In this work, we expand the scope of the present implications of the tight-binding microcanonical picture of electron transport, which is proposed by Di Ventra and co-workers as an alternative to the Landauer’s static scattering approach. We investigate the structure dependence of current flow in electrode-conductor-electrode systems and calculate the local occupation functions and time-dependent conductor current for various conductor lengths and electrode configurations. We also explore fundamental physical limits to the encoding of information in the nanoscale conductor by application of electrode bias in a model system. Using the microcanonical description of a nanoconductor, composed of linear chain of atoms, bridging two electrodes, we obtain upper bounds on the accessible information in the conductor as a function of electrode bias, when the current flow is governed by the conductance quantum.

Ce travail de thèse porte sur l'étude expérimentale et théorique de la fragmentation de molécules organiques. Nous avons pour cela construit un nouveau réacteur plasma non-thermique et transformé un modèle statistique de fragmentation nucléaire (Microcanonical Metropolis Monte Carlo ou MMMC) pour décrire la fragmentation d'espèces CnHm. Le plasma non-thermique est créé par une impulsion nanoseconde haute-tension (100 kV) avec un front de montée très raide (15-20 kV.ns-1). Cette impulsion permet d'obtenir un volume plasmagène diffus important et de créer de fortes densités d'espèces réactives (radicaux, métastables, etc.) pouvant réagir avec les molécules organiques. Dans le cas de la fragmentation du propane, la décharge hors-équilibre considérée permet de générer comme sous-produits majoritaires du méthane, de l'éthane et du propène. Son efficacité énergétique de conversion est deux fois plus élevée que celle obtenue dans le cas d'une décharge à barrière diélectrique ou d'une décharge pré-ionisée. Le modèle MMMC décrit, pour une énergie fixée, l'espace des phases accessible au système. L'ensemble des degrés de libertés statiques (dégénérescences, excitation interne, localisation, etc.) et dynamiques (translation et rotation) de tous des fragments de la molécule parent sont pris en compte. Les caractéristiques physiques des fragments (énergies de dissociations, géométries, fréquences de vibration, etc.), nécessaires pour ces calculs, sont déterminées à l'aide d'un code ab-initio. Différentes méthodes de calcul (composite ou DFT) et différents niveaux de calcul (sans ou avec polarisation de l'hydrogène) ont été comparés aux données expérimentales. Nous avons montré que la prise en compte de la polarisation de l'hydrogène avait une influence importante sur les résultats. Les probabilités des voies de fragmentation en fonction de l'énergie d'excitation pour les deux méthodes sont relativement proches. Les principaux écarts s’expliquent par des différences d’énergie du fondamental de certains fragments. La comparaison des résultats théoriques et expérimentaux est indirecte car le modèle MMMC ne décrit que la phase de fragmentation. Les produits résultants vont ensuite réagir entre eux et avec le milieu pendant et après l’excitation plasma. L’évolution cinétique complexe des produits doit donc être prise en compte. D’autre part, la distribution d’énergie déposée dans la molécule parent par les états métastables de l'azote et les collisions électroniques doit également être déterminée. Ces deux étapes sont nécessaires pour obtenir des résultats théoriques comparables aux observables expérimentales. Cette étude sera une prolongation naturelle de notre travail. Les résultats expérimentaux semblent toutefois montrer que le modèle surestime le nombre de ruptures de liaisons CH. Ceci est probablement du au fait que la première étape du modèle, la construction des fragments, opère uniquement par rupture de liaisons dans la molécule de propane ou de propène parent. Les molécules fragments H2 et CH4 ne sont donc pas autorisées alors qu’un schéma réactionnel les produisant en une étape est envisageable (et que les fragments C3H6 et C2H4 sont mesurés en abondance). L’énergie non consommée dans leur production est donc reportée sur la rupture de liaisons CH. / This thesis is an experimental and theoretical study of organic compounds fragmentation. For this purpose, we had to built a new non-thermal plasma reactor and modify a statistical model used for nuclear fragmentation (Microcanonical Metropolis Monte Carlo or MMMC) to describe the fragmentation of CnHm types species. The non-thermal plasma is created by a nanosecond high-voltage (100 kV) pulse with a steep rise front (15-20 kV.ns-1). This pulse allows to have a large volume of diffuse plasma and to create important quantities of reactive species (radicals, metastables, etc.), which could react with organic molecules. In the case of propane fragmentation, the non-equilibrium discharge used allows to product as major by-products methane, ethane and propene. The energetic efficiency of the conversion by this discharge is twice more efficient than the one obtained with a dielectric barrier discharge or a pre-ionised discharge. The MMMC model describes, for a given energy, the accessible phase space for the system. All static (discrepancy, internal excitation, position, etc.) and dynamic (translation and rotation) degrees of freedom for every fragment of the initial molecule are taken into account. The physical properties (dissociation energies, geometry, vibrational frequencies, etc.) of each fragment are needed to perform calculations and are obtained by using an ab-initio code. Different computation methods (composite or DFT) and different levels of calculation (with or without hydrogen polarisation) have been compared to experimental values. We have shown that the hydrogen polarisation has an important influence on the properties. Probabilities of fragmentation paths are slightly identical between the two methods. The main differences are explained by the existence of a variation between the ground energy of some fragments. Comparison between theoretical and experimental results is indirect because the MMMC model only described the fragmentation phase. By-products will react between them and with their environment during and after the excitation phase. The complex kinetic evolution of the by-products must be taken into account. Moreover, the energetic distribution injected in the initial molecule by metastable states of nitrogen and electronic collisions must be determined. These two steps are require to obtain theoretical results, which could be compared to experimental ones. This study should be the following work after our study. Experimental results seem to suggest that the model overestimates the number of C-H bonds, that are broken. Probably, because the first step of the model, the construction of fragments, works only by breaking bonds in the initial molecule of propane and propene. Les fragments H2 and CH4 are not allowed, but their production in one reaction is possible (C3H6 and C2H4 are experimentally measured). Non-used energy by their production is reported to break CH bonds

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT:In this thesis we discuss some of the anomalies present in systems with long-range interactions, for instance negative speci c heat and negative magnetic susceptibility, and show how they can be related to the convexity properties of the thermodynamic potentials and nonequivalence of ensembles. We also discuss the possibility of engineering long-range quantum spin systems with cold atoms in optical lattices to experimentally verify the existence of nonequivalence of ensembles. We then formulate an expression for the density of states when the energy and magnetisation correspond to a pair of non-commuting operators. Finally we analytically compute the entropy s( ;m) as a function of energy, , and magnetisation, m, for the anisotropic Heisenberg model with Curie-Weiss type interactions. The results show that the entropy is non-concave in terms of magnetisation under certain circumstances which in turn indicates that the microcanonical and canonical ensembles are not equivalent and that the magnetic susceptibility is negative. After making an appropriate change of variables we show that a second-order phase transition can be present at negative temperatures in the microcanonical ensemble which cannot be represented in the canonical ensemble. / AFRIKAANSE OPSOMMING: In hierdie tesis bespreek ons van die onverwagte eienskappe wat sisteme met lang afstand wisselwerkings kan openbaar, byvoorbeeld negatiewe spesi eke warmte en negatiewe magnetiese suseptibiliteit. Ons dui ook die ooreenkoms tussen hierdie gedrag en die konveksiteit van die termodinamiese potensiale en nie-ekwivalente ensembles aan. Hierna bespreek ons die moontlikheid om lang afstand kwantum spin sisteme te realiseer met koue atome in 'n optiese rooster. Daarna wys ons hoe dit moontlik is om 'n uitdrukking vir die digtheid van toestande te formuleer vir sisteme waar die energie en magnetisasie ooreenstem met operatore wat nie met mekaar kommuteer nie. Uiteindelik bepaal ons die entropie, s( ;m), in terme van die energie, , en magnetisasie, m, vir die anisotropiese Heisenberg model met Curie-Weiss tipe interaksies. Die resultate wys dat die entropie onder sekere omstandighede nie konkaaf in terme van magnetisasie is nie. Dit, op sy beurt, dui aan dat die mikrokanoniese en kanoniese ensembles nie ekwivalent is nie en dat die magnetiese suseptibiliteit negatief kan wees. Nadat ons 'n toepaslike transformasie van veranderlikes maak, wys ons dat 'n tweede orde fase-oorgang by negatiewe temperature kan plaasvind in die mikrokanoniese ensemble wat nie verteenwoordig kan word in die kanoniese ensemble nie.

This dissertation aims at addressing two important theoretical questions which are still debated in the statistical mechanical community. The first question has to do with the outstanding problem of how to reconcile time-reversal asymmetric macroscopic laws with the time-reversal symmetric laws of microscopic dynamics. This problem is addressed by developing a novel mechanical approach inspired by the work of Helmholtz on monocyclic systems and the Heat Theorem, i.e., the Helmholtz Theorem. By following a line of investigation initiated by Boltzmann, a Generalized Helmholtz Theorem is stated and proved. This theorem provides us with a good microscopic analogue of thermodynamic entropy. This is the volume entropy, namely the logarithm of the volume of phase space enclosed by the constant energy hyper-surface. By using quantum mechanics only, it is shown that such entropy can only increase. This can be seen as a novel rigorous proof of the Second Law of Thermodynamics that sheds new light onto the arrow of time problem. The volume entropy behaves in a thermodynamic-like way independent of the number of degrees of freedom of the system, indicating that a whole thermodynamic-like world exists at the microscopic level. It is also shown that breaking of ergodicity leads to microcanonical phase transitions associated with nonanalyticities of volume entropy. The second part of the dissertation deals with the problem of the foundations of generalized ensembles in statistical mechanics. The starting point is Boltzmann's work on statistical ensembles and its relation with the Heat Theorem. We first focus on the nonextensive thermostatistics of Tsallis and the associated deformed exponential ensembles. These ensembles are analyzed in detail and proved (a) to comply with the requirements posed by the Heat Theorem, and (b) to interpolate between canonical and microcanonical ensembles. Further they are showed to describe finite systems in contact with finite heat baths. Their mechanical and information-theoretic foundation, are highlighted. Finally, a wide class of generalized ensembles is introduced, all of which reproduce the Heat Theorem. This class, named the class of dual orthodes, contains microcanonical, canonical, Tsallis and Gaussian ensembles as special cases.

We compare the transition barrier that accompanies a first-order phase transition in the canonical and microcanonical ensemble. This is directly encoded in the probability distributions of standard Metropolis Monte Carlo simulations and a proper microcanonical sampling technique. For the example of droplet formation, we find that in both ensembles the transition barrier scales as expected but that the barrier is much smaller in the microcanonical ensemble. In addition its growth with system size is weaker which will enhance this difference for larger systems. We provide an intuitive physical explanation for this observation

Submitted by (ana.araujo@ufrpe.br) on 2016-07-05T16:55:56Z No. of bitstreams: 1 Evert Elvis Batista Almeida.pdf: 8214568 bytes, checksum: 34db767d9a38f53b7b60aaf92ca37a20 (MD5) / Made available in DSpace on 2016-07-05T16:55:56Z (GMT). No. of bitstreams: 1 Evert Elvis Batista Almeida.pdf: 8214568 bytes, checksum: 34db767d9a38f53b7b60aaf92ca37a20 (MD5) Previous issue date: 2009-02-26 / We applied a non-supervisioned data clustering technique based on a map of the problem into an inhomogeneous granular magnet problem. The physical behavior of the magnet is studied through the usual Monte Carlo method. Each data item is described by a set of numerical attributes, interpreted as points in a multiple-dimensional Euclidian space. The mapping consists in associating a Potts spin to each data point. The physical system is described by a disordered Potts Hamiltonian with several states with an exponentially decaying interaction among spins. The magnet reaches a superparamagnetic state at high temperatures in which the spins in certain grains are strongly correlated whereas the grains are loosely linked. In this way, each grain corresponds to a group or cluster. We implemented the method in a microcanonical ensemble where the conserved total energy is the control parameter. The temperature is calculated during the simulation and, besides thermodynamic stable states, it is possible to sample unstable and metastable state as well. We work with three artificial multiple-dimensional data set and a four-dimensional real data set. We obtained good results in all cases and discuss some issues concerning the microcanonical implementation of the superparamagnetic data clustering. / Aplicamos um método não supervisionado de agrupamento de dados para identificar padrões em vários conjuntos dados. A técnica baseia-se em um mapeamento do problema em um sistema magnético granular heterogêneo, cujo comportamento é investigado através de métodos Monte Carlo comumente empregado no campo da física estatística. Cada objeto é descrito por um conjunto de atributos de valores numéricos, interpretados como um ponto em um espaço euclidiano de dimensão apropriada. O mapeamento consiste em associar a cada item do conjunto, um ponto no espaço, um spin de Potts. O sistema físico é descrito por um hamiltoniano de Potts de muitos estados, no qual a interação entre os spins decai exponencialmente com a distância entre eles. Itens semelhantes, próximos, interagem fortemente enquanto que aqueles mais distantes entre si interagem apenas fracamente. O magneto atinge um estado superparamagnético para temperaturas suficientemente altas, no qual os spins de alguns grãos permanecem fortemente correlacionados, porém, os grãos estão fracamente ligados entre si. Cada grão corresponde a um grupo. Implementamos o método no ensemble microcanônico, no qual a energia total é conservada e constitui o parâmetro de controle. Nesse caso, a temperatura é calculada ao longo do processo e podemos acessar estados termodinamicamente estáveis, metaestáveis, bem como, instáveis. Trabalhamos com três conjuntos artificiais de dados, em duas e três dimensões, e um conjunto de dados reais com quatro dimensões. O desempenho do método foi satisfatório em todos os casos investigados.

Transições de fase termodinâmicas são usualmente estudadas por meio do ensemble canônico e estão associadas a sistemas macroscópicos. Entretanto, tem-se tornado cada vez mais frequente e importante o estudo de sistemas físicos pequenos, cujos alcances característicos das interações equivalem aos tamanhos dos sistemas. Nestes casos pode haver inequivalência entre grandezas físicas obtidas nos ensembles canônico e microcanônico. Encontramos inúmeros exemplos destes sistemas em diversas áreas da Física. Na área de matéria condensada temos, por exemplo, o modelo Blume-Capel com interações de alcance infinito. Neste modelo as soluções exatas canônica e microcanônica são inequivalentes. Este modelo é investigado nesta tese por meio de um ensemble interpolante, conhecido como gaussiano estendido, como uma aplicação teórica preliminar. Adicionalmente, empregamos o arcabouço mecânico-estatístico no estudo de certas biomoléculas com ampla importância biológica: proteínas. Atualmente o estudo do comportamento termodinâmico destas moléculas tem ficado restrito quase que exclusivamente a abordagem via ensemble canônico. Neste trabalho analisamos os resultados da etapa microcanônica de simulações multicanônicas procurando obter aspectos físicos de biomoléculas como os domínios Src SH3 (pdb: 1NLO) e as Príons humanas (pdb: 1HJM). Caracterizamos com esta abordagem as transições de fase de enovelamento e de agregação destes sistemas. Os resultados obtidos são interpretados à luz da termoestatística microcanônica, oferecendo um ponto de vista fenomenológico alternativo à abordagem usual. / Thermodynamic phase transitions are usualy studied by the canonical ensemble and they are associated to macroscopic systems. However, it is becoming more frequent and important the study of small physical systems: whose characteristic interaction-lengths are equivalent to system sizes. In these cases there can happen inequivalences among quantities computed im the canonical and microcanonical ensembles. There are inumerous examples of that systems in various areas of physics. In the field of condensed matter there is for instance the Blume-Capel model with infinite-range interactions. The canonical and microcanonical exact solutions of this model are inequivalents. That model is investigated on this thesis through an interpolating ensemble, known as the extended gaussian, as a preliminar theoretical application. Additionally, we have employed the statistic-mechanical framework to study some biomolecules of large biological interest: proteins. Nowadays the study of the thermodynamic behavior of that molecules has been restricted almost only to the canonical approach. However, in this work we have analysed by the microcanonical step of multicanonical simulations the physical aspects of biomolecules as the domain Src SH3 (pdb: 1NLO) and the human Prions (pdb: 1HJM). Thus, we characterize with this approach the phase transitions of folding and aggregation of that systems. The results obtained are interpretated under the light of the microcanonical thermostatistics, offering an alternative phenomenological viewpoint.

In this thesis, we introduce a new approach to wavefront phase reconstruction in Adaptive Optics (AO) from the low-resolution gradient measurements provided by a wavefront sensor, using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, it is naturally suited to the study of multiscale properties of complex natural signals, mainly due to the precise numerical estimate of geometrically localized critical exponents, called the singularity exponents. These exponents quantify the degree of predictability, locally, at each point of the signal domain, and they provide information on the dynamics of the associated system. We show that multiresolution analysis carried out on the singularity exponents of a high-resolution turbulent phase (obtained by model or from data) allows a propagation along the scales of the gradients in low-resolution (obtained from the wavefront sensor), to a higher resolution. We compare our results with those obtained by linear approaches, which allows us to offer an innovative approach to wavefront phase reconstruction in Adaptive Optics.

Transições de fase termodinâmicas são usualmente estudadas por meio do ensemble canônico e estão associadas a sistemas macroscópicos. Entretanto, tem-se tornado cada vez mais frequente e importante o estudo de sistemas físicos pequenos, cujos alcances característicos das interações equivalem aos tamanhos dos sistemas. Nestes casos pode haver inequivalência entre grandezas físicas obtidas nos ensembles canônico e microcanônico. Encontramos inúmeros exemplos destes sistemas em diversas áreas da Física. Na área de matéria condensada temos, por exemplo, o modelo Blume-Capel com interações de alcance infinito. Neste modelo as soluções exatas canônica e microcanônica são inequivalentes. Este modelo é investigado nesta tese por meio de um ensemble interpolante, conhecido como gaussiano estendido, como uma aplicação teórica preliminar. Adicionalmente, empregamos o arcabouço mecânico-estatístico no estudo de certas biomoléculas com ampla importância biológica: proteínas. Atualmente o estudo do comportamento termodinâmico destas moléculas tem ficado restrito quase que exclusivamente a abordagem via ensemble canônico. Neste trabalho analisamos os resultados da etapa microcanônica de simulações multicanônicas procurando obter aspectos físicos de biomoléculas como os domínios Src SH3 (pdb: 1NLO) e as Príons humanas (pdb: 1HJM). Caracterizamos com esta abordagem as transições de fase de enovelamento e de agregação destes sistemas. Os resultados obtidos são interpretados à luz da termoestatística microcanônica, oferecendo um ponto de vista fenomenológico alternativo à abordagem usual. / Thermodynamic phase transitions are usualy studied by the canonical ensemble and they are associated to macroscopic systems. However, it is becoming more frequent and important the study of small physical systems: whose characteristic interaction-lengths are equivalent to system sizes. In these cases there can happen inequivalences among quantities computed im the canonical and microcanonical ensembles. There are inumerous examples of that systems in various areas of physics. In the field of condensed matter there is for instance the Blume-Capel model with infinite-range interactions. The canonical and microcanonical exact solutions of this model are inequivalents. That model is investigated on this thesis through an interpolating ensemble, known as the extended gaussian, as a preliminar theoretical application. Additionally, we have employed the statistic-mechanical framework to study some biomolecules of large biological interest: proteins. Nowadays the study of the thermodynamic behavior of that molecules has been restricted almost only to the canonical approach. However, in this work we have analysed by the microcanonical step of multicanonical simulations the physical aspects of biomolecules as the domain Src SH3 (pdb: 1NLO) and the human Prions (pdb: 1HJM). Thus, we characterize with this approach the phase transitions of folding and aggregation of that systems. The results obtained are interpretated under the light of the microcanonical thermostatistics, offering an alternative phenomenological viewpoint.

Dans cette thèse nous introduisons une approche nouvelle pour la reconstruction d’un front d’ondes en Optique Adaptative (OA), à partir des données de gradients à basse résolution en provenance de l’analyseur de front d’ondes, et en utilisant une approche non-linéaire issue du Formalisme Multiéchelles Mi-crocanonique (FMM). Le FMM est issu de concepts établis en physique statistique, il est naturellement approprié à l’étude des propriétés multiéchelles des signaux naturels complexes, principalement grâce à l’estimation numérique précise des exposants critiques localisés géométriquement, appelés exposants de singularité. Ces exposants quantifient le degré de prédictabilité localement en chaque point du domaine du signal, et ils renseignent sur la dynamique du système associé. Nous montrons qu’une analyse multirésolution opérée sur les exposants de singularité d’une phase turbulente haute résolution (obtenus par modèle ou à partir des données) permet de propager, le long des échelles, les gradients en basse résolution issus de l’analyseur du front d’ondes jusqu’à une résolution plus élevée. Nous comparons nos résultats à ceux obtenus par les approches linéaires, ce qui nous permet de proposer une approche novatrice à la reconstruction de fronts d’onde en Optique Adaptative. / In this thesis, we introduce a new approach to wavefront phase reconstruction in Adaptive Optics (AO) from the low-resolution gradient measurements provided by a wavefront sensor, using a non-linear approach derived from the Microcanonical Multiscale Formalism (MMF). MMF comes from established concepts in statistical physics, it is naturally suited to the study of multiscale properties of complex natural signals, mainly due to the precise numerical estimate of geometrically localized critical exponents, called the singularity exponents. These exponents quantify the degree of predictability, locally, at each point of the signal domain, and they provide information on the dynamics of the associated system. We show that multiresolution analysis carried out on the singularity exponents of a high-resolution turbulent phase (obtained by model or from data) allows a propagation along the scales of the gradients in low-resolution (obtained from the wavefront sensor), to a higher resolution. We compare our results with those obtained by linear approaches, which allows us to offer an innovative approach to wavefront phase reconstruction in Adaptive Optics.