Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Purificação, modelagem e simulação da adsorção de bioprodutos por troca iônica em coluna de leito expandido

A produção de proteínas através de microrganismos tornou-se uma técnica muito importante na obtenção de compostos de interesse da indústria farmacêutica e alimentícia. Extratos brutos nos quais as proteínas são obtidas são geralmente complexos, contendo sólidos e células em suspensão. Usualmente, para uso industrial destes compostos, é necessário obtê-los puros, para garantir a sua atuação sem interferência. Um método que vem recebendo destaque especialmente nos últimos 10 anos é o uso da cromatografia de troca iônica em leito expandido, que combina em uma única etapa os passos de clarificação, concentração e purificação da molécula alvo, reduzindo assim o tempo de operação e também os custos com equipamentos para realização de cada etapa em separado. Combinado a este fato, a última década também é marcada por trabalhos que tratam da modelagem matemática do processo de adsorção de proteínas em resinas. Está técnica, além de fornecer informações importantes sobre o processo de adsorção, também é de grande valia na otimização da etapa de adsorção, uma vez que permite que simulações sejam feitas, sem a necessidade de gasto de tempo e material com experimentos em bancada, especialmente se é desejado uma ampliação de escala. Dessa forma, o objetivo desta tese foi realizar a modelagem e simulação do processo de adsorção de bioprodutos em um caldo bruto na presença de células, usando inulinase e C-ficocianina como objeto de estudo e purificar C-ficocianina utilizando resina de troca iônica em leito expandido. A presente tese foi então dividida em quatro artigos. O primeiro artigo teve como objeto de estudo a enzima inulinase, e a otimização da etapa de adsorção desta enzima em resina de troca iônica Streamline SP, em leito expandido, foi feita através da modelagem matemática e simulação das curvas de ruptura em três diferentes graus de expansão (GE). As máximas eficiências foram observadas quando utilizadas maiores concentrações de inulinase (120 a 170 U/mL), e altura de leito entre 20 e 30 cm. O grau de expansão de 3,0 vezes foi considerado o melhor, uma vez que a produtividade foi consideravelmente superior. O segundo artigo apresenta o estudo das condições de adsorção de C-ficocianina em resina de troca iônica, onde foi verificado o efeito do pH e temperatura na adsorção e após construída a isoterma de adsorção. A isoterma de adsorção da C-ficocianina em resina Streamline Q XL feita em pH 7,5 e a 25°C (ambiente), apresentou um bom ajuste ao modelo de Langmuir (R=0,98) e os valores qm (capacidade máxima de adsorção) e Kd (constante de equilíbrio) estimados pela equação linearizada da isoterma, foram de 26,7 mg/mL e 0,067mg/mL. O terceiro artigo aborda a modelagem do processo de adsorção de extrato não clarificado de C-ficocianina em resina de troca iônica Streamline Q XL em coluna de leito expandido. Três curvas de ruptura foram feitas em diferentes graus de expansão (2,0, 2,5 e 3,0). A condição de adsorção de extrato bruto não clarificado de C-ficocianina que se mostrou mais vantajosa, por apresentar maior capacidade de adsorção, é quando se alimenta o extrato até atingir 10% de saturação da resina, em grau de expansão 2,0, com uma altura inicial de leito de 30 cm. O último artigo originado nesta tese foi sobre a purificação de C-ficocianina através da cromatografia de troca iônica em leito expandido. Uma vez que a adsorção já havia sido estudada no artigo 2, o artigo 4 enfoca na otimização das condições de eluição, visando obter um produto com máxima pureza e recuperação. A pureza é dada pela razão entre a absorbância a 620 nm pela absorbância a 280 nm, e dizse que quando C-ficocianina apresenta pureza superior a 0,7 ela pode ser usada em como corante em alimentos. A avaliação das curvas de contorno indicou que a faixa de trabalho deve ser em pH ao redor de 6,5 e volumes de eluição próximos a 150 mL. Tais condições combinadas a uma etapa de pré-eluição com 0,1M de NaCl, permitiu obter C-ficocianina com pureza de 2,9, concentração 3 mg/mL, e recuperação ao redor de 70%.

Secagem convectiva da microalga spirulina platensis: avaliação das propriedades físicas e bioquímicas

O objetivo no presente estudo foi investigar a operação de secagem da microalga Spirulina platensis em camada delgada através da modelagem matemática e otimização da operação, avaliando as características do produto final através de análises físico-químicas. Foram analisados os dados da umidade de equilíbrio para a isoterma de adsorção a 10, 20 e 30°C e de dessorção a 40, 50 e 60°C, através dos modelos de GAB e BET. O calor isostérico foi determinado pela aplicação da equação de Clausius-Clapeyron. O modelo de GAB apresentou melhor ajuste aos dados experimentais. Os valores da área superficial calculados pelos modelos de GAB e BET foram próximos. O calor isostérico e a entropia diferencial da isoterma de dessorção apresentaram comportamento similar. A teoria da compensação entalpia-entropia foi aplicada nas isotermas, indicando que são controladas pela entalpia. A cinética de secagem foi analisada na faixa de temperatura de 50-70°C, através dos modelos de Lewis, Henderson e Pabis, Henderson, Page e Overhults. O modelo de Henderson e Pabis foi escolhido por apresentar maior significado físico para estimar o valor de difusividade efetiva (Def), sendo os valores encontrados na faixa de 5,54 - 6,60×10-11 m 2 /s, para as temperaturas de 50 e 60°C, respectivamente, e de 1,58×10-10 m2 /s para a temperatura de 70°C. A energia de ativação apresentou um valor de 47,9 kJ/mol. A secagem alterou a cor quando comparada ao material in natura. A secagem foi otimizada na faixa de espessuras e temperaturas do ar de secagem de 3-7 mm e de 50-70ºC, respectivamente, através da metodologia de superfície de resposta para ácido tiobarbitúrico (TBA) e perda de ficocianina no produto final. A melhor condição de secagem foi a 55°C e a 3,7 mm, apresentando uma perda de ficocianina de aproximadamente 37% e valor de TBA de 1,5 mgMDA/kgamostra. Nesta condição de secagem, a composição de ácidos graxos da microalga Spirulina não apresentou diferença significativa (P > 0,05) em relação a microalga in natura.

Computational modelling of non-equilibrium condensing steam flows in low-pressure steam turbines

The steam turbines play a significant role in global power generation. Especially, research on low pressure (LP) steam turbine stages is of special importance for steam turbine man- ufactures, vendors, power plant owners and the scientific community due to their lower efficiency than the high pressure steam turbine stages. Because of condensation, the last stages of LP turbine experience irreversible thermodynamic losses, aerodynamic losses and erosion in turbine blades. Additionally, an LP steam turbine requires maintenance due to moisture generation, and therefore, it is also affecting on the turbine reliability. Therefore, the design of energy efficient LP steam turbines requires a comprehensive analysis of condensation phenomena and corresponding losses occurring in the steam tur- bine either by experiments or with numerical simulations. The aim of the present work is to apply computational fluid dynamics (CFD) to enhance the existing knowledge and understanding of condensing steam flows and loss mechanisms that occur due to the irre- versible heat and mass transfer during the condensation process in an LP steam turbine. Throughout this work, two commercial CFD codes were used to model non-equilibrium condensing steam flows. The Eulerian-Eulerian approach was utilised in which the mix- ture of vapour and liquid phases was solved by Reynolds-averaged Navier-Stokes equa- tions. The nucleation process was modelled with the classical nucleation theory, and two different droplet growth models were used to predict the droplet growth rate. The flow turbulence was solved by employing the standard k-ε and the shear stress transport k-ω turbulence models. Further, both models were modified and implemented in the CFD codes. The thermodynamic properties of vapour and liquid phases were evaluated with real gas models. In this thesis, various topics, namely the influence of real gas properties, turbulence mod- elling, unsteadiness and the blade trailing edge shape on wet-steam flows, are studied with different convergent-divergent nozzles, turbine stator cascade and 3D turbine stator-rotor stage. The simulated results of this study were evaluated and discussed together with the available experimental data in the literature. The grid independence study revealed that an adequate grid size is required to capture correct trends of condensation phenomena in LP turbine flows. The study shows that accurate real gas properties are important for the precise modelling of non-equilibrium condensing steam flows. The turbulence modelling revealed that the flow expansion and subsequently the rate of formation of liquid droplet nuclei and its growth process were affected by the turbulence modelling. The losses were rather sensitive to turbulence modelling as well. Based on the presented results, it could be observed that the correct computational prediction of wet-steam flows in the LP turbine requires the turbulence to be modelled accurately. The trailing edge shape of the LP turbine blades influenced the liquid droplet formulation, distribution and sizes, and loss generation. The study shows that the semicircular trailing edge shape predicted the smallest droplet sizes. The square trailing edge shape estimated greater losses. The analysis of steady and unsteady calculations of wet-steam flow exhibited that in unsteady simulations, the interaction of wakes in the rotor blade row affected the flow field. The flow unsteadiness influenced the nucleation and droplet growth processes due to the fluctuation in the Wilson point.

Banana peel: an effective biosorbent for aflatoxins

This work reports the application of banana peel as a novel bioadsorbent for in vitro removal of five mycotoxins (aflatoxins (AFB1, AFB2, AFG1, AFG2) and ochratoxin A). The effect of operational parameters including initial pH, adsorbent dose, contact time and temperature were studied in batch adsorption experiments. Scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR) and point of zero charge (pHpzc) analysis were used to characterise the adsorbent material. Aflatoxins’ adsorption equilibrium was achieved in 15 min, with highest adsorption at alkaline pH (6–8), while ochratoxin has not shown any significant adsorption due to surface charge repulsion. The experimental equilibrium data were tested by Langmuir, Freundlich and Hill isotherms. The Langmuir isotherm was found to be the best fitted model for aflatoxins, and the maximum monolayer coverage (Q0) was determined to be 8.4, 9.5, 0.4 and 1.1 ng mg−1 for AFB1, AFB2, AFG1 and AFG2 respectively. Thermodynamic parameters including changes in free energy (ΔG), enthalpy (ΔH) and entropy (ΔS) were determined for the four aflatoxins. Free energy change and enthalpy change demonstrated that the adsorption process was exothermic and spontaneous. Adsorption and desorption study at different pH further demonstrated that the sorption of toxins was strong enough to sustain pH changes that would be experienced in the gastrointestinal tract. This study suggests that biosorption of aflatoxins by dried banana peel may be an effective low-cost decontamination method for incorporation in animal feed diets. © 2016 Informa UK Limited, trading as Taylor & Francis Group.

Adsorção de corantes têxteis aniônicos e catiônicos em resíduos do processamento de fios de algodão modificados quimicamente

The textile industry generates a large volume of high organic effluent loading whoseintense color arises from residual dyes. Due to the environmental implications caused by this category of contaminant there is a permanent search for methods to remove these compounds from industrial waste waters. The adsorption alternative is one of the most efficient ways for such a purpose of sequestering/remediation and the use of inexpensive materials such as agricultural residues (e.g., sugarcane bagasse) and cotton dust waste (CDW) from weaving in their natural or chemically modified forms. The inclusion of quaternary amino groups (DEAE+) and methylcarboxylic (CM-) in the CDW cellulosic structure generates an ion exchange capacity in these formerly inert matrix and, consequently, consolidates its ability for electrovalent adsorption of residual textile dyes. The obtained ionic matrices were evaluated for pHpcz, the retention efficiency for various textile dyes in different experimental conditions, such as initial concentration , temperature, contact time in order to determine the kinetic and thermodynamic parameters of adsorption in batch, turning comprehensive how does occur the process, then understood from the respective isotherms. It was observed a change in the pHpcz for CM--CDW (6.07) and DEAE+-CDW (9.66) as compared to the native CDW (6.46), confirming changes in the total surface charge. The ionized matrices were effective for removing all evaluated pure or residual textile dyes under various tested experimental conditions. The kinetics of the adsorption process data had best fitted to the model a pseudosecond order and an intraparticle diffusion model suggested that the process takes place in more than one step. The time required for the system to reach equilibrium varied according to the initial concentration of dye, being faster in diluted solutions. The isotherm model of Langmuir was the best fit to the experimental data. The maximum adsorption capacity varied differently for each tested dye and it is closely related to the interaction adsorbent/adsorbate and dye chemical structure. Few dyes obtained a linear variation of the balance ka constant due to the inversion of temperature and might have influence form their thermodynamic behavior. Dyes that could be evaluated such as BR 18: 1 and AzL, showed features of an endothermic adsorption process (ΔH° positive) and the dye VmL presented exothermic process characteristics (ΔH° negative). ΔG° values suggested that adsorption occurred spontaneously, except for the BY 28 dye, and the values of ΔH° indicated that adsorption occurred by a chemisorption process. The reduction of 31 to 51% in the biodegradability of the matrix after the dye adsorption means that they must go through a cleaning process before being discarded or recycled, and the regeneration test indicates that matrices can be reused up to five times without loss of performance. The DEAE+-CDW matrix was efficient for the removal of color from a real textile effluent reaching an UV-Visible spectral area decrease of 93% when applied in a proportion of 15 g ion exchanger matrix L-1 of colored wastewater, even in the case of the parallel presence of 50 g L-1 of mordant salts in the waste water. The wide range of colored matter removal by the synthesized matrices varied from 40.27 to 98.65 mg g-1 of ionized matrix, obviously depending in each particular chemical structure of the dye upon adsorption.

Other-Regarding Preferences in General Equilibrium

We study competitive market outcomes in economies where agents have other-regarding preferences. We identify a separability condition on monotone preferences that is necessary and sufficient for one’s own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify other-regarding preferences from market behavior: agents be- have as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Sec- ond Welfare Theorem holds as long as an increase in resources can be distributed such that all agents are better off. Nevertheless, the First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consump- tion possibilities in the economy, we provide a condition under which agents have no incentive to make direct transfers, and show that this condition implies that competitive equilibria are efficient given prices.

Rare sex or out of reach equilibrium? The dynamics of F-IS in partially clonal organisms

Background: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient (F-IS) over bar < 0. Yet in partially clonal species, both F-IS < 0 and F-IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F-IS over time under increasing rates of clonality. Results: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F-IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F-IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F-IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean (F-IS,F-infinity) over bar value expected at equilibrium. Conclusion: Our results argue for a dynamical interpretation of F-IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean (F-IS) over bar values deviating from zero and/or a large variation of F-IS over loci are observed.

Equilibrium Sorption Studies of Hg (II) Ions from Aqueous Solution using Powdered Swamp Arum ( Lasimorpha senegalensis ) Seeds.

The potential of swamp arum ( Lasimorpha senegalensis ) seeds as a low-cost adsorbent for the removal of Hg (II) ions from aqueous solution was investigated in this study. The influence of initial metal concentration on the percent adsorption of Hg (II) ions onto powdered swamp arum seeds was studied in a batch system and the filtrate was analyzed using Atomic Absorption Spectrometry (AAS). The percent adsorbed for 10, 20, 40, 60 and 80 mg/L of the aqueous solution were 97.7, 98.9, 99.3, 99.7, and 96.5% respectively. Three isotherms; Langmuir, Freundlich, and BET were used to model the equilibrium sorption of Hg (II) ions onto powdered swamp arum seeds, with a correlation coefficient of 0.998, 0.784 and0.842 respectively. The Langmuir model fitted the equilibrium data best, with a correlation coefficient of 0.998 and a maximum adsorption capacity qm, of 5.917 mg/g. Thus, indicating monolayer coverage on the adsorbent. The results showed that swamp arum seed have the potential to be applied as alternative lowcost biosorbent in the remediation of heavy metal contamination in waste water.

THE EFFECT of ANIONIC SORPTION on THE METAKAOLINITE

This paper reports an investigation on the effect of thermal activation of kaolinite. It is well known that during calcinations (400-650 degrees C), kaolinite loses the OH lattice water and is transformed into metakaolinite or amorphous material. Arsenic is trace element that is toxic to animals including humans. The adsorption of arsenic on kaolinite was investigated at varying pH and thermal pretreatment. Calcination of sample is carried out at 650 degrees C for 3 h. The decomposition of kaolinite is recorded using methods of thermal analysis. The resultant product is identified by XRD. Laboratory experiments were conducted examining the effect of arsenic by thermally modified kaolinite. The Langmuir isotherm was used to describe arsenite and arsenate sorption by the calcined kaolinite. The equilibrium parameters used were based on experimental data obtained for the dynamic adsorption process of arsenic. Removal of arsenate using natural kaolinite was satisfactory, whereas arsenic was not removed by adsorption with thermally modified kaolinite. Moreover, the adsorption of arsenic by kaolinite and metakaolinite decreases with increasing pH.

Vapor–liquid equilibrium of binary mixtures containing isopropyl acetate and alkanols at 101.32 kPa

Isobaric vapor-liquid equilibria of binary mixtures of isopropyl acetate plus an alkanol (1-propanol, 2-propanol, 1-butanol, or 2-butanol) were measured at 101.32 kPa, using a dynamic recirculating still. An azeotropic behavior was observed only in the mixtures of isopropyl acetate + 2-propanol and isopropyl acetate + 1-propanol. The application of four thermodynamic consistency tests (the Herington test, the Van Ness test, the infinite dilution test, and the pure component test) showed the high quality of the experimental data. Finally, both NRTL and UNIQUAC activity coefficient models were successfully applied in the correlation of the measured data, with the average absolute deviations in vapor phase composition and temperature of 0.01 and 0.16 K, respectively.

Methane seep carbonates yield clumped isotope signatures out of equilibrium with formation temperatures

Methane cold seep systems typically exhibit extensive buildups of authigenic carbonate minerals, resulting from local increases in alkalinity driven by methane oxidation. Here, we demonstrate that modern seep authigenic carbonates exhibit anomalously low clumped isotope values (Delta(47)), as much as similar to 0.2 parts per thousand lower than expected values. In modern seeps, this range of disequilibrium translates into apparent temperatures that are always warmer than ambient temperatures, by up to 50 degrees C. We examine various mechanisms that may induce disequilibrium behaviour in modern seep carbonates, and suggest that the observed values result from several factors including kinetic isotopic effects during methane oxidation, mixing of inorganic carbon pools, pH effects and rapid precipitation. Ancient seep carbonates studied here also exhibit potential disequilibrium signals. Ultimately, these findings indicate the predominance of disequilibrium clumped isotope behaviour in modern cold seep carbonates that must be considered when characterizing environmental conditions in both modern and ancient cold seep settings.

Equilibrium Assignments in Competitive and Cooperative Traffic Flow Routing

Part 18: Optimization in Collaborative Networks

Designing Efficient Subsidy Policies in a Regional Economy: A Multicriteria Decision-Making (MCDM)-Computable General Equilibrium (CGE) Approach

Since policy-makers usually pursue several conflicting objectives, policy-making can be understood as a multicriteria decision problem. Following the methodological proposal by André and Cardenete (2005) André, F. J. and Cardenete, M. A. 2005. Multicriteria Policy Making. Defining Efficient Policies in a General Equilibrium Model, Seville: Centro de Estudios Andaluces. Working Paper No. E2005/04, multi-objective programming is used in connection with a computable general equilibrium model to represent optimal policy-making and to obtain so-called efficient policies in an application to a regional economy (Andalusia, Spain). This approach is applied to the design of subsidy policies under two different scenarios. In the first scenario, it is assumed that the government is concerned just about two objectives: ensuring the profitability of a key strategic sector and increasing overall output. Finally, the scope of the exercise is enlarged by solving a problem with seven policy objectives, including both general and sectorial objectives. It is concluded that the observed policy could have been Pareto-improved in several directions.