On the thermal budget of Pahoehoe lava flows

In this thesis I investigate some aspects of the thermal budget of pahoehoe lava flows. This is done with a combination of general field observations, quantitative modeling, and specific field experiments. The results of this work apply to pahoehoe flows in general, even though the vast bulk of the work has been conducted on the lavas formed by the Pu'u 'O'o - Kupaianaha eruption of Kilauea Volcano on Hawai'i. The field observations rely heavily on discussions with the staff of the United States Geological Survey's Hawaiian Volcano Observatory (HVO), under whom I labored repeatedly in 1991-1993 for a period totaling about 10 months.

The quantitative models I have constructed are based on the physical processes observed by others and myself to be active on pahoehoe lava flows. By building up these models from the basic physical principles involved, this work avoids many of the pitfalls of earlier attempts to fit field observations with "intuitively appropriate" mathematical expressions. Unlike many earlier works, my model results can be analyzed in terms of the interactions between the different physical processes. I constructed models to: (1) describe the initial cooling of small pahoehoe flow lobes and (2) understand the thermal budget of lava tubes.

The field experiments were designed either to validate model results or to constrain key input parameters. In support of the cooling model for pahoehoe flow lobes, attempts were made to measure: (1) the cooling within the flow lobes, (2) the amount of heat transported away from the lava by wind, and (3) the growth of the crust on the lobes. Field data collected by Jones [1992], Hon et al. [1994b], and Denlinger [Keszthelyi and Denlinger, in prep.] were also particularly useful in constraining my cooling model for flow lobes. Most of the field observations I have used to constrain the thermal budget of lava tubes were collected by HVO (geological and geophysical monitoring) and the Jet Propulsion Laboratory (airborne infrared imagery [Realmuto et al., 1992]). I was able to assist HVO for part of their lava tube monitoring program and also to collect helicopterborne and ground-based IR video in collaboration with JPL [Keszthelyi et al., 1993].

The most significant results of this work are (1) the quantitative demonstration that the emplacement of pahoehoe and 'a'a flows are the fundamentally different, (2) confirmation that even the longest lava flows observed in our Solar System could have formed as low effusion rate, tube-fed pahoehoe flows, and (3) the recognition that the atmosphere plays a very important role throughout the cooling of history of pahoehoe lava flows. In addition to answering specific questions about the thermal budget of tube-fed pahoehoe lava flows, this thesis has led to some additional, more general, insights into the emplacement of these lava flows. This general understanding of the tube-fed pahoehoe lava flow as a system has suggested foci for future research in this part of physical volcanology.

Essays on economics networks

This thesis belongs to the growing field of economic networks. In particular, we develop three essays in which we study the problem of bargaining, discrete choice representation, and pricing in the context of networked markets. Despite analyzing very different problems, the three essays share the common feature of making use of a network representation to describe the market of interest.

In Chapter 1 we present an analysis of bargaining in networked markets. We make two contributions. First, we characterize market equilibria in a bargaining model, and find that players' equilibrium payoffs coincide with their degree of centrality in the network, as measured by Bonacich's centrality measure. This characterization allows us to map, in a simple way, network structures into market equilibrium outcomes, so that payoffs dispersion in networked markets is driven by players' network positions. Second, we show that the market equilibrium for our model converges to the so called eigenvector centrality measure. We show that the economic condition for reaching convergence is that the players' discount factor goes to one. In particular, we show how the discount factor, the matching technology, and the network structure interact in a very particular way in order to see the eigenvector centrality as the limiting case of our market equilibrium.

We point out that the eigenvector approach is a way of finding the most central or relevant players in terms of the “global” structure of the network, and to pay less attention to patterns that are more “local”. Mathematically, the eigenvector centrality captures the relevance of players in the bargaining process, using the eigenvector associated to the largest eigenvalue of the adjacency matrix of a given network. Thus our result may be viewed as an economic justification of the eigenvector approach in the context of bargaining in networked markets.

As an application, we analyze the special case of seller-buyer networks, showing how our framework may be useful for analyzing price dispersion as a function of sellers and buyers' network positions.

Finally, in Chapter 3 we study the problem of price competition and free entry in networked markets subject to congestion effects. In many environments, such as communication networks in which network flows are allocated, or transportation networks in which traffic is directed through the underlying road architecture, congestion plays an important role. In particular, we consider a network with multiple origins and a common destination node, where each link is owned by a firm that sets prices in order to maximize profits, whereas users want to minimize the total cost they face, which is given by the congestion cost plus the prices set by firms. In this environment, we introduce the notion of Markovian traffic equilibrium to establish the existence and uniqueness of a pure strategy price equilibrium, without assuming that the demand functions are concave nor imposing particular functional forms for the latency functions. We derive explicit conditions to guarantee existence and uniqueness of equilibria. Given this existence and uniqueness result, we apply our framework to study entry decisions and welfare, and establish that in congested markets with free entry, the number of firms exceeds the social optimum.

Vibrational pooling and constrained equilibration on surfaces

In this thesis, we provide a statistical theory for the vibrational pooling and fluorescence time dependence observed in infrared laser excitation of CO on an NaCl surface. The pooling is seen in experiment and in computer simulations. In the theory, we assume a rapid equilibration of the quanta in the substrate and minimize the free energy subject to the constraint at any time t of a fixed number of vibrational quanta N(t). At low incident intensity, the distribution is limited to one- quantum exchanges with the solid and so the Debye frequency of the solid plays a key role in limiting the range of this one-quantum domain. The resulting inverted vibrational equilibrium population depends only on fundamental parameters of the oscillator (ω_e and ω_eχ_e) and the surface (ω_D and T). Possible applications and relation to the Treanor gas phase treatment are discussed. Unlike the solid phase system, the gas phase system has no Debye-constraining maximum. We discuss the possible distributions for arbitrary N-conserving diatom-surface pairs, and include application to H:Si(111) as an example.

Computations are presented to describe and analyze the high levels of infrared laser-induced vibrational excitation of a monolayer of absorbed ¹³CO on a NaCl(100) surface. The calculations confirm that, for situations where the Debye frequency limited n domain restriction approximately holds, the vibrational state population deviates from a Boltzmann population linearly in n. Nonetheless, the full kinetic calculation is necessary to capture the result in detail.

We discuss the one-to-one relationship between N and γ and the examine the state space of the new distribution function for varied γ. We derive the Free Energy, F = NγkT − kTln(∑P_n), and effective chemical potential, μn ≈ γkT, for the vibrational pool. We also find the anti correlation of neighbor vibrations leads to an emergent correlation that appears to extend further than nearest neighbor.

Temperature effects on the activity coefficient of the bicarbonate ion

Natural waters may be chemically studied as mixed electrolyte solutions. Some important equilibrium properties of natural waters are intimately related to the activity-concentration ratios (i.e., activity coefficients) of the ions in solution. An Ion Interaction Model, which is based on Pitzer's (1973) thermodynamic model, is proposed in this dissertation. The proposed model is capable of describing the activity coefficient of ions in mixed electrolyte solutions. The effects of temperature on the equilibrium conditions of natural waters and on the activity coefficients of the ions in solution, may be predicted by means of the Ion Interaction Model presented in this work.

The bicarbonate ion, HCO₃^-, is commonly found in natural waters. This anion plays an important role in the chemical and thermodynamic properties of water bodies. Such properties are usually directly related to the activity coefficient of HCO₃^- in solution. The Ion Interaction Model, as proposed in this dissertation, is used to describe indirectly measured activity coefficients of HCO₃^- in mixed electrolyte solutions.

Experimental pH measurements of MCl-MHCO₃ and MCl-H₂CO₃ solutions at 25°C (where M = K⁺, Na⁺, NH₄⁺, Ca²⁺ or Mg²⁺) are used in this dissertation to evaluate indirectly the MHCO₃ virial coefficients. Such coefficients permit the prediction of the activity coefficient of HCO₃^- in mixed electrolyte solutions. The Ion Interaction Model is found to be an accurate method for predicting the activity coefficient of HCO₃^- within the experimental ionic strengths (0.2 to 3.0 m). The virial coefficients of KHCO₃ and NaHCO₃ and their respective temperature variations are obtained from similar experimental measurements at 10° and 40°C. The temperature effects on the NH₄HCO₃, Ca(HCO₃)₂, and Mg(HCO₃)₂ virial coefficients are estimated based on these results and the temperature variations of the virial coefficients of 40 other electrolytes.

Finally, the Ion Interaction Model is utilized to solve various problems of water chemistry where bicarbonate is present in solution.

I. The crystal structure of potassium bis(tricyanovinyl)amine. II. Nuclear magnetic resonance studies of alkali halide solutions. III. Elucidation of the intramolecular hydrogen bond in acetylacetone by the deuterium isotope effect on the chemical shift of the bridge hydrogen

Part I

Potassium bis-(tricyanovinyl) amine, K⁺N[C(CN)=C(CN)₂]₂^-, crystallizes in the monoclinic system with the space group Cc and lattice constants, a = 13.346 ± 0.003 Å, c = 8.992 ± 0.003 Å, B = 114.42 ± 0.02°, and Z = 4. Three dimensional intensity data were collected by layers perpendicular to b* and c* axes. The crystal structure was refined by the least squares method with anisotropic temperature factor to an R value of 0.064.

The average carbon-carbon and carbon-nitrogen bond distances in –C-CΞN are 1.441 ± 0.016 Å and 1.146 ± 0.014 Å respectively. The bis-(tricyanovinyl) amine anion is approximately planar. The coordination number of the potassium ion is eight with bond distances from 2.890 Å to 3.408 Å. The bond angle C-N-C of the amine nitrogen is 132.4 ± 1.9°. Among six cyano groups in the molecule, two of them are bent by what appear to be significant amounts (5.0° and 7.2°). The remaining four are linear within the experimental error. The bending can probably be explained by molecular packing forces in the crystals.

Part II

The nuclear magnetic resonance of ⁸¹Br and ¹²⁷I in aqueous solutions were studied. The cation-halide ion interactions were studied by studying the effect of the Li⁺, Na⁺, K⁺, Mg⁺⁺, Cs⁺ upon the line width of the halide ions. The solvent-halide ion interactions were studied by studying the effects of methanol, acetonitrile, and acetone upon the line width of ⁸¹Br and ¹²⁷I in the aqueous solutions. It was found that the viscosity plays a very important role upon the halide ions line width. There is no specific cation-halide ion interaction for those ions such as Mg⁺⁺, Di⁺, Na⁺, and K⁺, whereas the Cs⁺ - halide ion interaction is strong. The effect of organic solvents upon the halide ion line width in aqueous solutions is in the order acetone ˃ acetonitrile ˃ methanol. It is suggested that halide ions do form some stable complex with the solvent molecules and the reason Cs⁺ can replace one of the ligands in the solvent-halide ion complex.

Part III

An unusually large isotope effect on the bridge hydrogen chemical shift of the enol form of pentanedione-2, 4(acetylacetone) and 3-methylpentanedione-2, 4 has been observed. An attempt has been made to interpret this effect. It is suggested from the deuterium isotope effect studies, temperature dependence of the bridge hydrogen chemical shift studies, IR studies in the OH, OD, and C=O stretch regions, and the HMO calculations, that there may probably be two structures for the enol form of acetylacetone. The difference between these two structures arises mainly from the electronic structure of the π-system. The relative population of these two structures at various temperatures for normal acetylacetone and at room temperature for the deuterated acetylacetone were calculated.