopartículas, foi realizada uma caracterização cuidadosa em meio de cultura com e sem a adição de soro fetal de bovino (SFB). A caracterização em termos do tamanho físico da nanopartícula (NP) foi realizada utilizando um microscópio eletrônico de transmissão (TEM); os tamanhos hidrodinâmicos dos aglomerados e as cargas de superfície foram acessados por medidas de DLS (diameter light scattering) e potencial zeta, respectivamente utilizando um espectrofotômetro. A viabilidade celular foi avaliada por três ensaios diferentes, o ensaio de exclusão do corante azul de tripano (integridade de membrana), ensaio de redução do sal MTT (atividade metabólica mitocondrial) e ensaio de retenção do corante vermelho neutro (viabilidade dos lisossomos). A indução de apoptose e necrose foi avaliada por citometria de fluxo. A genotoxicidade foi determinada pela observação da fragmentação do DNA por meio do ensaio do cometa, enquanto a mutagenicidade foi determinada pelo ensaio de micronúcleos com bloqueio da citocinese. A análise DLS mostrou que o SFB foi eficaz quanto à dispersão das nanopartículas e preveniu a formação de grandes aglomerados, o que permitiu a obtenção de respostas mais robustas relativas à toxicidade real das nanopartículas. Após 24 horas de tratamento, houve ruptura das membranas celulares diminuindo a viabilidade celular a 35,33%, na concentração mais elevada (1,0 μg mL-1). A atividade metabólica mitocondrial manteve-se inalterada, mas foi possível detectar a proliferação dos lisossomos, que foi atribuída principalmente à endocitose das NP. A indução de apoptose foi de 50,4%, e de necrose de 13,9%, ambos na concentração 1,0 μg mL-1 NP-TiO2. No caso da necrose, um resultado 10 vezes maior do que o apresentado pelo controle negativo. Necrose e apoptose somadas indicaram a diminuição da viabilidade celular a 35,7%. O teste do cometa mostrou a fragmentação do DNA, também foi possível observar a formação de micronúcleos, pontes e brotos demonstrados pelo ensaio do micronúcleo. Em geral, este estudo demonstrou que as NP-TiO2, após 24 horas de exposição, afetam significativamente a viabilidade celular e causam danos ao DNA, que podem se tornar irreversíveis. Em conclusão, este estudo mostrou o potencial citotóxico, genotóxicos e mutagênico das NP-TiO2 para células ZF-L. Respostas mitocondriais e dos lisossomos requerem novos estudos quanto ao efeito das NP-TiO2 sobre essas organelas.

Made available in DSpace on 2014-07-29T16:21:15Z (GMT). No. of bitstreams: 1 Dissertacao Dilermando P L Jr.pdf: 360879 bytes, checksum: 1c2f22ea2b7828ee7c6779ffd933fed4 (MD5) Previous issue date: 2008-02-27 / The establishment of exotic species is known for the negative impacts it causes. However, it can be used as models to study the ecological and evolutionary causes of biogeography patterns and access whether the niche conservatism is the determinant of the species limits distribution. The main purpose of this study is to evaluate the difference between pools of exotic fish species in biogeographical regions of the world based on the theories of Niche Conservatism and Evolutionary Dynamics of Latitudinal Gradients of Diversity. We found a strong tendency of the niche conservatism with exotic fishes, but no phylogentic structures of the invaders fishes were found. Therefore, predictive models that purpose to evaluate the potential invasion of fishes has to, include extrinsic factors as climatic conditions, propagule pressure, environmental disturbance, human use and intrinsic factors as parental care and body size of the species. / Os estabelecimentos de espécies exóticas são muito conhecidos por seus impactos, contudo podem servir como modelo de estudo das causas ecológicas e evolutivas dos padrões biogeográficos e avaliar se a conservação de nicho é determinante dos limites de distribuições das espécies. Este estudo tem por objetivo avaliar a diferença entre o conjunto de espécies exóticas de peixes nas diferentes regiões biogeográficas do planeta tendo como base as teorias de conservação filogenética e da dinâmica evolutiva de gradientes latitudinais de diversidade. Encontramos uma forte tendência de conservação de nicho, mas nenhum sinal de estruturação filogenética da invasão. Portanto, modelos preditivos que possuem o intuito de avaliar o potencial invasor de peixes têm, necessariamente, têm que incluir fatores extrínsecos às espécies e à condição climática da região nativa, pressão de propágulos, distúrbios no ambiente, uso humano e fatores intrínsecos como cuidado parental e tamanho corporal das espécies.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2016-09-20T11:12:34Z No. of bitstreams: 2 Dissertação - Anderson Barros Caixeta Araújo - 2016.pdf: 3153002 bytes, checksum: ba1e261db38d81f09762632dfc921e8b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-09-20T11:58:38Z (GMT) No. of bitstreams: 2 Dissertação - Anderson Barros Caixeta Araújo - 2016.pdf: 3153002 bytes, checksum: ba1e261db38d81f09762632dfc921e8b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-20T11:58:39Z (GMT). No. of bitstreams: 2 Dissertação - Anderson Barros Caixeta Araújo - 2016.pdf: 3153002 bytes, checksum: ba1e261db38d81f09762632dfc921e8b (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The naphthenic acids comprise a complex mixture of carboxylic acids that are present in petroleum. They are directly responsible for the oil acidity and its corrosiveness in liquid phase during the refining process. Such compounds are also presents in the derivatives, causing several problems to product quality. A possible way of removing these acids from those oil fractions is using the adsorption process in porous solids, as activated carbons. There are few studies about the removal of naphthenic acids on coals. For this reason, we chose four types of activated carbons for adsorption tests, and they coal babassu, palm kernel, coconut and of Bahia ox bone. In order to assess the possibility of further removing acidic compounds, the four carbons were subjected to a chemical treatment with concentrated sodium hydroxide. Physical and chemical analyzes were performed in order to promote the characterization of all adsorbents, showing that the treatment previously mentioned was leading to an increase in the adsorption capacity of the coals. The adsorption experiments with commercial batch naphthenic acid solution showed that the treated ox bone char had the highest retention efficiency, which is the adsorbent used to construct the adsorption isotherms. The isotherms were better adjusted by Langmuir model, revealing the chemisorption of character adsorptive process. The thermodynamic data showed that the process is spontaneous and endothermic, is favored by increasing the temperature. Regarding the crude oil sample, batch adsorption experiments were conducted in such a way as to determine the removal efficiency of class O2 and reducing the Total Acid Number (IAT). The results spectrometry FTICR ix MS Pasta, they showed that all coals chemically treated were able to remove more acidic compounds in relation to their untreated related. The raw coals babassu oil, palm oil and coconut Bahia showed a potential for adsorption of nitrogen compounds from oil, given that there was a decrease in its class in the class chart. As a final analysis, all the coals were evaluated for their ability to lower oil IAT, it was found that the ox bone char treated again achieved the best result, reducing by 70% the value of the IAT. / Os ácidos naftênicos correspondem à complexa mistura de ácidos carboxílicos presentes no petróleo, responsáveis diretamente pela sua acidez e pela sua corrosividade em fase líquida durante o refino. Tais compostos também estão presentes nas frações destiladas do petróleo, causando diversos problemas na qualidade final do produto. Uma alternativa para a remoção desses ácidos das frações destiladas é por meio da adsorção em materiais porosos, como os carvões ativados. Poucos são os estudos a respeito da remoção de ácidos naftênicos em carvões. Por esta razão, foram escolhidos quatro tipos de carvões ativados para os ensaios de adsorção, sendo eles carvão de babaçu, dendê, coco da Bahia e osso de boi. A fim de avaliar a possibilidade de uma maior remoção de compostos ácidos, os quatro carvões foram submetidos a um tratamento químico com solução concentrada de hidróxido de sódio. Análises físico-químicas foram realizadas com o intuito de promover a caracterização de todos os adsorventes, revelando que o tratamento anteriormente citado foi preponderante para um aumento na capacidade adsortiva dos carvões. Os ensaios de adsorção em batelada com solução comercial de ácidos naftênicos mostraram que o carvão de osso de boi tratado apresentou a maior eficiência de retenção, sendo este o adsorvente utilizado para a construção das isotermas de adsorção. As isotermas foram melhor ajustadas pelo Modelo de Langmuir, revelando o caráter de quimiossorção do processo adsortivo. Os dados termodinâmicos mostraram que o processo é espontâneo e endotérmico, sendo mais favorecido pelo aumento da temperatura. Em relação à amostra de petróleo bruto, ensaios de adsorção em batelada foram conduzidos de tal forma a averiguar a eficiência na remoção da classe O2 e na redução do Índice de Acidez Total (IAT). Os resultados de Espectrometria de Massas FT-ICR MS, mostraram que todos os carvões tratados quimicamente conseguiram remover mais compostos ácidos em relação a seus correlatos não tratados. Os carvões brutos de babaçu, dendê e coco da Bahia apresentaram uma potencialidade para adsorção de compostos nitrogenados do petróleo, haja vista que houve a diminuição desta classe no gráfico de classes. Como análise final, todos os carvões foram avaliados quanto suas capacidades de redução do IAT do petróleo, em que foi constatado que o carvão de osso de boi tratado novamente conseguiu o melhor resultado, reduzindo em 70% o valor do IAT.

The study of experimental recording of dynamical systems often consists in the analysis of signals produced by that system. Time series analysis consists of a wide range of methodologies ultimately aiming at characterizing the signals and, eventually, gaining insights on the underlying processes that govern the evolution of the system. A standard way to tackle this issue is spectrum analysis, which uses Fourier or Laplace transforms to convert time-domain data into a more useful frequency space. These analytical methods allow to highlight periodic patterns in the signal and to reveal essential characteristics of linear systems. Most experimental signals, however, exhibit strange and apparently unpredictable behavior which require more sophisticated analytical tools in order to gain insights into the nature of the underlying processes generating those signals. This is the case when nonlinearity enters into the dynamics of a system. Nonlinearity gives rise to unexpected and fascinating behavior, among which the emergence of deterministic chaos. In the last decades, chaos theory has become a thriving field of research for its potential to explain complex and seemingly inexplicable natural phenomena. The peculiarity of chaotic systems is that, despite being created by deterministic principles, their evolution shows unpredictable behavior and a lack of regularity. These characteristics make standard techniques, like spectrum analysis, ineffective when trying to study said systems. Furthermore, the irregular behavior gives the appearance of these signals being governed by stochastic processes, even more so when dealing with experimental signals that are inevitably affected by noise. Nonlinear time series analysis comprises a set of methods which aim at overcoming the strange and irregular evolution of these systems, by measuring some characteristic invariant quantities that describe the nature of the underlying dynamics. Among those quantities, the most notable are possibly the Lyapunov ex- ponents, that quantify the unpredictability of the system, and measure of dimension, like correlation dimension, that unravel the peculiar geometry of a chaotic system’s state space. These methods are ultimately analytical techniques, which can often be exactly estimated in the case of simulated systems, where the differential equations governing the system’s evolution are known, but can nonetheless prove difficult or even impossible to compute on experimental recordings. A different approach to signal analysis is provided by information theory. Despite being initially developed in the context of communication theory, by the seminal work of Claude Shannon in 1948, information theory has since become a multidisciplinary field, finding applications in biology and neuroscience, as well as in social sciences and economics. From the physical point of view, the most phenomenal contribution from Shannon’s work was to discover that entropy is a measure of information and that computing the entropy of a sequence, or a signal, can answer to the question of how much information is contained in the sequence. Or, alternatively, considering the source, i.e. the system, that generates the sequence, entropy gives an estimate of how much information the source is able to produce. Information theory comprehends a set of techniques which can be applied to study, among others, dynamical systems, offering a complementary framework to the standard signal analysis techniques. The concept of entropy, however, was not new in physics, since it had actually been defined first in the deeply physical context of heat exchange in thermodynamics in the 19th century. Half a century later, in the context of statistical mechanics, Boltzmann reveals the probabilistic nature of entropy, expressing it in terms of statistical properties of the particles’ motion in a thermodynamic system. A first link between entropy and the dynamical evolution of a system is made. In the coming years, following Shannon’s works, the concept of entropy has been further developed through the works of, to only cite a few, Von Neumann and Kolmogorov, being used as a tool for computer science and complexity theory. It is in particular in Kolmogorov’s work, that information theory and entropy are revisited from an algorithmic perspective: given an input sequence and a universal Turing machine, Kolmogorov found that the length of the shortest set of instructions, i.e. the program, that enables the machine to compute the input sequence was related to the sequence’s entropy. This definition of the complexity of a sequence already gives hint of the differences between random and deterministic signals, in the fact that a truly random sequence would require as many instructions for the machine as the size of the input sequence to compute, as there is no other option than programming the machine to copy the sequence point by point. On the other hand, a sequence generated by a deterministic system would simply require knowing the rules governing its evolution, for example the equations of motion in the case of a dynamical system. It is therefore through the work of Kolmogorov, and also independently by Sinai, that entropy is directly applied to the study of dynamical systems and, in particular, deterministic chaos. The so-called Kolmogorov-Sinai entropy, in fact, is a well-established measure of how complex and unpredictable a dynamical system can be, based on the analysis of trajectories in its state space. In the last decades, the use of information theory on signal analysis has contributed to the elaboration of many entropy-based measures, such as sample entropy, transfer entropy, mutual information and permutation entropy, among others. These quantities allow to characterize not only single dynamical systems, but also highlight the correlations between systems and even more complex interactions like synchronization and chaos transfer. The wide spectrum of applications of these methods, as well as the need for theoretical studies to provide them a sound mathematical background, make information theory still a thriving topic of research. In this thesis, I will approach the use of information theory on dynamical systems starting from fundamental issues, such as estimating the uncertainty of Shannon’s entropy measures on a sequence of data, in the case of an underlying memoryless stochastic process. This result, beside giving insights on sensitive and still-unsolved aspects when using entropy-based measures, provides a relation between the maximum uncertainty on Shannon’s entropy estimations and the size of the available sequences, thus serving as a practical rule for experiment design. Furthermore, I will investigate the relation between entropy and some characteristic quantities in nonlinear time series analysis, namely Lyapunov exponents. Some examples of this analysis on recordings of a nonlinear chaotic system are also provided. Finally, I will discuss other entropy-based measures, among them mutual information, and how they compare to analytical techniques aimed at characterizing nonlinear correlations between experimental recordings. In particular, the complementarity between information-theoretical tools and analytical ones is shown on experimental data from the field of neuroscience, namely magnetoencefalography and electroencephalography recordings, as well as mete- orological data.

The work presents the recent developments in Quantum Monte Carlo calculations for nuclear systems including strange degrees of freedom. The Auxiliary Field Diffusion Monte Carlo algorithm has been extended to the strange sector by the inclusion of the lightest among the hyperons, the Λ particle. This allows to perform detailed calculations for Λ hypernuclei, providing a microscopic framework for the study of the hyperon-nucleon interaction in connection with the available experimental information. The extension of the method for strange neutron matter, put the basis for the first Diffusion Monte Carlo analysis of the hypernuclear medium, with the derivation of neutron star observables of great astrophysical interest.

The present work analyzes and describes a method for the direct numerical solution of the Maxwell's equations of classical electromagnetism. This is the FDTD (Finite-Difference Time-Domain) method, along with its implementation in an "in-house" computing code for large parallelized simulations. Both are then applied to the modelization of photonic and plasmonic structures interacting with light. These systems are often too complex, either geometrically and materially, in order to be mathematically tractable and an exact analytic solution in closed form, or as a series expansion, cannot be obtained. The only way to gain insight on their physical behavior is thus to try to get a numerical approximated, although convergent, solution. This is a current trend in modern physics because, apart from perturbative methods and asymptotic analysis, which represent, where applicable, the typical instruments to deal with complex physico-mathematical problems, the only general way to approach such problems is based on the direct approximated numerical solution of the governing equations. Today this last choice is made possible through the enormous and widespread computational capabilities offered by modern computers, in particular High Performance Computing (HPC) done using parallel machines with a large number of CPUs working concurrently. Computer simulations are now a sort of virtual laboratories, which can be rapidly and costless setup to investigate various physical phenomena. Thus computational physics has become a sort of third way between the experimental and theoretical branches. The plasmonics application of the present work concerns the scattering and absorption analysis from single and arrayed metal nanoparticles, when surface plasmons are excited by an impinging beam of light, to study the radiation distribution inside a silicon substrate behind them. This has potential applications in improving the eciency of photovoltaic cells. The photonics application of the present work concerns the analysis of the optical reflectance and transmittance properties of an opal crystal. This is a regular and ordered lattice of macroscopic particles which can stops light propagation in certain wavelenght bands, and whose study has potential applications in the realization of low threshold laser, optical waveguides and sensors. For these latters, in fact, the crystal response is tuned to its structure parameters and symmetry and varies by varying them. The present work about the FDTD method represents an enhacement of a previous one made for my MSc Degree Thesis in Physics, which has also now geared toward the visible and neighboring parts of the electromagnetic spectrum. It is organized in the following fashion. Part I provides an exposition of the basic concepts of electromagnetism which constitute the minimum, although partial, theoretical background useful to formulate the physics of the systems here analyzed or to be analyzed in possible further developments of the work. It summarizes Maxwell's equations in matter and the time domain description of temporally dispersive media. It addresses also the plane wave representation of an electromagnetic field distribution, mainly the far field one. The Kirchhoff formula is described and deduced, to calculate the angular radiation distribution around a scatterer. Gaussian beams in the paraxial approximation are also slightly treated, along with their focalization by means of an approximated diraction formula useful for their numericall FDTD representation. Finally, a thorough description of planarly multilayered media is included, which can play an important ancillary role in the homogenization procedure of a photonic crystal, as described in Part III, but also in other optical analyses. Part II properly concerns the FDTD numerical method description and implementation. Various aspects of the method are treated which globally contribute to a working and robust overall algorithm. Particular emphasis is given to those arguments representing an enhancement of previous work.These are: the analysis from existing literature of a new class of absorbing boundary conditions, the so called Convolutional-Perfectly Matched Layer, and their implementation; the analysis from existing literature and implementation of the Auxiliary Differential Equation Method for the inclusion of frequency dependent electric permittivity media, according to various and general polarization models; the description and implementation of a "plane wave injector" for representing impinging beam of lights propagating in an arbitrary direction, and which can be used to represent, by superposition, focalized beams; the parallelization of the FDTD numerical method by means of the Message Passing Interface (MPI) which, by using the here proposed, suitable, user dened MPI data structures, results in a robust and scalable code, running on massively parallel High Performance Computing Machines like the IBM/BlueGeneQ with a core number of order 2X10^5. Finally, Part III gives the details of the specific plasmonics and photonics applications made with the "in-house" developed FDTD algorithm, to demonstrate its effectiveness. After Chapter 10, devoted to the validation of the FDTD code implementation against a known solution, Chapter 11 is about plasmonics, with the analytical and numerical study of single and arrayed metal nanoparticles of different shapes and sizes, when surface plasmon are excited on them by a light beam. The presence of a passivating embedding silica layer and a silicon substrate are also included. The next Chapter 12 is about the FDTD modelization of a face-cubic centered (FCC) opal photonic crystal sample, with a comparison between the numerical and experimental transmittance/reflectance behavior. An homogenization procedure is suggested of the lattice discontinuous crystal structure, by means of an averaging procedure and a planarly multilayered media analysis, through which better understand the reflecting characteristic of the crystal sample. Finally, a procedure for the numerical reconstruction of the crystal dispersion banded omega-k curve inside the first Brillouin zone is proposed. Three Appendices providing details about specific arguments dealt with during the exposition conclude the work.

This thesis investigates two biological systems using atomistic modelling and molecular dynamics simulation. The work is focused on: (a) the study of the interaction between a segment of a DNA molecule and a functionalized surface; (b) the dynamical modelling of protein tau, an intrinsically disordered protein. We briefly describe here the two problems; for their detailed introduction we refer respectively to chapter DNA and chapter TAU. The interest in the study of the adsorption of DNA on functionalized surfaces is related to the considerable effort that in recent years has been devoted in developing technologies for faster and cheaper genome sequencing. In order to sequence a DNA molecule, it has to be extracted from the cell where it is stored (e.g. the blood cells). As a consequence any genomic analysis requires a purification process in order to remove from the DNA molecule proteins, lipids and any other contaminants. The extraction and purification of DNA from biological samples is hence the first step towards an efficient and cheap genome sequencing. Using the chemical and physical properties of DNA it is possible to generate an attractive interaction between this macromolecule and a properly treated surface. Once positioned on the surface, the DNA can be more easily purified. In this work we set up a detailed molecular model of DNA interacting with a surface functionalized with amino silanes. The intent is to investigate the free energy of adsorption of small DNA oligomers as a function of the pH and ionic strength of the solution. The tau protein belongs to the category of Intrinsically Disordered Proteins (IDP), which in their native state do not have an average stable structure and fluctuate between many conformations. In its physiological state, tau protein helps nucleating and stabilizing the microtubules in the axons of the neurons. On the other hand, the same tau - in a pathological aggregation - is involved in the development of the Alzheimer disease. IDPs do not have a definite 3D structure, therefore their dynamical simulation cannot start from a known list of atomistic positions, like a protein data bank file. We first introduce a procedure to find an initial dynamical state for a generic IDP, and we apply it to the tau protein. We then analyze the dynamical properties of tau, like the propensity of residues to form temporary secondary structures like beta-sheets or alpha-helices.