Rozprawy doktorskie na temat „Equilibrium”

This thesis is concerned with the problem of incorporating consumer search in to equilibrium-in particular with the relationship between oligopoly models where consumers search and those which assume perfect information. Two chapters consider duality in search. The conventional way of expressing a consumer's search strategy is to describe his decision variable as a function of the search cost. The dual approach is to find the search cost that leaves the consumer just indifferent between two decisions. Since cost is continuous this search-cost function is differentiable in more parameters than its inverse and so more readily yields comparative static results. Using this function it is possible to express the demand facing firms as explicit functions of the distribution of consumers search costs. The belief is commonly expressed in the literature that adaptive search models add little insight compared to the analytically simpler

Thesis (Ph. D.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

The objective of this work has been to study equilibrium and non equilibrium situations during high pressure gas processing operations with emphasis on utilization of the high reservoir pressure. The well stream pressures of some of the condensate and gas fields in the North Sea are well above 200 bar. Currently the gas is expanded to a specified processing condition, typically 40-70 bar, before it is recompressed to the transportation conditions. It would be a considerable environmental and economic advantage to be able to process the natural gas at the well stream pressure. Knowledge of thermodynamic- and kinetic properties of natural gas systems at high pressures is needed to be able to design new high pressure process equipment.

Nowadays, reactive absorption into a methyldiethanolamine (MDEA)solution in a packed bed is a frequently used method to perform acid gas treating. The carbon dioxide removal process on the Sleipner field in the North Sea uses an aqueous MDEA solution and the operation pressure is about 100 bar. The planed carbon dioxide removal process for the Snøhvit field in the Barents Sea is the use of an activated MDEA solution.

The aim of this work has been to study high-pressure effects related to the removal of carbon dioxide from natural gas. Both modelling and experimental work on high-pressure non-equilibrium situations in gas processing operations have been done.

Few experimental measurements of mass transfer in high pressure fluid systems have been published. In this work a wetted wall column that can operate at pressures up to 200 bar was designed and constructed. The wetted wall column is a pipe made of stainless steel where the liquid is distributed as a thin liquid film on the inner pipewall while the gas flows co- or concurrent in the centre of the pipe. The experiments can be carried out with a well-defined interphase area and with relatively simple fluid mechanics. In this way we are able to isolate the effects we want to study in a simple and effective way.

Experiments where carbon dioxide was absorbed into water and MDEA solutions were performed at pressures up to 150 bar and at temperatures 25 and 40°C. Nitrogen was used as an inert gas in all experiments.

A general non-equilibrium simulation program (NeqSim) has been developed. The simulation program was implemented in the object-oriented programming language Java. Effort was taken to find an optimal object-oriented design. Despite the increasing popularity of object-oriented programming languages such as Java and C++, few publications have discussed how to implement thermodynamic and fluid mechanic models. A design for implementation of thermodynamic, mass transfer and fluid mechanic calculations in an object-oriented framework is presented in this work.

NeqSim is based on rigorous thermodynamic and fluid mechanic models. Parameter fitting routines are implemented in the simulation tool and thermodynamic-, mass transfer- and fluid mechanic models were fitted to public available experimental data. Two electrolyte equations of state were developed and implemented in the computer code. The electrolyte equations of state were used to model the thermodynamic properties of the fluid systems considered in this work (non-electrolyte, electrolyte and weak-electrolyte systems).

The first electrolyte equation of state (electrolyte ScRK-EOS) was based on a model previously developed by Furst and Renon (1993). The molecular part of the equation was based on a cubic equation of state (Scwarzentruber et.al. (1989)’s modification of the Redlich-Kwong EOS) with the Huron-Vidal mixing rule. Three ionic terms were added to this equation – a short-range ionic term, a long-range ionic term (MSA) and a Born term. The thermodynamic model has the advantage that it reduces to a standard cubic equation of state if no ions are present in the solution, and that public available interaction parameters used in the Huron-Vidal mixing rule could be utilized. The originality of this electrolyte equation of state is the use of the Huron-Vidal mixing rule and the addition of a Born term. Compared to electrolyte models based on equations for the gibbs excess energy, the electrolyte equation of state has the advantage that the extrapolation to higher pressures and solubility calculations of supercritical components is less cumbersome. The electrolyte equation of state was able to correlate and predict equilibrium properties of CO₂-MDEA-water solutions with a good precision. It was also able to correlate high pressure data of systems of methane-CO₂-MDEA and water.

The second thermodynamic model (electrolyte CPA-EOS) evaluated in this work is a model where the molecular interactions are modelled with the CPA (cubic plus association) equation of state (Kontogeorgios et.al., 1999) with a classical one-parameter Van der Walls mixing rule. This model has the advantage that few binary interaction parameters have to be used (even for non-ideal solutions), and that its extrapolation capability to higher pressures is expected to be good. In the CPA model the same ionic terms are used as in the electrolyte ScRK-EOS.

A general non-equilibrium two-fluid model was implemented in the simulation program developed in this work. The heat- and mass-transfer calculations were done using an advanced multicomponent mass transfer model based on non-equilibrium thermodynamics. The mass transfer model is flexible and able to simulate many types of non-equilibrium processes we find in the petroleum industry. A model for reactive mass transfer using enhancement factors was implemented for the calculation of mass transfer of CO₂ into amine solutions. The mass transfer model was fitted to the available mass transfer data found in the open literature.

The simulation program was used to analyse and perform parameter fitting to the high pressure experimental data obtained during this work. The mathematical models used in NeqSim were capable of representing the experimental data of this work with a good precision. From the experimental and modelling work done, we could conclude that the mass transfer model regressed to pure low-pressure data also was able to represent the high-pressure mass transfer data with an acceptable precision. Thus the extrapolation capability of the model to high pressures was good.

For a given partial pressure of CO₂ in the natural gas, calculations show a decreased CO₂ capturing capacity of aqueous MDEA solutions at increased natural gas system pressure. A reduction up to 40% (at 200 bar) compared to low pressure capacity is estimated. The pressure effects can be modelled correctly by using suitable thermodynamic models for the liquid and gas. In a practical situation, the partial pressure of CO₂ in the natural gas will be proportional to the total pressure. In these situations, it is shown that the CO₂ capturing capacity of the MDEA solution will be increased at rising total pressures up to 200 bar. However, the increased capacity is not as large as we would expect from the higher CO₂ partial pressure in the gas.

The reaction kinetics of CO₂ with MDEA is shown to be relatively unaffected by the total pressure when nitrogen is used as inert gas. It is however important that the effects of thermodynamic and kinetic non- ideality in the gas and liquid phase are modelled in a consistent way. Using the simulation program NeqSim – some selected high-pressure non-equilibrium processes (e.g. absorption, pipe flow) have been studied. It is demonstrated that the model is capable of simulating equilibrium- and non-equilibrium processes important to the process- and petroleum industry.

This thesis divides very naturally into three chapters, reflecting the three separate areas I have worked in throughout my PhD studies. During my PhD, I published two papers, one relating to the work in the first chapter, and one to that of the second. At the time of submission, the project which the third chapter relates to was still ongoing, with plans for a future publication. The first chapter discusses work done on the real space renormalisation group (RG) for Ising and Potts models in 2 dimensions. Taking inspiration from Hasenbusch's work, a new framework for carrying out the RG is developed, its computational implementation discussed in some detail, as well as the results for a variety of systems and the implications of these results. The numerical scaling of the procedure and the consequences of this for future work are also covered. The results documented in chapter two are purely theoretical and presented in closed form. The research conducted is to do with properties of free interfaces. The second chapter is by and large critical of previous assumptions which have been made about the so-called wave vector dependent, in order to attempt to experimentally measure it and use these measurements to make further predictions. Using some simple toy models, many of these assumptions are shown to be false. In a sense, the goal of the research presented in the chapter two, is not to motivate further research, but to dissuade research in a direction we consider to be misguided, due to the faulty assumptions it is based on. The third chapter covers a small subset of a project concerned with studying correlations within the so-called Abelian Manna Model. The majority of the project involves (computational) Monte Carlo simulations of the dynamics of such systems, but as these results are not ready to present at the time of writing, the chapter is mainly concerned with some analytical results which were derived in order to validate our models for small systems, explain certain quirky phenomena arising from our simulations, and help quantify errors. Finally, there is an appendix which expands upon various topics from the first two chapters.

Un grand nombre de problèmes ouverts parmi les plus importants en mécanique statistique sont liés aux systèmes hors de l'équilibre thermique. Dans ce travail, nous utilisons des méthodes de théorie de champs pour étudier certains de ces systèmes. Pour ce faire, nous introduisons une représentation de type théorie de champs pour les systèmes d'intérêt, ainsi que le formalisme spécifique utilisé partout dans ce travail, le groupe de renormalisation non perturbatif (NPRG). Ce formalisme a émergé dans les dernières années comme un moyen très efficace pour étudier les systèmes fortement corrélés, et il a été appliqué avec succès à certains problèmes dans et hors de l'équilibre thermique. Avant de traiter les systèmes qui nous intéressent, nous développons de nouveaux outils et méthodes dans le cadre du NPRG, et nous les testons dans le cas relativement simple d'une théorie de champ scalaire, appartenant à la classe d'universalité d'Ising. Celui ci nous permet d'obtenir la fonction d'échelle du modèle d'Ising en d = 3, sans avoir à fixer aucun paramètre libre. En outre, afin de faire face de manière efficace à la physique des systèmes hors d'équilibre, nous étudions en détail certains aspects formels de leur passage à une représentation de type théorie des champs, ainsi que les équivalences entre les différentes voies possibles pour mettre en oeuvre ce passage. Après ces préliminaires, nous nous concentrons sur les transitions de phase hors d'équilibre dans des systèmes de réaction-diffusion, et en particulier dans la sous-classe connue sous le nom de marches aléatoires avec branchement et annihilation (BARW). Parmi d'autres résultats, nous utilisons le NPRG pour trouver une solution exacte pour un des cas les plus simples de système de réaction-diffusion, connu comme l'annihilation pure. Avec cette solution, nous analysons certaines propriétés des systèmes BARW à bas taux de branchement, en utilisant un développement autour de l'annihilation pure. Ce développement perturbatif, qui est réalisé autour d'un modèle non trivial, nous permet de trouver des résultats exacts pour certaines des plus importantes classes d'universalité de ces systèmes
Many of the most important open problems in statistical mechanics are related with systems out of thermal equilibrium. In this work we use field theory methods to study some of these systems. To do so, we first introduce a field theory representation for the systems of interest, as well as the specific formalism to be used throughout, the so-called non perturbative renormalization group (NPRG). This formalism has emerged in the last years as a very efficient way to deal with strongly correlated systems, and has been applied with success to problems both in and out of equilibrium. Before treating the actual systems of interest, we develop some new tools and methods within the NPRG context, and test them in a simple scalar field theory, belonging to the Ising universality class. We are able to obtain results for the momentum-dependent scaling function of the d=3 Ising model, without having to fix any free parameter. Also, in order to tackle in an efficient way the physics of out of equilibrium systems, we study in detail some formal aspects of their passage to a field theory representation, as well as the equivalences between different possible ways to perform this passage. After these preliminaries, we concentrate in out of equilibrium active-to-absorbing phase transitions in reaction-diffusion systems, and in particular in the subclass known as branching and annihilating random walks (BARW). Among other results, we use the NPRG to find an exact solution to any vertex in a simple system, known as pure annihilation. With this, we analyze some properties of BARW at low branching rates, by means of an expansion in the branching rate around pure annihilation. This perturbative expansion, which is performed around a nontrivial model, allows us to find some striking exact results for some of the most important universality classes in these systems

In this thesis we investigate properties of equilibrium and non-equilibrium systems by means of renormalization group (RG) analysis. In the study of the d-dimensional Coulomb gas we have formulated a continuum model from the underlying hyper-cubic lattice and employed the irreducible differential formulation of the Wilson RG.We have identified a Thouless-Kosterletz transition in d=2 and found no non-trivial fixed points for d>2. As an example of a non-equilibrium system, we have investigated properties of quasi-neutral plasmas which are governed by stochastic magnetohydrodynamic (MHD) equations. The present method is based upon the Martin-Siggia-Rose field-theory formulation of stochastic dynamics. We develop a diagrammatic representation for the theory and carry out a momentum-shell RG of Wilson-Kadanoff type. An infinite set of diagrams is identified which are marginal in the RG sense. We have shown, in accordance with previous literature, that the same problem arises for the randomly-forced Navier-Stokes equation. The problem of marginal variables can be suppressed by working near equilibrium, where stochastic forcing represents thermal fluctuations. In a similar manner we have considered regimes when MHD equations are subject either to kinetic or magnetic forcing only. In such models the macroscopic limit can be taken such that all marginal terms are irrelevant and the dynamics is governed by linear equations. Furthermore, non-trivial fixed points are identified in such regimes and limiting values of either kinematic viscosity or magnetic diffusivity are derived. A consistent description of MHD dynamics far from equilibrium is still absent. We highlight some of the aspects of the functional integral formulation with regards to the symmetries of the system and propose possible ways in which the system can be studied non-pertubatively.

The research reported in this dissertation explores the observable effects that individual heterogeneity implies in strategic environments. The first chapter provides a focused experimental test of mixed strategy play in strictly competitive games. The experiment directly tests whether serial correlation results from subjects' inability to generate sequences of actions that appear to be time independent, or instead from the play of non-equilibrium strategies. This is achieved by allowing the subjects to generate actions via a simple randomizing device. It is found that serial correlation is not reduced and that subjects adopt a wide variety of non-equilibrium mixed strategies. This wide variety of mixtures potentially explains the seeming paradox of minimax winning proportions with a high variance of win rates across pairs of players. In the second chapter a theoretical model is developed for simultaneous move games in which the observable outcomes are allocations of monetary payoffs or commodity bundles, not expected utility levels. It is assumed that the players' mappings from the uncertain money amounts or commodity bundle allocations to expected utility levels are heterogeneous and are private information. The third chapter applies this framework to investigate the incentives to form agricultural marketing pools.

Thesis (Ph. D.)--University of California, San Diego, 2007.
Title from first page of PDF file (viewed April 3, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 75-79).

Die vorliegende Arbeit beschaeftigt sich mit Gleichgewichtsproblemen unter Gleichgewichtsrestriktionen, sogenannten EPECs (Englisch: Equilibrium Problems with Equilibrium Constraints). Konkret handelt es sich um gekoppelte Zwei-Ebenen-Optimierungsprobleme, bei denen Nash- Gleichgewichte fuer die Entscheidungen der oberen Ebene gesucht sind. Ein Ziel der Arbeit besteht in der Formulierung dualer Stationaritaetsbedingungen zu solchen Problemen. Als Anwendung wird ein oligopolistisches Wettbewerbsmodell fuer Strommaerkte betrachtet. Zur Gewinnung qualitativer Hypothesen ueber die Struktur der betrachteten Modelle (z.B. Inaktivitaet bestimmter Marktteilnehmer) aber auch fuer moegliche numerische Zugaenge ist es wesentlich, EPEC-Loesungen explizit bezueglich der Eingangsdaten des Problems zu formulieren. Der Weg dorthin erfordert eine Strukturanalyse der involvierten Optimierungsprobleme (constraint qualifications, Regularitaet), die Herleitung von Stabilitaetsresultaten bestimmter mengenwertiger Abbildungen und die Nutzung von Transformationsformeln fuer die sogenannte Ko-Ableitung. Weitere Schwerpunkte befassen sich mit der Beziehung zwischen verschiedenen dualen Stationaritaetstypen (S- und M-Stationaritaet) sowie mit stochastischen Erweiterungen der betrachteten Problemklasse, sogenannten SEPECs.
This thesis is concerned with equilibrium problems with equilibrium constraints or EPECs. Concretely, we consider models composed by coupling together two-level optimization problems, the upper-level solutions to which are non-cooperative (Nash-Cournot) equilibria. One of the main goals of the thesis involves the formulation of dual stationarity conditions to EPECs. A model of oligopolistic competition for electricity markets is considered as an application. In order to profit from qualitative hypotheses concerning the structure of the considered models, e.g., inactivity of certain market participants at equilibrium, as well as to provide conditions useful for numerical procedures, the ablilty to formulate EPEC solutions in relation to the input data of the problem is of considerable importance. The way to do this requires a structural analysis of the involved optimization problems, e.g., constraints qualifications, regularity; the derivation of stability results for certain multivalued mappings, and the usage of transformation formulae for so-called coderivatives. Further important topics address the relationship between various dual stationarity types, e.g., S- and M-stationarity, as well as the extension of the considered problem classes to a stochastic setting, i.e., stochastic EPECs or SEPECs.

Cooling down a liquid below its melting temperature can lead to an amorphous frozen system commonly known as a glass. Despite glasses are common in everyday life, the nature of the glass transition still remains one of the most intriguing unsolved problems of condensed matter physics. In this Thesis the atomic length-scale rearrangements of glassy systems close to the glass transition temperature are explored under equilibrium and non-equilibrium conditions with X-Ray Photon Correlation Spectroscopy (XPCS). In particular, we explore the role of directional stresses on the dynamics in a colloidal glass of silica nanoparticles dispersed in a binary solvent. Our results show that the macroscopic stress stored in this glass relaxes via the cooperative ballistic motion of groups of particles with a characteristic size of the order of ten particle diameters. The role of stresses is further investigated in borate-based glasses, where the dynamics well below the glass transition are dictated by the recently discovered X-ray beam-induced dynamics. We show that these dynamics are related to the topology of the network, with peculiar similarities with the stress-phenomenology observed in colloids and metallic glasses.

Cooling down a liquid below its melting temperature can lead to an amorphous frozen system commonly known as a glass. Despite glasses are common in everyday life, the nature of the glass transition still remains one of the most intriguing unsolved problems of condensed matter physics. In this Thesis the atomic length-scale rearrangements of glassy systems close to the glass transition temperature are explored under equilibrium and non-equilibrium conditions with X-Ray Photon Correlation Spectroscopy (XPCS). In particular, we explore the role of directional stresses on the dynamics in a colloidal glass of silica nanoparticles dispersed in a binary solvent. Our results show that the macroscopic stress stored in this glass relaxes via the cooperative ballistic motion of groups of particles with a characteristic size of the order of ten particle diameters. The role of stresses is further investigated in borate-based glasses, where the dynamics well below the glass transition are dictated by the recently discovered X-ray beam-induced dynamics. We show that these dynamics are related to the topology of the network, with peculiar similarities with the stress-phenomenology observed in colloids and metallic glasses.

The physics of ultracold quantum gases has been the subject of a long-lasting and intense research activity, which started almost a century ago with purely theoretical studies and had a fluorishing experimental development after the implementation of laser and evaporative cooling techniques that led to the first realization of a Bose Einstein condensate (BEC) over 25 years ago. In recent years, a great interest in ultracold atoms has developed for their use as platforms for quantum technologies, given the high degree of control and tunability offered by ultracold atom systems. These features make ultracold atoms an ideal test bench for simulating and studying experimentally, in a controlled environment, physical phenomena analogous to those occurring in other, more complicated, or even inaccessible systems, which is the idea at the heart of quantum simulation. In the rapidly developing field of quantum technologies, it is highly important to acquire an in-depth understanding of the state of the quantum many-body system that is used, and of the processes needed to reach the desired state. The preparation of the system in a given target state often involves the crossing of second order phase transitions, bringing the system strongly out-of-equilibrium. A better understanding of the out-of-equilibrium processes occurring in the vicinity of the transition, and of the relaxation dynamics towards the final equilibrium condition, is crucial in order to produce well-controlled quantum states in an efficient way. In this thesis I present the results of the research activity that I performed during my PhD at the BEC1 laboratory of the BEC center, working on ultracold gases of 23Na atoms in an elongated harmonic trap. This work had two main goals: the accurate determination of the equilibrium properties of a Bose gas at finite temperature, by the measurement of its equation of state, and the investigation of the out-of-equilibrium dynamics occurring when a Bose Einstein condensate is prepared by cooling a thermal cloud at a finite rate across the BEC phase transition.To study the equilibrium physics of a trapped atomic cloud, it is crucial to be able to observe its density distribution in situ. This requires a high optical resolution to accurately obtain the density profile of the atomic distribution, from which thermodynamic quantities can then be extracted. In particular, in a partially condensed atomic cloud at finite temperature, it is challenging to resolve well also the boundaries of the BEC, where the condensate fraction rapidly drops in a narrow spatial region. This required an upgrade of the experimental apparatus in order to obtain a high enough resolution. I designed, tested and implemented in the experimental setup new imaging systems for all main directions of view. Particular attention was paid for the vertical imaging system, which was designed to image the condensates in trap with a resolution below 2 μm, with about a factor 4 improvement compared to the previous setup. The implementation of the new imaging systems involved a partial rebuilding of the experimental apparatus used for cooling the atoms. This created the occasion for an optimization of the whole system to obtain more stable working conditions. Concurrently I also realized and included in the experiment an optical setup for the use of a Digital Micromirror Device (DMD) to project time-dependent arbitrary light patterns on the atoms, creating optical potentials that can be controlled at will. The use of this device opens up exciting future scenarios where it will be possible to locally modify the trapping potential and to create well-controlled barriers moving through the atomic cloud. Another challenge in imaging the density distribution in situ is determined by the fact that the maximum optical density (OD) of the BEC, in the trap center, exceeds the low OD of the thermal tails by several orders of magnitude. In order to obtain an accurate image of the whole density profile, we developed a minimally destructive, multi-shot imaging technique, based on the partial transfer of a fraction of atoms to an auxiliary state, which is then probed. Taking multiple images at different extraction fractions, we are able to reconstruct the whole density profile of the atomic cloud avoiding saturation and maintaining a good signal to noise ratio. This technique, together with the improvements in the imaging resolution, has allowed us to accurately obtain the optical density profile of the Bose gas in trap, from which the 3D density profile was then calculated applying an inverse Abel transform, taking advantage of the symmetry of the trap. From images of the same cloud after a time-of-flight expansion, we measured the temperature of the gas. From these quantities we could find the pressure as a function of the density and temperature, determining the canonical equation of state of the weakly interacting Bose gas in equilibrium at finite temperature. These measurements also allowed us to clearly observe the non-monotonic temperature behavior of the chemical potential near the critical point for the phase transition, a feature that characterizes also other superfluid systems, but that had never been observed before in weakly interacting Bose gases. The second part of this thesis work is devoted to the study of the dynamical processes that occur during the formation of the BEC order parameter within a thermal cloud. The cooling at finite rate across the Bose-Einstein condensation transition brings the system in a strongly out-of-equilibrium state, which is worth investigating, together with the subsequent relaxation towards an equilibrium state. This is of interest also in view of achieving a better understanding of second order phase transitions in general, since such phenomena are ubiquitous in nature and relevant also in other platforms for quantum technologies. A milestone result in the study of second order phase transitions is given by the Kibble-Zurek mechanism, which provides a simple model capturing important aspects of the evolution of a system that crosses a second-order phase transition at finite rate. It is based on the principle that in an extended system the symmetry breaking associated with a continuous phase transition can take place only locally. This causes the formation of causally disconnected domains of the order parameter, at the boundaries of which topological defects can form, whose number and size scale with the rate at which the transition is crossed, following a universal power law. It was originally developed in the context of cosmology, but was later successfully tested in a variety of systems, including superfluid helium, superconductors, trapped ions and ultracold atoms. The BEC phase transition represents in this context a paradigmatic test-bench, given the high degree of control at which this second-order phase transition can be crossed by means of cooling ramps at different rates. Already early experiments investigated the formation of the BEC order parameter within a thermal cloud, after quasi-instantaneous temperature quenches or very slow evaporative cooling. In the framework of directly testing the Kibble-Zurek mechanism, further experiments were performed, both in 2D and 3D systems, focusing on the emergence of coherence and on the statistics of the spontaneously generated topological defects as a function of the cooling rate. The Kibble-Zurek mechanism, however, does not fully describe the out-of-equilibrium dynamics of the system at the transition, nor the post-quench interaction mechanisms between domains that lead to coarse-graining. Most theoretical models are based on a direct linear variation of a single control parameter, e.g. the temperature, across the transition. In real experiments, the cooling process is controlled by the tuning of other experimental parameters and a global temperature might not even be well defined, in a thermodynamic sense, during the whole process. Moreover, the temperature variation is usually accompanied by the variation of other quantities, such as the number of atoms and the collisional rate, making it difficult to accurately describe the system and predict the post-quench properties. Recent works included effects going beyond the Kibble-Zurek mechanism, such as the inhomogeneity introduced by the trapping potential, the role of atom number losses, and the saturation of the number of defects for high cooling rates. These works motivate further studies, in particular of the dynamics taking place at early times, close to the crossing of the critical point. The aim of the work presented in this thesis is to further investigate the timescales associated to the formation and evolution of the BEC order parameter and its spatial fluctuations, as a function of the rate at which the transition point is crossed. We performed experiments producing BECs by means of cooling protocols that are commonly used in cold-atom laboratories, involving evaporative cooling in a magnetic trap. We explored a wide range of cooling rates across the transition and found a universal scaling for the growth of the BEC order parameter with the cooling rate and a finite delay in its formation. The latter was already observed in earlier works, but for a much more limited range of cooling rates. The evolution of the fluctuations of the order parameter was also investigated, with an analysis of the timescale of their decay during the relaxation of the system, from an initial strongly out-of-equilibrium condition to a final equilibrium state. This thesis is structured as follows: The first chapter presents the theoretical background, starting with a brief introduction to the concept of Bose Einstein condensation and a presentation of different models describing the thermodynamics of an equilibrium Bose gas. The second part of this chapter then deals with the out-of-equilibrium dynamics that is inevitably involved in the crossing of a second-order phase transition such as the one for Bose-Einstein condensation. The Kibble-Zurek mechanism is briefly reviewed and beyond KZ effects are pointed out, motivating a more detailed investigation of the timescales involved in the BEC formation. In the second chapter, I describe the experimental apparatus that we use to cool and confine the atoms. Particular detail is dedicated to the parts that have been upgraded during my PhD, such as the imaging system. In the third chapter I show our experimental results on the measurement of the equation of state of the weakly interacting uniform Bose gas at finite temperature. In the fourth chapter I present our results on the out-of-equilibrium dynamics in the formation of the condensate order parameter and its spatial fluctuations, as a function of different cooling rates.

This thesis consists of five chapters, based on four different articles. All of them are devoted to different aspects of spatial heterogeneity and its impact on economic equilibrium in space. The concept of heterogeneous continuous space is discussed in the introductory chapter.
The first model "Equilibrium in Continuous Space under Decentralized Production" addresses the issue of the impact of differences across locations in exogeneous productivity on the structure of equilibrium prices, production and trade. The goal is to describe the general equilibrium in a spatially decentralized economy, when production, consumption and markets are distributed in continuous space and transportation costs are essentially linear. It is shown that an autarky equilibrium can exist only if transport costs are high enough. In the general case, the general equilibrium in this model includes some endogeneously determined trade areas, with flows of goods across space, and autarky areas where production and consumption activities take place only at the same point. An analytical solution in explicit functions is obtained; it contains equilibrium prices, labor supply and flows of goods as functions of the spatial variable. The model can be applied to a set of practical questions in regional economics. In particular, it is able to describe persistent price differentials across regions and non-local consequences of road construction and transportation cost shocks for the economy. The differences across locations in population density may have either historical or economic reasons.
The second model "Hotelling's Revival" extends a well-known research of H.Hotelling (1929) to the two-dimensional case with spatially heterogeneous demand density, preserving the rest of his classical assumptions. It is shown that the problem of demand discontinuity in the one-dimensional model, which was discovered by d'Aspremont, Gabszewich and Thisse (1979), disappears in this case. This also holds for any bounded distribution of consumers on any compact set on a plane, which can describe real geographical situations. Demand continuity still holds for any transport costs, strictly increasing in distance and not necessarily linear. Although this is sufficient for the existence of Nash equilibrium in mixed strategies, in pure strategies it exists only for some subset of cases. Examples of both existence and non-existence are constructed, and for some family of densities the separation point between the two cases is found.
The third model addresses locational choice of heterogeneous consumers, when land is also heterogeneous in quality. It is based on two articles. The first, "Dacha Pricing", is presented in chapter 4 and studies the problem of locational rent in a city-neighbourhood when utility includes both the impact of transport costs and time for transportation. For the case of identical agents the problem is solved explicitly and comparative statics with respect to exogeneous changes in transport cost and speed is studied. For the case of agents who are heterogeneous with respect to their income, a solution is also obtained. The model explains some evidence about dacha pricing in Russia and its dynamics during the transition period. The second article related to this model is "Location and Land Size Choice by Heterogeneous Agents". It generalizes the first one and form a separate chapter 5. A new approach about the general equilibrium allocation of heterogeneous divisible good (like land) among a continuum of heterogeneous consumers is proposed. The model is based on continuity of primitives which allow not only to finding a general equilibrium solution in a class of continuous functions, but also to treat the solution to a continuous problem as the limit of the corresponding sequence of discrete problems. This solves one of Berliant's paradoxes, related to spatial economics. The multiplicity of equilibria is shown to take place.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2001.
Includes bibliographical references (p. 111-112).
The first two chapters of this thesis explore how coordination happens in simple games. The first chapter models the adaptive play of a 2 x 2 game by pairs of agents matched together from a large population. In contrast with the existing literature, I assume that agents have some control over who they are matched with - specifically, I give them the option to sometimes continue playing against the same opponent. This renewal option allows agents playing efficiently to isolate themselves from those who are not. Perhaps counterintuitively, efficient play may be less likely to survive in the long run when agents have this additional instrument, even in games with common interests. This is because isolation has two effects: it raises the returns to an efficient but fragile strategy, but it also "ghettoizes" agents playing inefficiently - they rarely learn about the efficient strategy and when they do learn about it, they rarely hear good news. I look at an extension in which agents have long memories about the performance of a strategy. With long memories, good news about an efficient strategy will be more likely to trickle down to ghettoized agents, mitigating the bias in learning. With this bias removed, long run survival of efficient play becomes more likely - even when it is not a static Nash equilibrium. Essentially, agents learn to use the renewal option to punish non-cooperators. However, the speed of learning may still be quite slow, so that ghettoization persists for a long time.
(cont.) The second chapter investigates the interaction of strategic uncertainty and timing in a coordination game. Carlsson and van Damme have shown that small departures from common knowledge of the game being played can dramatically alter the equilibrium set. In the game I look at, there are two equilibria, but only the risk dominant equilibrium survives such a perturbation. I augment this model by giving agents a costly option to delay choosing a strategy (thereby observing any actions that were taken without delay). Strategic uncertainty gives agents a reason to exercise this option (under complete information, it never would be). In turn, the fact that Agent B sometimes waits and chooses an action after observing Agent A's choice, mitigates the risk that A faces when taking an action that is efficient but sensitive to coordination. As a result, the efficient equilibrium is played more often; in fact, as the cost of delay vanishes, it is always played. In Chapter 3, I explore the interaction between imperfect consumer information and the endogenous level of product differentiation in a non-spatial model of monopolistic competition with horizontally differentiated products. A principle of extreme differentiation is derived: firms will always choose to differentiate either maximally or minimally. In equilibrium, differentiation is maximal when search costs are low and minimal when search costs are high, providing a new interpretation of Hotelling's classic result.
by Nathan Larson.
Ph.D.

This paper presents the concept of numerical CGE modeling with the help of a 2-country general equilibrium model. In the framework of this simple dynamic monetary model the effects of a (unilateral) monetary and fiscal expansion are simulated. The exchange rate of the home vis-à-vis the foreign currency depreciates in response to both types of shocks. The monetary expansion leads to an increase in home relative to foreign private consumption and to a sharp increase in relative home output in the short run, while in the long run output increases in the foreign country and decreases in the home country. The unilateral fiscal expansion, on the other hand, results in a fall of private consumption in the home relative to the foreign country, and in an increase in relative home output in the short as well as in the long run. The world real interest rate falls quite substantially in response to both shocks. (author's abstract)
Series: Department of Economics Working Paper Series

This thesis studies the application of Statistical Association Fluid Theory (SAFT) in the prediction of hydrate formation conditions. The main objective is to develop a robust, reliable and purely predictive model for calculating the formation of single hydrates former gases. The current study is based on the use of the algorithm proposed by Englezos et al. (1991). Simplified SAFT (Fu & Sandler 1995) was employed to model the vapor and liquid phases as well as the van der Waals-Platteew model to represent the hydrate phase. The predictive ability of the model was investigated on single hydrate formers in the presence of inhibitors. With this end in mind, the inhibiting effects of methanol and ethylene glycol on methane, ethane, propane and carbon dioxide incipient hydrate forming were studied. The calculated results were compared to the experimental data obtained from the literature. A deviation of less than 10% in pressure or 1℃ in temperature was desired. Additionally, the phase equilibria of water-methanol, methanol-methaen, methanol-ethane and methanol-propane were also studied. Excellent results were obtained from incipient hydrate calculations and the SAFT equation of state was found to be highly capable of tackling non-ideal mixtures such as water-alcohol and water-alcohol-hydrocarbon systems. Estimation of the SAFT pure component parameters and the temperature range over which the SAFT parameters are estimated was found to be crucial. To overcome this issue, several parameters were estimated over various different temperature ranges, and the one which provided the smallest average absolute deviation was selected.

Graphene has displayed much promise as an electrical conductor and as a optical material. To date there is a large body of literature dedicated to the equilibrium properties of graphene. In this thesis the properties of graphene out of equilibrium are probed. Through combined optical and transport measurements the behaviour of hot electrons are probed at temperatures over five orders of magnitude from 50mK to 2000K. This wide range of temperatures allows access to the behaviour of quantum corrections at the lowest temperatures to the highest energy phonon modes. From ultrafast femtosecond laser pulses to steady state heating from an electric field the cooling of hot electron populations through coupling to various phonon modes in the graphene and the substrate are explored. Additionally the effect of an electric field on the weak localisation correction to the conductivity was separated from heating effects using applied magnetic fields combined with careful modelling of the heat transport properties of the graphene. Finally the desorption dynamics of oxygen bound to the surface are shown using a combination of transport and two pulse correlation technique using an ultrafast laser. Surprisingly the cooling of hot carriers in graphene at low energies shows substrate surface phonons as an important cooling mechanism, highlighting the importance of substrate choice in future graphene devices. In contrast at the very highest energy scales accessed only by photoexcitation the cooling is shown not to be influenced by the presence of a substrate, but out-of-plane phonon modes increase cooling of the hot optical phonons.

This thesis is a collection of three essays in which the behaviour of unemployment is studied in different dynamic environments. Throughout, unemployment is understood to be involuntary, arising due to the uncoordinated nature of trade in the labour market as viewed from the perspective of the Diamond-Mortensen-Pissarides equilibrium matching model. It goes without saying that the fundamental motivation for pursuing this line of research is provided by the untold consequences, both human and economic, of otherwise capable people remaining involuntarily idle. An attempt, therefore, is made to contribute to the understanding of how various aspects of macroeconomic policy can influence unemployment outcomes. The approach maintained throughout is to combine general equilibrium modelling with simulation techniques in order to provide not only qualitative inferences but also quantitative descriptions of equilibrium dynamics. The dynamic environments considered cover both the business cycle (the first two chapters) and the life cycle (the third chapter). In the first chapter, Structural Tax Reform and the Cyclical Behaviour of the Labour Market, we build a real business cycle model with frictional unemployment and distortionary tax rates which are increasing in individual taxable labour income. The cyclical aspects of tax reform that are addressed in this chapter are distinct from the stationary state distributional issues that have garnered most of the attention in the existing literature on structural tax reform. Estimating the tax code parameters from federal income tax return data for the U.S., we find that a reduction in the progressivity of the tax system is associated with a significant increase in the volatility of hours per worker. The intuition is simply that the greater the extent to which marginal tax rates fluctuate in response to shocks, the smaller the incentive to adjust working hours. But in a frictional labour market in which it is costly for forms to issue vacancies, the behaviour of hours - i.e. intensive adjustment, or adjustment in the intensive margin - is a determining factor of job creation - i.e. extensive adjustment. We then explain how the dynamic behaviour of hours along the adjustment path to an aggregate productivity shock generates o¤setting incentives for job creation, with the result that tax reform has little impact on unemployment fluctuations. The welfare cost of the business cycle is also computed under different tax regimes. It is found that although business cycles are more costly under a flat tax, the overall welfare implications are quantitatively negligible regardless of the tax system. Having described the effects of the tax system on equilibrium dynamics when perturbed by a productivity disturbance, we then consider business cycle adjustment to an aggregate demand shock in the form of fiscal stimulus. In light of recent fiscal developments in the U.S. and Europe, the ability of expansionary fiscal policy to stimulate output has gained renewed interest in the business cycle literature. We contribute to the analysis by assessing whether the efficacy of government expenditure in reducing unemployment depends on the structure of the tax system. It is demonstrated that a less progressive tax policy increases the ability of expansionary fiscal policy to stimulate output due to a larger response in hours, but this comes at the cost of a smaller unemployment multiplier. Tax reform therefore causes a compositional shift in labour market adjustment in response to aggregate demand shocks, with relatively more adjustment occurring in the intensive margin and less adjustment in the extensive margin the flatter the tax schedule is. The reason why this compositional shift occurs for a demand shock but not a supply shock is that the adjustment path of hours is qualitatively dependent on the type of disturbance. In particular, we describe how equilibrium undershooting in hours occurs only in response to an aggregate productivity (supply) shock, whereas the negative wealth effects arising from increased government expenditure exert sustained upward pressure on hours along the entire adjustment path, thus providing a significant incentive for firms to substitute away from job creation. The second chapter, Monetary Policy and Job Creation in a New Keynesian Model, is motivated by the work of Cooley and Quadrini (1999) and Krause and Lubik (2007). These studies indicate that a typical monetary business cycle model with frictional unemployment and endogenous job destruction tends to encounter difficulty in generating a rise in job creation in response to expansionary monetary policy, rendering the model inconsistent with the downward sloping Beveridge curve that appears in the data and implying only a limited policy role for inflationary job creation. Matching frictions in the labour market congest the job creation process so that firms tend to skew adjustment to shocks towards the job destruction margin. In recognition of the assertion put forth but unpursued by Cooley and Quadrini (1999) that fluctuations in the size of the labour force may ease labour market congestion and therefore amplify cyclical job creation, in Chapter II we extend a New Keynesian model with unemployment to feature an endogenous labour market participation decision. However, a baseline model with a standard degree of risk aversion tends to exhibit countercyclical labour force participation, which is inconsistent with the data. In order to address this issue, we propose the notion of labour market participation as a social consideration, which we demonstrate to be capable of generating procyclical participation incentives. The basic idea is that agents will tend not to exit the labour force during booms in order to "keep up with the Joneses". We then find that plausible fluctuations in the size of the labour force do not exert a quantitatively significant effect on job creation. In light of this result, we search for alternative mechanisms which may overturn the conclusion that inflationary policy is incapable of incentivising job creation. The approach taken involves switching focus to the characteristics of aggregate demand dynamics along the adjustment path to a monetary shock. It is well known that standard New Keynesian models fail to deliver the gradual, hump-shaped adjustment path to monetary policy shocks that is observed in the data. We argue that if aggregate demand experiences a persistent increase in response to a monetary shock instead of peaking on impact, the incentive for firms to create jobs becomes amplified. The intuition is that, since the job creation decision is forward-looking due to the presence of matching frictions, aggregate demand must rise persistently even after the shock takes place so that firms anticipate a further increase in aggregate demand in order for the time consuming process of issuing a vacancy to be justified. To demonstrate this, it is shown that, by altering the dynamics of aggregate demand, time-inseparability in the utility function can significantly improve the ability of expansionary monetary policy to increase job creation, allowing the model to generate a downward sloping Beveridge curve conditional on monetary shocks. In the appendix to Chapter II, we lend further credence to this hypothesis by describing how the manner in which monetary policy it- self is specified may give rise to hump-shaped adjustment dynamics and, consequently, amplify inflationary job creation. Finally, in Chapter III on Equilibrium Matching and Age Discrimination Policy, we abstract from business cycle issues and concentrate instead on the life cycle. Federal legislation prohibiting the discrimination of workers on the basis of age has been in place in the United States since the 1967 Age Discrimination in Employment Act.

This thesis analyses inventories empirically and theoretically. Inventories are important in miderstanding business cycles, not only because inventory investment accounts for a large share of GDP growth rate. This thesis also emphasises the cyclicality of inventories. Often, business cycles are regarded as exponential decays, i.e., successive deviations from the steady state and their returning processes. In contrast, this thesis offers a battery of evidence that economic variables, such as sales and inventories, follow damping oscillations, i.e., stable sine waves. This means that a boom is the seed of the recession that follows, and vice versa. This thesis also reveals inventories' role in such endogenous cycles. The first chapter presents empirical evidence of periodicity. VAR estimations find evidence of sine waves - namely, complex roots. Indeed, the detected complex roots seem to capture the actual business cycles; the estimated lengths of one business cycle are close to those of the post-war average in both Japan and the United States. This chapter also shows that peaks and bottoms of inventories lag behind those of production; such a time lag is called a phase shift. In addition, this chapter finds that the U.S. Federal Reserve anticipates inventory cycles, while the Bank of Japan does not. The second chapter constructs a theoretical model with a stockout constraint and a production chain in the rational dynamic general equilibrium framework, which quantitatively satisfies stylised inventory facts. Importantly, the model successfully mimics observed inventory cycles. Moreover, working hours are more volatile and the correlation between labour productivity and output is lower than in the standard real business cycle model. Finally, the third chapter offers a solution algorithm for linear rational expectation models under imperfect information. Inventories are closely related to imperfect information, and inventories are often regarded as buffers against unobserved demand shocks.

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
O objetivo desta tese é entender o papel de frições de credito em modelos de Equilíbrio Geral com mercados financeiros incompletos. Primeiro, o trabalho estuda a importância das restrições ao endividamento dos agentes para a existência de equilíbrio monetário em uma economia com informação simétrica onde a moeda (aqui caracterizada como um ativo que não paga dividendos, pode ser vendido a descoberto e está em oferta líquida positiva) tem apenas o papel de reserva de valor e é o único ativo da economia. Além disso, mostra que, apesar da moeda possibilitar as transferências de riqueza intertemporais e entre os estados da natureza, o equilíbrio monetário ainda é Pareto ineficiente. A tese também caracteriza a hipótese de impaciência uniforme, um importante requerimento para a existência de equilibrio, em termos das propriedades assintóticas dos fatores de desconto intertemporal. Como consequência, mostra que desconto hiperbólico é incompatível com a impaciência uniforme de funções de utilidade separáveis. Finalmente, mostra que, se os ativos financeiros são colateralizados para a proteção dos emprestadores em caso de default, sempre existe equilíbrio em um modelo de dois períodos com mercados incompletos e informação assimétrica onde os ativos são nominais, independente da estrutura informacional.
This thesis aims to understand the role of credit frictions in general equilibrium models with incomplete financial markets. First, this work studies the importance of debt constraints for the existence of monetary equilibrium in an economy with symmetric information and where money has only the role of store of value. It also characterizes the uniform impatience assumption, an important requirement to equilibrium existence, in terms of asymptotic properties on intertemporal discount factors. Finally, it shows that, if assets are collateralized in order to protect lenders in the case of default, equilibrium always exists in a two-period incomplete markets model of asymmetric information with nominal assets, independently of the financial-informational structure.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 1986.
MICROFICHE COPY AVAILABLE IN ARCHIVES AND DEWEY.
Vita.
Includes bibliographies.
by William Berkeley English.
Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2006.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 121-123).
This thesis developed a new method to analyze the structural behavior of masonry domes: the modified thrust line analysis. This graphical-based method offers several advantages to existing methods. It is the first to account for the ability of domes to achieve a range of internal forces, gaining potentially an infinite number of equilibrium solutions that could not be derived otherwise. This method can also analyze non-conventional axisymmetrical dome geometries that are difficult or impossible to analyze with existing methods. Abiding by limit state conditions and the principles of the lower bound theorem, the modified thrust line method was used to ascertain the theoretical minimum thrust of spherical and pointed domes, a parameter that was previously unsolved. Several methods to estimate minimum thrust to-weight ratio were provided. For spherical domes, this ratio may be estimated as -0.583[alpha] + 1.123; for pointed domes, the estimated ratio is 0.551[delta] -1.061[delta]/[alpha] -0.615[alpha] + 1.164, where [alpha] and [delta] are the embrace and truncating angles, respectively.
(cont.) From the results, salient relationships between minimum thrust and dome geometry were derived, including an inverse relationship between the minimum thrust and the thickness-to-radius ratio, angle of embrace, and, for pointed domes, the truncation angle of the crown for a constant angle of embrace. The capabilities of the modified thrust line method were demonstrated in two masonry dome case studies that existing methods could not successfully analyze. The potential of this method to predict the ultimate load capacity of masonry domes was also explored. The method overpredicted the capacity of two small-scale masonry domes loaded to failure by a concentrated applied load at the crown; however the small size of the domes compared to real-world domes suggested that scale effects may have influenced their behavior. Finally, interactive geometry programs of the modified thrust line method and other existing graphical analysis methods were created to disseminate these illustrative tools to understanding the structural behavior of masonry domes.
by Wanda W. Lau.
S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2010.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 195-202).
This thesis consists of three chapters studying dynamic economies in general equilibrium. The first chapter considers an economy in business cycles with potentially imperfect financial markets. The second chapter investigates an economy in its balanced growth path with heterogeneous firms. The third chapter analyzes dynamic competitions that these firms are potentially engaged in. The first chapter, "Asset Price and Real Investment Volatility with Heterogeneous Beliefs," sheds light on the role of imperfect financial markets on the economic and financial crisis 2007-2008. This crisis highlights the role of financial markets in allowing economic agents, including prominent banks, to speculate on the future returns of different financial assets, such as mortgage-backed securities. I introduce a dynamic general equilibrium model with aggregate shocks, potentially incomplete markets and heterogeneous agents to investigate this role of financial markets. In addition to their risk aversion and endowments, agents differ in their beliefs about the future aggregate states of the economy. The difference in beliefs induces them to take large bets under frictionless complete financial markets, which enable agents to leverage their future wealth. Consequently, as hypothesized by Friedman (1953), under complete markets, agents with incorrect beliefs will eventually be driven out of the markets. In this case, they also have no influence on asset prices and real investment in the long run. In contrast, I show that under incomplete markets generated by collateral constraints, agents with heterogeneous (potentially incorrect) beliefs survive in the long run and their speculative activities drive up asset price volatility and real investment volatility permanently. I also show that collateral constraints are always binding even if the supply of collateralizable assets endogenously responds to their price. I use this framework to study the effects of different types of regulations and the distribution of endowments on leverage, asset price volatility and investment. Lastly, the analytical tools developed in this framework enable me to prove the existence of the recursive equilibrium in Krusell and Smith (1998) with a finite number of types. This has been an open question in the literature. The second chapter, "Innovation from Incumbents and Entrants," is a joint work with Daron Acemoglu. We propose a simple modification of the basic Schumpeterian endogenous growth models, by allowing incumbents to undertake innovations to improve their products. This model provides a tractable framework for a simultaneous analysis of entry of new firms and the expansion of existing firms, as well as the decomposition of productivity growth between continuing establishments and new entrants. One lesson we learn from this analysis is that, unlike in the basic Schumpeterian models, taxes or entry barriers on potential entrants might increase economic growth. It is the outcome of the greater productivity improvements by incumbents in response to reduced entry, which outweighs the negative effect of the reduction in creative destruction. As the model features entry of new firms and expansion and exit of existing firms, it also generates an equilibrium firm size distribution. We show that the stationary firm size distribution is Pareto with an exponent approximately equal to one (the so-called "Zipf distribution"). The third chapter, "Racing: when should we handicap the advantaged competitor?" studies dynamic competitions, for example R&D competitions used in the second chapters. Two competitors with different abilities engage in a winner-take-all race; should we handicap the advantaged competitor in order to reduce the expected completion time of the race? I show that if the discouragement effect is strong, i.e., both competitors are discouraged from exerting effort when it becomes more certain who will win the race, we should handicap the advantaged. We can handicap him either by reducing his ability or by offering him a lower reward if he wins. Doing so induces higher effort not only from the disadvantaged competitor because of his higher incentive from a higher chance of winning the race but also from the advantaged competitor because of their strategic interactions. Therefore, the expected completion time is strictly shortened. To prove the existence and uniqueness of the equilibria (including symmetric and asymmetric equilibria) that leads to the conclusion, I use a boundary value problem formulation which is novel to the dynamic competition literature. In some cases, I obtain closed-form solutions of the equilibria.
by Dan Cao.
Ph.D.

In this thesis we introduce a new bootstrap method for testing structural DSGE models according to their dynamic performance. The method maintains a separation between the structural (non-linear) model as the null hypothesis and its dynamic time series representation. The model's errors are discovered and used for bootstrapping (after whitening) the resulting pseudo-samples are used to discover the sampling distribution of the dynamic time series model. The test then consists of discovering whether the parameters of the time-series model estimated on the actual data lie within some confidence interval of this distribution. A test statistic for the parameters taken as a whole is developed (the M-metric, a Wald statistic).

We study non-equilibrium and strongly-correlated dynamics in two contexts. We begin by analysing quantum many-body systems out of equilibrium through the lens of cold atomic impurities in Bose gases. Such highly-imbalanced mixtures provide a controlled arena for the study of interactions, dissipation, decoherence and transport in a many-body quantum environment. Specifically we investigate the oscillatory dynamics of a trapped and initially highly-localised impurity interacting with a weakly-interacting trapped quasi low-dimensional Bose gas. This relates to and goes beyond a recent experiment by the Inguscio group in Florence. We witness a delicate interplay between the self-trapping of the impurity and the inhomogeneity of the Bose gas, and describe the dissipation of the energy of the impurity through phononic excitations of the Bose gas. We then study the transport of a driven, periodically-trapped impurity through a quasi one-dimensional Bose gas. We show that placing the weakly-interacting Bose gas in a separate periodic potential leads to a phononic excitation spectrum that closely mimics those in solid state systems. As a result we show that the impurity-Bose gas system exhibits phonon-induced resonances in the impurity current that were predicted to occur in solids decades ago but never clearly observed. Following this, allowing the bosons to interact strongly, we predict the effect of different strongly-correlated phases of the Bose gas on the motion of the impurity. We show that, by observing the impurity, properties of the excitation spectrum of the Bose gas, e.g., gap and bandwidth, may be inferred along with the filling of the bosonic lattice. In other words the impurity acts as a probe of its environment. To describe the dynamics of such a strongly-correlated system we use the powerful and near-exact time-evolving block decimation (TEBD) method, which we describe in detail. The second part of this thesis then analyses, for the first time, the performance of this method when applied to simulate non-equilibrium classical stochastic processes. We study its efficacy for a well-understood model of transport, the totally-asymmetric exclusion process, and find it to be accurate. Next, motivated by the inefficiency of sampling-based numerical methods for high variance observables we adapt and apply TEBD to simulate a path-dependent observable whose variance increases exponentially with system size. Specifically we calculate the expected value of the exponential of the work done by a varying magnetic field on a one-dimensional Ising model undergoing Glauber dynamics. We confirm using Jarzynski's equality that the TEBD method remains accurate and efficient. Therefore TEBD and related methods complement and challenge the usual Monte Carlo-based simulators of non-equilibrium stochastic processes.

Complex fluids are commercially- and industrially-important materials which exhibit ordering on scales much larger than atomic. Their usage is typically in non-equilibrium conditions, however traditional methods for measuring rheology are not appropriate for measuring samples with gradients present, such as temperature and concentration. In this work a safe and easy to use optical tweezer (OT) apparatus has been developed in order to facilitate the investigation of various systems during dilution or drying. In contrast to other OT setups, this equipment is safe to use without laser goggles or interlocked rooms, yet still allows full access to the microscope. Proof-of-concept experiments are performed on aqueous poly (ethylene oxide) (PEO) solutions to demonstrate the changes in viscosity and concentration over time, and the OT is then used in a rheological investigation into a commercially-relevant wormlike micelle (WLM) system, in conjunction with Diffusing Wave Spectroscopy (DWS) and traditional bulk rheology. It is shown for the first time that equimolar (eM) SDS:CAPB WLM samples can be considered ‘model’ systems, and form close approximations of Maxwellian systems on the addition of extra salt or surfactant above 0.1eM. The effect of an uncharged polymer (PEO 4M MW) on this WLM network structure was subsequently investigated; its effects are consistent with current theories of polymer-surfactant interactions. The effect of a conditioning polyelectrolyte on the network structure was also studied; its effect was highly dependent on surfactant and electrolyte concentration, but hinted at the previously unreported behaviour of a polyelectrolyte initiating micellar branching. A precursor investigation into evaporation of sessile droplets of aqueous PEO solutions is presented last, reporting a previously unseen droplet evaporation regime in which the solid deposits grow to nearly twice their starting height. This research concludes that the growth phenomena is due to the unusual solvation mechanism of PEO, and a predictive theory is presented in support of this.

In this paper the main results about existence of Stationary Sunspot Equilibrium are given. Sketch of the proves and examples are commented. The types of economies included in the framework of this work are the intertemporal one-step forward looking economies.

Autor no autoriza el acceso a texto completo de su documento hasta el 15/1/2021.
Ingeniero Civil Industrial
Se presenta un modelo dinámico de múltiples mercados financieros, organizados como limit order markets, en el cual agentes endógenamente toman decisiones óptimas para maximizar el valor esperado de sus ganacias. Los agentes toman sus decisiones considerando incentivos propios, condiciones de mercado, potenciales decisiones de trading futuras y diferentes estrategias adoptadas por otros agentes. Para efectos de la presente investigación, se compara el escenario de un único mercado financiero ( single market ) con un escenario de dos mercados interconectados que compiten por el flujo de órdenes ( multi markets ). Los resultados indican que la posibilidad de transar en múltiples mercados, beneficia ampliamente a agentes sin valoración privada por el activo, ya que buscan oportunidades de transar en ambos mercados, mientras que perjudica el bienestar de agentes con motivación intrínseca para transar, dado que obtienen peores condiciones de negociación. Por otro lado, se observa una reducción en varias medidas de liquidez en multi markets, lo que sugiere la existencia de externalidades positivas asociadas a mercados consolidados.