The storage and dissipation of magnetic energy in the quiet sun corona determined from SDO/HMI magnetograms

In recent years, higher cadence, higher resolution observations have revealed the quiet-Sun photosphere to be complex and rapidly evolving. Since magnetic fields anchored in the photosphere extend up into the solar corona, it is expected that the small-scale coronal magnetic field exhibits similar complexity. For the first time, the quiet-Sun coronal magnetic field is continuously evolved through a series of non-potential, quasi-static equilibria, deduced from magnetograms observed by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory, where the photospheric boundary condition which drives the coronal evolution exactly reproduces the observed magnetograms. The build-up, storage, and dissipation of magnetic energy within the simulations is studied. We find that the free magnetic energy built up and stored within the field is sufficient to explain small-scale, impulsive events such as nanoflares. On comparing with coronal images of the same region, the energy storage and dissipation visually reproduces many of the observed features. The results indicate that the complex small-scale magnetic evolution of a large number of magnetic features is a key element in explaining the nature of the solar corona.

Multiscale morphology design of hybrid halide perovskites through a polymeric template

Hybrid halide perovskites have emerged as promising active constituents of next generation solution processable optoelectronic devices. During their assembling process, perovskite components undergo very complex dynamic equilibria starting in solution and progressing throughout film formation. Finding a methodology to control and affect these equilibria, responsible for the unique morphological diversity observed in perovskite films, constitutes a fundamental step towards a reproducible material processability. Here we propose the exploitation of polymer matrices as cooperative assembling components of novel perovskite CH3NH3PbI3 : polymer composites, in which the control of the chemical interactions in solution allows a predictable tuning of the final film morphology. We reveal that the nature of the interactions between perovskite precursors and polymer functional groups, probed by Nuclear Magnetic Resonance (NMR) spectroscopy and Dynamic Light Scattering (DLS) techniques, allows the control of aggregates in solution whose characteristics are strictly maintained in the solid film, and permits the formation of nanostructures that are inaccessible to conventional perovskite depositions. These results demonstrate how the fundamental chemistry of perovskite precursors in solution has a paramount influence on controlling and monitoring the final morphology of CH3NH3PbI3 (MAPbI3) thin films, foreseeing the possibility of designing perovskite : polymer composites targeting diverse optoelectronic applications.

Liquid film dynamics in horizontal and tilted tubes: dry spots and sliding drops

Using a model derived from lubrication theory, we consider the evolution of a thin viscous film coating the interior or exterior of a cylindrical tube. The flow is driven by surface tension and gravity and the liquid is assumed to wet the cylinder perfectly. When the tube is horizontal, we use large-time simulations to describe the bifurcation structure of the capillary equilibria appearing at low Bond number. We identify a new film configuration in which an isolated dry patch appears at the top of the tube and demonstrate hysteresis in the transition between rivulets and annular collars as the tube length is varied. For a tube tilted to the vertical, we show how a long initially uniform rivulet can break up first into isolated drops and then annular collars, which subsequently merge. We also show that the speed at which a localized drop moves down the base of a tilted tube is non-monotonic in tilt angle.

Leader Based Cyclic Pursuit

In this work a system of autonomous agents engaged in cyclic pursuit (under constant bearing (CB) strategy) is considered, for which one informed agent (the leader) also senses and responds to a stationary beacon. Building on the framework proposed in a previous work on beacon-referenced cyclic pursuit, necessary and suffi- cient conditions for the existence of circling equilibria in a system with one informed agent are derived, with discussion of stability and performance. In a physical testbed, the leader (robot) is equipped with a sound sensing apparatus composed of a real time embedded system, estimating direction of arrival of sound by an Interaural Level and Phase Difference Algorithm, using empirically determined phase and level signatures, and breaking front-back ambiguity with appropriate sensor placement. Furthermore a simple framework for implementing and evaluating the performance of control laws with the Robot Operating System (ROS) is proposed, demonstrated, and discussed.

Cassini states for black hole binaries

Cassini states correspond to the equilibria of the spin axis of a body when its orbit is perturbed. They were initially described for planetary satellites, but the spin axes of black hole binaries also present this kind of equilibria. In previous works, Cassini states were reported as spin-orbit resonances, but actually the spin of black hole binaries is in circulation and there is no resonant motion. Here we provide a general description of the spin dynamics of black hole binary systems based on a Hamiltonian formalism. In absence of dissipation, the problem is integrable and it is easy to identify all possible trajectories for the spin for a given value of the total angular momentum. As the system collapses due to radiation reaction, the Cassini states are shifted to different positions, which modifies the dynamics around them. This is why the final spin distribution may differ from the initial one. Our method provides a simple way of predicting the distribution of the spin of black hole binaries at the end of the inspiral phase.

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.

Fluorinated surfactants in solution: Diffusion coefficients of fluorinated alcohols in water

Intra-diffusion coefficients of three fluorinated alcohols, 2,2,3,3,3-pentafluoropropan-1-ol (PFP), 2,2,3,3,4,4,4-heptafluorobutan-1-ol (HFB) and 2,2,3,3,4,4,5,5,5-nonafluoropentan-1-ol (NFP) in water have been measured by the PFG–NMR spin-echo technique as a function of temperature and composition, focusing on the alcohol dilute region. For comparison, intra-diffusion coefficients of 2,2,2- trifluoroethanol (TFE) and HFB have also been measured in heavy water using the same method and conditions. As far as we know, these are the first experimental measurements of this property for these binary systems. Intra-diffusion coefficients for NFP in water and for TFE and HFB in heavy water have also been obtained by molecular dynamics simulation, complementing those for TFE, PFP and HFB reported in a previous work. The agreement between experimental and simulated results for PFP, HFB and NFP in water is reasonable, although presenting higher deviations than for the TFE/water system. From the dependence of the intra-diffusion coefficients on temperature, diffusion activation energies were estimated for all the solutes in water and heavy water.

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Strategic interactions of urban land developers in the housing market

This thesis studies the supply side of the housing market taking into account the strategic interactions that occur between urban land developers. The thesis starts by reviewing the literature on new housing supply, concluding that there are very few studies where strategic interactions are taken into account. Next, we develop a model with two urban land developers, who rst decide the quality of housing and then compete in prices, considering that the marginal production costs depend on the housing quality. First, we analyze the price competition game and characterize the Nash equilibrium of the price game. Finally, we examine the rst stage of the game and determine numerically the subgame perfect Nash equilibrium (SPNE) of the quality-price game. In the price competition game, our results show that the equilibrium price of an urban land developer is an increasing function of its own quality, while it is a non-monotonic function of the rival s quality. The behavior of the equilibrium pro ts reveals that, in general, urban land developers gain by di¤erentiating their quality. However, the urban land developer located at the Central Business District (CBD), may prefer to have the same quality than the rival when transportation costs are high by exploiting its locational advantage. The analysis of the rst stage of the game also reveals that, in general, the rms best response is to di¤erentiate their quality and that, in most cases, there are two subgame perfect Nash equilibria that involve quality di¤erentiation. However, the results depend on transportation costs and the quality valuation parameter. For small quality valuations, in equilibrium, the market is not fully covered and, if the unit transportation costs are high, only the urban land developers located at the CBD operates. For higher quality valuations, all the consumers are served. Furthermore, the equilibrium qualities and pro ts are increasing with quality valuation parameter. RESUMO: Esta tese estuda a oferta no mercado da habitação, tendo em conta as interações es- tratégicas que ocorrem entre os produtores de habitação. A tese revê a literatura sobre a oferta de habitação, concluindo que existem poucos estudos que tenham tido em conta as interações estratégicas. De seguida, desenvolvemos um modelo com dois produtores de habitação, que primeiro decidem a qualidade da habitação e depois competem em preços, considerando que os custos marginais de produção dependem da qualidade. Primeiro analisamos o jogo em preços e caracterizamos o equilíbrio de Nash. Posteriormente, ex- aminamos o primeiro estágio do jogo e determinamos numericamente o equilíbrio perfeito em todos os subjogos (SPNE) do jogo. No jogo de competição em preços, os resultados mostram que, o preço de equilíbrio, é uma função crescente da qualidade da habitação, sendo uma função não monótona da qualidade do rival. O lucro de equilíbrio revela que, geralmente, os produtores de habitação têm ganhos em diferenciar a qualidade. No entanto, o produtor localizado no Centro (CBD), pode preferir oferecer a mesma qualidade que o rival, caso os custos unitários de transporte sejam elevados, através da sua vantagem de localização. A análise do primeiro estágio do jogo, revela que, geralmente, a melhor resposta de um produtor é a de diferenciar a qualidade. Na maior parte dos casos existem dois SPNE que envolvem essa diferenciação. No entanto, os resultados dependem dos custos unitários de transporte e da valorização da qualidade por parte do consumidor. Para uma reduzida valorização da qualidade, em equilíbrio, o mercado não é totalmente coberto e, se o custo unitário de transporte é elevado, apenas o produtor localizado no CBD opera no mercado. Para uma valorização elevada da qualidade, todos os consumidores são servidos. Além disso, as qualidades e os lucros de equilíbrio são crescentes com a valorização da qualidade.

Assessing the activity coefficients of water in cholinium-based ionic liquids: experimental measurements and COSMO-RS modeling

The vapor liquid-equilibrium of water + ionic liquids is relevant for a wide range of applications of these compounds. It is usually measured by ebulliometric techniques, but these are time consuming and expensive. In this work it is shown that the activity coefficients of water in a series of cholinium-based ionic liquids can be reliably and quickly estimated at 298.15K using a humidity meter instrument. The cholinium based ionic liquids were chosen to test this experimental methodology since data for water activities of quaternary ammonium salts are available in the literature allowing the validation of the proposed technique. The COSMO-RS method provides a reliable description of the data and was also used to understand the molecular interactions occurring on these binary systems. The estimated excess enthalpies indicate that hydrogen bonding between water and ionic liquid anion is the dominant interaction that governs the behavior of water and cholinium-based ionic liquids systems, while the electrostatic-misfit and van der Walls forces have a minor contribution to the total excess enthalpies.

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.

Analysis of the isomerism effect on the mutual solubilities of bis(trifluoromethylsulfonyl)imide-based ionic liquids with water

The knowledge of the liquid-liquid equilibria (LLE) between ionic liquids (ILs) and water is of utmost importance for environmental monitoring, process design and optimization. Therefore, in this work, the mutual solubilities with water, for the ILs combining the 1-methylimidazolium, [C(1)im](+); 1-ethylimidazolium, [C(2)im](+); 1-ethyl-3-propylimidazolium, [C(2)C(3)im](+); and 1-butyl-2,3-dimethylimidazolium, [C(4)C(1)C(1)im](+) cations with the bis(trifluoromethylsulfonyl)imide anion, were determined and compared with the isomers of the symmetric 1,3-dialkylimidazolium bis(trifluoromethylsulfonyl)imide ([C(n)C(n)im][NTf2], with n=1-3) and of the asymmetric 1-alkyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([C(n)C(1)im][NTf2], with n = 2-5) series of ILs. The results obtained provide a broad picture of the impact of the IL cation structural isomerism, including the number of alkyl side chains at the cation, on the water-IL mutual solubilities. Despite the hydrophobic behaviour associated to the [NTf2](-) anion, the results show a significant solubility of water in the IL-rich phase, while the solubility of ILs in the water-rich phase is much lower. The thermodynamic properties of solution indicate that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Using the results obtained here in addition to literature data, a correlation between the solubility of [NTf2]-based ILs in water and their molar volume, for a large range of cations, is proposed. The COnductor like Screening MOdel for Real Solvents (COSMO-RS) was also used to estimate the LLE of the investigated systems and proved to be a useful predictive tool for the a priori screening of ILs aiming at finding suitable candidates before extensive experimental measurements.

Computational and experimental study of the behavior of cyano-based ionic liquids in aqueous solution

The solvation of cyano- (CN-) based ionic liquids (ILs) and their capacity to establish hydrogen bonds (H-bonds) with water was studied by means of experimental and computational approaches. Experimentally, water activity data were measured for aqueous solutions of ILs based on 1-butyl-3-methylimidazolium ([BMIM](+)) cation combined with one of the following anions: thiocyanate ([SCN](-)), dicyanamide ([DCA](-)), or tricyanomethanide ([TCM](-)), and of 1-ethyl-3-methylimidazolium tetracyanoborate ([EMIM][TCB]). From the latter data, water activity coefficients were estimated showing that [BMIM][SCN] and [BMIM][DCA], unlike [BMIM][TCM] and [EMIM][TCB], are able to establish favorable interactions with water. Computationally, the conductor like screening model for real solvents (COSMO-RS) was used to estimate the water activity coefficients which compare well with the experimental ones. From the COSMO-RS results, it is suggested that the polarity of each ion composing the ILs has a strong effect on the solvation phenomena. Furthermore, classical molecular dynamics (MD) simulations were performed for obtaining an atomic level picture of the local molecular neighborhood of the different species. From the experimental and computational data it is showed that increasing the number of CN groups in the ILs' anions does not enhance their ability to establish H-bonds with water but decreases their polarities, being [BMIM][DCA] and [BMIM][SCN] the ones presenting higher propensity to interact.

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.

Densities, viscosities and derived thermophysical properties of water-saturated imidazolium-based ionic liquids

In order to evaluate the impact of the alkyl side chain length and symmetry of the cation on the thermophysical properties of water-saturated ionic liquids (ILs), densities and viscosities as a function of temperature were measured at atmospheric pressure and in the (298.15 to 363.15) K temperature range, for systems containing two series of bis(trifluoromethylsulfonyl)imide-based compounds: the symmetric [C n C n im][NTf2] (with n = 1-8 and 10) and asymmetric [C n C1im][NTf2] (with n = 2-5, 7, 9 and 11) ILs. For water-saturated ILs, the density decreases with the increase of the alkyl side chain length while the viscosity increases with the size of the aliphatic tails. The saturation water solubility in each IL was further estimated with a reasonable agreement based on the densities of water-saturated ILs, further confirming that for the ILs investigated the volumetric mixing properties of ILs and water follow a near ideal behaviour. The water-saturated symmetric ILs generally present lower densities and viscosities than their asymmetric counterparts. From the experimental data, the isobaric thermal expansion coefficient and energy barrier were also estimated. A close correlation between the difference in the energy barrier values between the water-saturated and pure ILs and the water content in each IL was found, supporting that the decrease in the viscosity of ILs in presence of water is directly related with the decrease of the energy barrier.