The power of thermodynamics in the calculation of complex chemical and metallurgical equilibria of importance to industry has, over the last 15 years, been considerably enhanced by the availability of computers. It has resulted in the storage of data in databanks, the use of physical but complex models to represent thermodynamic data, the vast effort spent in the generation of critically assessed data and the development of sophisticated software for their application in equilibrium calculations. This thesis is concerned with the generation and application of metallurgical thermodynamic data in which the computer plays a central and essential role. A very wide range of topics have been covered from the generation of data by experiment and critical assessment through to the application of these data in calculations of importance to industry. Particular emphasis is placed on the need for reliable models and expressions which can represent the molar Gibbs energy as a function of temperature and composition. In addition a new computer program is described and used for the automatic calculation of phase diagrams for binary systems. Measurements of the enthalpies of formation of alloys in the Fe-Ti system are reported. All data for this system have been critically assessed to provide a dataset consistent with the published phase diagram. Critically assessed data for a number of binary alloy systems have been combined in order to perform quantitative calculations in two types of steel system. Firstly data for the Cr-Fe-Ni-Si-Ti system have been used to provide information about the long term stability of alloys used in fast breeder nuclear reactors. Secondly very complex calculations involving nine elements have been made to predict the distribution of carbon and various impurities between competing phases in low alloy steels on the addition of Mischmetall. Finally a new model is developed to represent the thermodynamic data for sulphide liquids and is used in the critical assessment and calculation of data for the Cu-Fe-Ni-S system. The phase diagram and thermodynamic data calculated from the assessed data are in excellent agreement with those observed experimentally. The work reported in this thesis, whilst successful, has also indicated areas which will benefit from further study particularly the development of reliable data and models for pure elements, ordered solid phases and liquid phases for high affinity systems.

Primitive, mantle-derived magmas provide important clues about the formation and equilibration conditions of magmas at depth. In subduction zones, it is uncommon for primitive magmas to ascend through the shallow mantle and crust without undergoing chemical modification. Instead, magmas commonly differentiate through fractional crystallization, crustal assimilation, or magma mixing. Those rare primitive lavas that do erupt along a volcanic arc are useful for elucidating subduction-related processes within the mantle wedge (~30–80 km depth) and are the focus of this research. I used piston-cylinder apparatuses to investigate the high-pressure, high-temperature, H2O-undersaturated phase equilibria for several primitive compositions that have erupted at volcanic arcs. I aimed to reveal the permissible residual mantle mineralogy, as well as the P-T- H2O conditions over which the putative mantle melts last equilibrated before erupting. My work focuses on the Trans-Mexican Volcanic Belt (TMVB), where primitive compositions span a range of SiO2, total alkalies (K2O+Na2O), magmatic H2O, and incompatible trace element enrichments. Variations among these components are presumed to result from melting heterogeneous mantle that has been affected, to varying degrees, by a subduction component. Chapter III focuses on the phase equilibria of a Mexican basaltic andesite and an Aleutian basalt. Results show that hydrous basaltic andesite equilibrated with harzburgite in the shallow mantle, whereas the basalt equilibrated with lherzolite. The former appears more common in continental arcs and the latter in intraoceanic arcs. Chapter IV focuses on two alkaline lavas of varying K2O content from the TMVB that are transitional between potassic, hydrous minette and H2O-poor intraplate alkali basalt. Experimental phase relations and trace element modeling reveals that melting and/or mixing of peridotite and clinopyroxene-rich veins are likely involved in producing these transitional lava types. These experimental data are integrated with other petrologic and geophysical data to provide an along-arc perspective of mantle-melt equilibration in the TMVB. Primitive melts appear to commonly equilibrate with chemically heterogeneous mantle at depths above the "hot nose" of the mantle wedge. It is apparent that the shallow mantle wedge is a key component for understanding the geochemical complexities of subduction zone magmas. This dissertation includes previously published and unpublished co-authored material.

Protactinium (Pa) is an actinide with chemical properties that are unique among the actinide elements. While the properties of other actinides are to a large extent understood, much of the chemistry of Pa remains a mystery. This thesis aims to illuminate new understanding of Pa chemistry through behavioral analysis using analytical techniques including liquid-liquid extraction (LL); extraction chromatography (ExC); and spectroscopic studies. Applications of radioanalytical chemistry and Pa: Through the research presented in this dissertation, we have developed a new way to separate uranium (U), thorium (Th), and Pa from complex environmental samples. The approach has been demonstrated for U-series dating of materials by alpha spectrometry. The method can be applied to geochronology, as well as to nuclear-forensic analysis of uranium-containing materials. In studies presented here, samples from a Paleolithic lake (Lake Bonneville, Utah USA) were analyzed for the radioactivity concentration of 230Th, 231Pa, 234U, 235U, and 238U by isotope dilution alpha spectrometry. Radioactivities were used to estimate of the time period of formation of the deposit from which the samples were collected. Ages were determined from the isotopics ratios; i.e., 231Pa/235U (40 ka); and 230Th/238U (39.5 ka) we found to be concordant with radiocarbon-14 dates (37 ka) obtained by collaborators at Brigham Young University. These studies inspired the development of a novel ExC resin to facilitate preparation of highly pure tracer isotope (233Pa) from a neptunium-237 (237Np) source. The material used for this development comprised 1-octanol adsorbed to a semi-porous resin material. The new approach greatly improved the yield and purity of 233Pa used for these chronometric analyses Developing an understanding of the chemistry of Pa at trace concentrations: The new-improved analytical described above led to the hypothesis that analytical separations approaches could be used to develop a more detailed understanding of Pa chemistry. Toward this goal, experiments were conducted to understand how the extraction of Pa is impacted by solution acidity [H+], anion concentration [A-; Cl-, NO3-], and extractant concentration ([2,6-dimethyl-4-heptanol, DIBC]). A full-factorial experimental design was employed to create a model that would allow for predictions in Pa behavior, as well as describe the nature of the observations. This model generated a multivariate equation that relates the distribution coefficient ([Pa] organic phase/ [Pa] aqueous phase) to each of the parameters ([H+], [A-], and [DIBC]). Further studies expanded to other alcohols (ROH) used as extractants (1-octanol, (2,6)-dimthyl-4-heptanol, and 2-ethyl-hexanol); and the results were analyzed using the slope analysis and comparative extraction studies using the model and compared to other actinide elements (Th, U, Np, americium (Am)) by both LL and ExC systems. These experiments revealed unique chemical behavior of Pa with respect to the other actinides. For example, it was found that Pa was the only actinide element to be extracted into the organic phase under acidic conditions (HCl and HNO3). Slope analysis experiments elucidated the stoichiometric identity of Pa species, with respect to the anion and extractant. Future studies will aim to identify the oxygen stoichiometry and species by X-ray absorption techniques. Investigations of the organic phase: In the final sections of this thesis, experiments are presented that are intended to determine if aggregation plays a key role in the extraction of Pa in systems containing 1-octanol and 2-ethyl-hexanol. This work is done in the absence of metal ions to control the dynamics of the organic phase, and are analyzed by tensiometry and Karl Fisher titrations with small angle X-ray scattering and molecular dynamic simulations. A key novel finding of these studies in that ROH molecules arrange in nanoscale aggregates that decrease the interfacial tension between the phases and extract a significant amount of water into the aggregates stabilized by a network of H-bonding. These studies lead to the hypothesis for future studies that Pa extraction is likely facilitated by solvation into the organic phase via ROH aggregates. The sum of the findings and observations of this dissertation provide insight into the chemical nature of Pa: (1) Novel extraction methods to obtain radiochemically pure fractions show that Pa can be efficiently extracted and separated from complex matrices to aid in chronometric analysis for geochronology or nuclear forensics; (2) Statistical modeling to develop a better understanding of the main effects of solvent extraction parameters; (3) Equilibrium analysis to improve our understanding of chemistry of Pa and how it is unique to the actinides; (4) Aggregation analysis to demonstrate a solvent centric understanding of extraction studies, these results lead to future experiments to investigate how organic phase aggregation can influence solvent extraction selectivity.

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

En aquesta tesi es té en compte un model no lineal de creixement de població de cèl·lules que s'estructuren pel seu contingut de ciclina i cinases depenents de ciclina (CDK). Aquest model condueix a un sistema no lineal d'equacions en derivades parcials de primer ordre amb termes no locals. Per estudiar aquest sistema utilitzem la teoria de semigrups lineals positius i la formulació semilineal, que són eines molt poderoses per fer front a l'anàlisi d'aquest tipus de models, tant des del punt de vista del problema de valor inicial, com de l'existència i l'estabilitat d'estats estacionaris. El model que es considera a la tesi descriu la següent situació biològica: les cèl·lules s'estructuren en relació amb el contingut d'un determinat grup de proteïnes anomenades ciclines i CDK i es divideixen en dos tipus: proliferants i quiescents. Les cèl·lules proliferants creixen i es divideixen, donant a lloc al final del cicle cel·lular a noves cèl·lules, o bé van cap al compartiment de les quiescents, mentre que les cèl·lules quiescents no envelleixen ni es divideixen, ni canvien el seu contingut de ciclina, però o tornen cap al compartiment de proliferació o bé romanen en l’estat de repòs. D'altra banda, tant les cèl·lules proliferants com les quiescents poden experimentar l'apoptosi, la mort cel·lular programada. L'únic terme no lineal en el model és un terme de reclutament de cèl·lules quiescents cap a la fase de proliferació. En aquest treball demostrem l'existència global, unicitat i positivitat de les solucions del problema de valor inicial. Reescrivint el nostre sistema en una forma abstracta podem demostrar que un cert operador lineal és el generador infinitesimal d'un semigrup positiu fortament continu. D'altra banda s'utilitza la formulació semilineal estàndard per a l’equació no lineal abstracta i obtenim una única solució global positiva per a qualsevol condició inicial positiva a L1. També es prova l'existència i unicitat d'un estat estacionari no trivial del nostre sistema sota hipòtesis adequades. Com es fa sovint en situacions similars, el problema és relacionat amb provar l'existència (i unicitat) d'un vector propi positiu normalitzat. Això correspon als vectors propis del valor propi dominant d'un determinat operador lineal positiu parametritzat pel valor de la variable de feedback. L'existència tant del valor propi dominant i de (l’únic) vector propi positiu està donat per una versió del teorema de Perron- Frobenius en dimensió infinita. També s’inclouen simulacions numèriques basades en la integració al llarg de les línies característiques. Amb l'ajuda d'aquestes simulacions numèriques trobem inestabilitat de l'estat estacionari per a valors de paràmetres compatibles amb els que donen inestabilitat en el model de dimensió finita. També s'inclou la demostració de l'existència de solucions independents del contingut de ciclina per a una elecció molt particular dels valors dels paràmetres i funcions que defineixen el model. Finalment s'utilitza la formulació anomenada cumulativa (o en retard) de la dinàmica de poblacións estructurades. En particular s'ha considerat una versió diferent del model estudiat abans, on es suposa que el pas de proliferants a quiescents només pot ocórrer una sola vegada, enfocament oposat al primer model on aquestes transicions poden ocórrer infinites vegades. A més a més, també suposem que hi ha un valor particular x del contingut de ciclina que separa les cèl·lules que encara no es poden dividir de les altres que sí que poden dividir-se. L'equació del model resulta ser una equació amb retard que relaciona els valors actuals d'aquestes variables amb la seva història (el seu valor en el passat). Fent servir aquest enfocament, es pot provar l'existència i unicitat de solucions del problema de valor inicial, i el principi d'estabilitat lineal a través d'una formulació semilineal en el marc dels semigrups duals. / In this thesis we consider a nonlinear cell population model where cells are structured with respect to the content of cyclin and cyclin dependent kinases (CDK). This model leads to a first order nonlinear partial differential equations system with non local terms. To study this system we use the theory of positive linear semigroups and the semilinear formulation, which are very powerful tools to deal with the analysis of this kind of models, both from the point of view of the initial value problem as well as the existence and stability of steady states. The model considered in the thesis describes the following biological situation: cells are structured with respect to the content of a certain group of proteins called cyclin and CDK and are distributed into two types: proliferating and quiescent cells. The proliferating cells grow and divide, giving birth at the end of the cell cycle to new cells, or else transit to the quiescent compartment, whereas quiescent cells do not age nor divide nor change their cyclin content but either transit back to the proliferating compartment or else stay in the quiescent compartment. Moreover, both proliferating and quiescent cells may experiment apoptosis, i.e. programmed cell death. The only nonlinear term is a recruitment term of quiescent cells going back to the proliferating phase. In this work we start proving global existence, uniqueness and positiveness of the solutions of the initial value problem. We rewrite our system in an abstract form and show that some linear operator is the infinitesimal generator of a positive strongly continuous semigroup. On the other hand we use the standard semilinear formulation for the nonlinear (abstract) equation and obtain a unique global positive solution for any positive initial condition in L1. We also prove the existence and uniqueness of a nontrivial steady state of our system under suitable hypotheses. As it is often done in similar situations, the problem is related to proving the existence (and uniqueness) of a positive normalized eigenvector. This eigenvector corresponds to the dominant eigenvalue of a certain positive linear operator parameterized by the value of the (one dimensional) feedback variable G. The existence of both dominant eigenvalue and (unique) positive eigenvector is given by a version of the infinite dimensional Perron-Frobenius theorem. We include numerical simulations based on the integration along characteristic lines. With the help of these numerical simulations we find instability of the steady state for parameter values compatible with the ones which give instability in the finite dimensional model. We also include a computation showing the existence of cyclin-independent solutions for a very particular choice of the parameter values and functions defining the model. Finally we use the so-called cumulative or delayed formulation of the structured population dynamics. In particular we have considered a different version of the model studied before, where one assumes that proliferating cells can become quiescent only once opposed to the other approach where these transitions can occur infinitely many times and moreover, we also assume that there is a particular value x of the cyclin content that separates cells which still cannot divide from the others which are able to divide. The model equation turns out to be a delay equation relating the current values of these variables with their history (their value in the past). Using this approach, one can prove existence and uniqueness of solutions of the initial value problem, and the linear stability principle by means of a semi-linear formulation in the framework of dual semigroups.

The study of infinitely long cylinders of constant cross-section floating in an infinite fluid bath in zero-gravity environments has primarily been focused on bodies whose cross-sections are strictly convex and sufficiently smooth. In this thesis, our efforts are concentrated on the consideration of bodies that are only convex and piecewise smooth. These types of bodies are seldom considered in current literature. We have worked with a series expansion of the energy function in order to determine when configurations of a given body will be in equilibrium, stable or otherwise. We have proven that any convex body with a straight side cannot float in a stable equilibrium with the fluid interface intersecting the interior of the straight side in a single point. This fact is then used to prove necessary and sufficient conditions for stable equilibrium of polygons, bodies whose cross-sections are comprised of only straight sides. We illustrate these conditions with several examples. In the latter portion of the thesis, we turn our attention to bodies in three dimensions. While past research has again been focused on strictly convex bodies, we began to consider bodies that do not meet these requirements by examining bodies of revolution. A condition for stability with respect to vertical variations of bodies of revolution is derived. We conclude with several examples of bodies of revolution, some of which interestingly relate back to an analogous two-dimensional shape.

The dynamics of a single underwater vehicle in an ideal irrotational fluid may be modeled by a Lagrangian system with configuration space the Euclidean group. If hydrodynamic coupling is ignored then two coupled vehicles may be modeled by the direct product of two single-vehicle systems. We consider this system in the case that the vehicles are coupled mechanically, with an ideal spherically symmetric joint, finding all of the relative equilibria. We demonstrate that there are relative equilibria in certain novel momentum-generator regimes identified by Patrick et.al. "<i>Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods</i>", Arch. Rational Mech. Anal., 174:301--344, 2004.

Solvent selection is an important factor in chemical process efficiency, profitability, and environmental impact. Prediction of solvent phase behavior will allow for the identification of novel solvent systems that could offer some economic or environmental advantage. A modified cohesive energy density model is used to predict the solid-liquid-equilibria for multifunctional solids in pure and mixed solvents for rapid identification of process solvents for design of crystallization processes. Some solubility data at several temperatures are also measured to further test the general applicability of the model. Gas-expanded liquids have potential environmentally advantageous applications as pressure tunable solvents for homogeneous and heterogeneous catalytic reactions and as novel solvent media for anti-solvent crystallizations. The phase behavior of some carbon dioxide/organic binary systems is measured to provide basic process design information. Solvent selection is also an important factor in the anti-solvent precipitation of solid compounds. The influence of organic solvent on the solid-liquid equilibria for two solid pharmaceutical compounds in several carbon dioxide expanded solvents is explored. A novel solvent system is also developed that allows for homogeneous catalytic reaction and subsequent catalyst sequestration by using carbon dioxide as a miscibility switch. The fundamental biphasic solution behavior of some polar organics with water and carbon dioxide are investigated.

Comments and Discussion : Toshiki Tamai

Peer-to-peer (p2p) approaches are an increasingly effective way to deploy services. Popular examples include BitTorrent, Skype, and KaZaA. These approaches are attractive because they can be highly fault-tolerant, scalable, adaptive, and less expensive than a more centralized solution. Cooperation lies at the heart of these strengths. Yet, in settings where working together is crucial, a natural question is: "What if users stop cooperating?" After all, cooperative services are typically deployed over multiple administrative domains, and thus vulnerable to Byzantine failures and users who may act selfishly. This dissertation explores how to construct p2p systems to tolerate Byzantine participants while also incentivizing selfish participants to contribute resources. We describe how to balance obedience against choice in building a robust p2p live streaming system. Imposing obedience is desirable as it leaves little room for peers to attack or cheat the system. However, providing choice is also attractive as it allows us to engineer flexible and efficient solutions. We first focus on obedience by using Nash equilibria to drive the design of BAR Gossip, the first gossip protocol that is resilient to Byzantine and selfish nodes. BAR Gossip relies on verifiable pseudo-random partner selection to eliminate non-determinism, which can be used to game the system, while maintaining the robustness and rapid convergence of traditional gossip. A novel fair enough exchange primitive entices cooperation among selfish peers on short timescales, thereby avoiding the need for distributed reputation schemes. We next focus on tempering obedience with choice by using approximate equilibria to guide the construction of a novel p2p live streaming system. These equilibria allow us to design incentives to limit selfish behavior rigorously, yet provide sufficient flexibility to build practical systems. We show the advantages of using an [element of]-Nash equilibrium, instead of an exact Nash, to design and implement FlightPath, our live streaming system that uses bandwidth efficiently, absorbs flash crowds, adapts to sudden peer departures, handles churn, and tolerates malicious activity. / text