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Microscopic Foundations of Thermodynamics and Generalized Statistical Ensembles

Description: This dissertation aims at addressing two important theoretical questions which are still debated in the statistical mechanical community. The first question has to do with the outstanding problem of how to reconcile time-reversal asymmetric macroscopic laws with the time-reversal symmetric laws of microscopic dynamics. This problem is addressed by developing a novel mechanical approach inspired by the work of Helmholtz on monocyclic systems and the Heat Theorem, i.e., the Helmholtz Theorem. By following a line of investigation initiated by Boltzmann, a Generalized Helmholtz Theorem is stated and proved. This theorem provides us with a good microscopic analogue of thermodynamic entropy. This is the volume entropy, namely the logarithm of the volume of phase space enclosed by the constant energy hyper-surface. By using quantum mechanics only, it is shown that such entropy can only increase. This can be seen as a novel rigorous proof of the Second Law of Thermodynamics that sheds new light onto the arrow of time problem. The volume entropy behaves in a thermodynamic-like way independent of the number of degrees of freedom of the system, indicating that a whole thermodynamic-like world exists at the microscopic level. It is also shown that breaking of ergodicity leads to microcanonical phase transitions associated with nonanalyticities of volume entropy. The second part of the dissertation deals with the problem of the foundations of generalized ensembles in statistical mechanics. The starting point is Boltzmann's work on statistical ensembles and its relation with the Heat Theorem. We first focus on the nonextensive thermostatistics of Tsallis and the associated deformed exponential ensembles. These ensembles are analyzed in detail and proved (a) to comply with the requirements posed by the Heat Theorem, and (b) to interpolate between canonical and microcanonical ensembles. Further they are showed to describe finite systems in contact with finite heat baths. ...
Date: May 2008
Creator: Campisi, Michele
Partner: UNT Libraries

Thermodynamical Formalism

Description: Thermodynamical formalism is a relatively recent area of pure mathematics owing a lot to some classical notions of thermodynamics. On this thesis we state and prove some of the main results in the area of thermodynamical formalism. The first chapter is an introduction to ergodic theory. Some of the main theorems are proved and there is also a quite thorough study of the topology that arises in Borel probability measure spaces. In the second chapter we introduce the notions of topological pressure and measure theoretic entropy and we state and prove two very important theorems, Shannon-McMillan-Breiman theorem and the Variational Principle. Distance expanding maps and their connection with the calculation of topological pressure cover the third chapter. The fourth chapter introduces Gibbs states and the very important Perron-Frobenius Operator. The fifth chapter establishes the connection between pressure and geometry. Topological pressure is used in the calculation of Hausdorff dimensions. Finally the sixth chapter introduces the notion of conformal measures.
Date: August 2004
Creator: Chousionis, Vasileios
Partner: UNT Libraries

Thermodynamic Calculations Relating to Chloride Volatility Processing of Nuclear Fuels: [Part] 2. The Capacity of Chlorine for Transporting Plutonium Tetrachloride Vapor During Reaction of U3O8-PuO2 with Carbon Tetrachloride

Description: Report issued by the Oak Ridge National Laboratory discussing thermodynamic calculations of nuclear fuels. As stated in the introduction, "the equations developed in this report could be used to calculate the capacity of chlorine for transporting plutonium tetrachloride" (p. 2). This report includes tables, and illustrations.
Date: October 1964
Creator: Gens, T. A.
Partner: UNT Libraries Government Documents Department

Electronic Distribution Functions and Thermodynamic Properties at High Temperatures

Description: Report issued by the Argonne National Laboratory discussing the thermodynamics and electronic distribution of high temperatures. As stated in the introduction, "in the present paper, a model for computing is described which takes into account in detail the interactions between bound electrons and the average interaction of the bound electrons with the free ones" (p. 4). This report includes tables, and illustrations.
Date: May 1953
Creator: Brachman, Malcolm K. & Meyerott, Roland E.
Partner: UNT Libraries Government Documents Department

Transient Temperature in Infinite Plates, Infinite Cylinders, and Spheres Following a Simultaneous Step Change in Internal Heat Generation Rate, Coolant Temperature and Heat Transfer Coefficient

Description: Report regarding the problem of transient temperature in infinite plates, infinite cylinders, and spheres following during convective cooling after heat generation.
Date: 1958
Creator: Epel, Lester G.
Partner: UNT Libraries Government Documents Department

Dynamics, Thermodynamic formalism and Perturbations of Transcendental Entire Functions of Finite Singular Type

Description: In this dissertation, we study the dynamics, fractal geometry and the topology of the Julia set of functions in the family H which is a set in the class S, the Speiser class of entire transcendental functions which have only finitely many singular values. One can think of a function from H as a generalized expanding function from the cosh family. We shall build a version of thermodynamic formalism for functions in H and we shall show among others, the existence and uniqueness of a conformal measure. Then we prove a Bowen's type formula, i.e. we show that the Hausdorff dimension of the set of returning points, is the unique zero of the pressure function. We shall also study conjugacies in the family H, perturbation of functions in the family and related dynamical properties. We define Perron-Frobenius operators for some functions naturally associated with functions in the family H and then, using fundamental properties of these operators, we shall prove the important result that the Hausdorff dimension of the subset of returning points depends analytically on the parameter taken from a small open subset of the n-dimensional parameter space.
Date: May 2005
Creator: Coiculescu, Ion
Partner: UNT Libraries

A Dynamic and Thermodynamic Approach to Complexity.

Description: The problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, non-extensive , form of thermodynamics, and another, proposed by the UNT Center for Nonlinear Science, on complexity as a new condition that, for physical systems, would be equivalent to a state of matter intermediate between dynamics and thermodynamics. In the first part of this dissertation, the concept of Kolmogorov-Sinai entropy is introduced. The Pesin theorem is generalized in the formalism of Tsallis non-extensive thermodynamics. This generalized form of Pesin theorem is used in the study of two major classes of problems, whose prototypes are given by the Manneville and the logistic map respectively. The results of these studies convince us that the approach to complexity must be made along lines different from those of the non-extensive thermodynamics. We have been convinced that the Lévy walk can be used as a prototype model of complexity, as a condition of balance between order and randomness that yields new phenomena such as aging, and multifractality. We reach the conclusions that these properties must be studied within a dynamic rather than thermodynamic perspective. The second part focuses on the study of the heart beating problem using a dynamic model, the so-called memory beyond memory, based on the Lévy walker model. It is proved that the memory beyond memory effect is more obvious in the healthy heart beating sequence. The concepts of fractal, multifractal, wavelet transformation and wavelet transform maximum modulus (WTMM) method are introduced. Artificial time sequences are generated by the memory beyond memory model to mimic the heart beating sequence. Using WTMM method, the multifratal singular spectrums of the sequences ...
Date: August 2003
Creator: Yang, Jin
Partner: UNT Libraries

ANL/HTP: A Computer Code for the Simulation of Heat Pipe Operation

Description: ANL/HTP is a computer code for the simulation of heat pipe operation, to predict heat pipe performance and temperature distributions during steady state operation. Source and sink temperatures and heat transfer coefficients can be set as input boundary conditions, and varied for parametric studies. Five code options are included to calculate performance for fixed operating conditions, or to vary any one of the four boundary conditions to determine the heat pipe limited performance. The performance limits included are viscous, sonic, entrainment capillary, and boiling, using the best available theories to model these effects. The code has built-in models for a number of wick configurations - open grooves, screen-covered grooves, screen-wrap, and arteries, with provision for expansion. The current version of the code includes the thermophysical properties of sodium as the working fluid in an expandable subroutine. The code-calculated performance agrees quite well with measured experiment data.
Date: November 1983
Creator: McLennan, G. A.
Partner: UNT Libraries Government Documents Department

Electronic Transport Properties in Copper Oxides

Description: Oxidation of copper and electronic transport in thermally grown large-grain poly-crystals of non-stoichiometric copper oxides were studied at elevated temperatures. Thermogravimetric copper oxidation was studied in air and oxygen at temperatures between 350 and 100 C. From the temperature-dependence of oxidation rates, three different processes can be identified for the oxidation of copper: bulk diffusion, grain-boundary diffusion, and surface control with whisker growth; these occur at high, intermediate, and low temperatures, respectively. Electrical conductivity measurements as a function of temperature (350 - 1134 C) and pO2 (10(sup⁻⁸-1.0 atm) indicated intrinsic electronic conduction in CuO over the entire range of conditions. Electronic behavior of non-stoichiometric Cu(sub 2)O indicates that the charge defects are doubly ionized oxygen interstitials and holes. The calculated enthalpy of formation of oxygen ((Delta)H(sub O(sub 2))) and the hole conduction energy (E(sub H)) at constant composition for non-stoichiometric Cu2O are 2.0 (plus minus) 0.2 eV and 0.82 (plus minus) 0.02 eV, respectively.
Date: July 1991
Creator: Park, J.-H. & Natesan, K.
Partner: UNT Libraries Government Documents Department

Corrosion and Mechanical Behavior of Materials for Coal Gasification Applications

Description: A state-of-the-art review is presented on the corrosion and mechanical behavior of materials at elevated temperatures in coal-gasification environments. The gas atmosphere in coal-conversion processes are, in general, complex mixtures which contain sulfur-bearing components (hydrogen sulfide, SO2, and COS) as well as oxidants (carbon dioxide/carbon monoxide and water/hydrogen). The information developed over the last five years clearly shows sulfidation to be the major mode of material degradation in these environments. The corrosion behavior of structural materials in complex gas environments is examined to evaluate the interrelationships between gas chemistry, alloy chemistry, temperature, and pressure. Thermodynamic aspects of high-temperature corrosion processes that pertain to coal conversion are discussed, and kinetic data are used to compare the behavior of different commercial materials of interest. The influence of complex gas environments on the mechanical properties such as tensile, stress-rupture, and impact on selected alloys is presented. The data have been analyzed, wherever possible, to examine the role of environment on the property variation. The results from ongoing programs on char effects on corrosion and on alloy protection via coatings, cladding, and weld overlay are presented. Areas of additional research with particular emphasis on the development of a better understanding of corrosion processes in complex environments and on alloy design for improved corrosion resistance are discussed.
Date: May 1980
Creator: Natesan, K.
Partner: UNT Libraries Government Documents Department

COMMIX-SA-1: a Three-Dimensional Thermohydrodynamic Computer Program for Solar Applications

Description: COMMIX-SA-1 is a three-dimensional, transient, single-phase, compressible-flow, component computer program for thermohydrodynamic analysis. It was developed for solar applications in general, and for analysis of thermocline storage tanks in particular. The conservation equations (in cylindrical coordinates) for mass, momentum, and energy are solved as an initial-boundary-value problem. The detailed numerical-solution procedure based on a modified ICE (Implicit Continuous-Fluid Eulerian) technique is described. A method for treating the singularity problem arising at the origin of a cylindrical-coordinate system is presented. In addition, the thermal interactions between fluid and structures (tank walls, baffles, etc.) are explicitly accounted for. Finally, the COMMIX-SA-1 code structure is delineated, and an input description and sample problems are presented.
Date: November 1980
Creator: Sha, W. T.; Lin, E. I. H.; Schmitt, R. C.; Liu, K. V.; Hull, J. R.; Oras, J. J. et al.
Partner: UNT Libraries Government Documents Department

Thermal-Performance Study of Liquid Metal Fast Breeder Reactor Insulation

Description: Three types of metallic thermal insulation were investigated analytically and experimentally: multilayer reflective plates, multilayer honeycomb composite, and multilayer screens. Each type was subjected to evacuated and non-evacuated conditions, where thermal measurements were made to determine thermal-physical characteristics. A variation of the separation distance between adjacent reflective plates of multilayer reflective plates and multilayer screen insulation was also experimentally studied to reveal its significance. One configuration of the multilayer screen insulation was further selected to be examined in sodium and sodium oxide environments. The emissivity of Type 304 stainless steel used in comprising the insulation was measured by employing infrared technology. A comprehensive model was developed to describe the different proposed types of thermal insulation. Various modes of heat transfer inherent in each type of insulation were addressed and their relative importance compared. Provision was also made in the model to allow accurate simulation of possible sodium and sodium oxide contamination of the insulation. The thermal-radiation contribution to heat transfer in the temperature range of interest for LMFBR's was found to be moderate, and the suppression of natural convection within the insulation was vital in preserving its insulating properties. Experimental data were compared with the model and other published results. Moreover, the three proposed test samples were assessed and compared under various conditions as viable LMFBR thermal insulations.
Date: September 1980
Creator: Shiu, Kelvin Kwok-Kay
Partner: UNT Libraries Government Documents Department

Chemical Engineering Division Basic Energy Sciences Research: July 1976-September 1977

Description: Studies in basic energy science covered many different activities, nearly all of which were designed to gain information required for a better understanding of systems important to national needs in energy and environment. Studies of associating gases included measurements of thermal conductivities and basic molecular orbital calculations. Raman spectroscopy and spectrophotometry were used to determine thermodynamic and spectroscopic data on salt vapor complexes. Polarized Raman spectra of As2S3 thin films and vapors were recorded. Halogenation of lanthanide oxides with aluminum chloride allowed the separation of the resultant chloride complexes by vapor transport. Electrochemical titrations were used to obtain the solubility product of iron sulfide in molten LiCl-KCl eutectic. Solubility products of eleven sulfides in the same eutectic mixture were calculated. Galvanostatic techniques were used to study metal deposition/dissolution reactions in molten salts. Activity coefficients of lithium in lithium-lead alloys were determined electrochemically; phase diagrams of ternary alloys of Li-Al-Mg and Li-Ca-Mg were computed. Thermodynamic studies are being made of the sorption of hydrogen by Li-Al and Li-Pb alloys. The study of the solubility of oxygen in liquid lithium was completed. An electric resistance method for measuring distribution properties of nonmetallic elements in binary metallic systems containing lithium is being developed. Calorimetric methods were used to measure standard enthalpies of formation of some coal components, lanthanum and rare earth trifluorides, and gamma-UO3, UF6, Cs3CrO4, Cs4CrO4, As4S4, and As2S3. High-temperature enthalpy increments were measured for LaF3 and beta-As4S4. The acidities of airborne ammonium sulfate-bearing particles from various areas of the U.S. were measured using Fourier-transform infrared spectroscopy.
Date: 1978?
Creator: Cafasso, F. A.; Blander, M.; Maroni, V. A.; Johnson, C. E.; Kumar, R. & Siegel, S.
Partner: UNT Libraries Government Documents Department

Dispersive Approximations for Hyperbolic Conservation Laws

Description: Necessary and sufficient conditions are given so that the Sobolev-type partial differential equations generate a contraction semigroup. It is shown that any nonlinear contraction from L/sup 1/(R) to itself that preserves the integral and commutes with translations satisfies maximum and minimum principles. This lemma is applied to the solution operator S/sub t/ to give necessary and sufficient conditions that S/t/ satisfy a maximum principle, despite the dispersive nature. Sufficient conditions are given so that the solutions converge, as nu and beta tend to zero, to the entropy solution of the conservation law. A larger class of monotone finite-difference schemes for the numerical solution of the conservation law motivated by finite-difference discretizations of the Sobolev equations, is introduced, and convergence results are proved for methods in this class. The methods analyzed include some that were previously used to approximate the solution of a linear waterflood problem in petroleum engineering.
Date: December 1981
Creator: Lucier, Bradley J.
Partner: UNT Libraries Government Documents Department

Light-Water-Reactor Fission-Product Data Assessment

Description: This assessment seeks (1) to determine the most probable chemical compounds formed between fission products and actinides in urania fuels under normal and accident conditions and (2) to identify gaps in knowledge of these fission-product compounds. The ultimate goal of this effort is to develop predictive capability about the behavior of fission products under normal and accident conditions. The relevant thermochemical data have been organized by compound type, the chemical stability of resultant compounds determined, and data uncertainty evaluated. The assessment focused on fission-product and actinide oxides, halides, tellurides, and hydroxides. Free energy equations are given for those compounds for which data were available.
Date: September 1982
Creator: Blackburn, P. E. & Johnson, C. E.
Partner: UNT Libraries Government Documents Department

Thermodynamic Analysis of Multicomponent Working Fluids for Rankine Bottoming Cycle Applications

Description: The basic equations underlying a computer code are developed to describe the thermodynamic behavior of multi-component working fluids in Rankine cycles. The code is to be employed in the performance analysis of Rankine bottoming cycle systems. The performance of such systems depends strongly on the working fluid characteristics. The introduction of multi-component mixtures makes available a broad spectrum of fluid properties achievable by varying the mixture composition. The code provides a tool to analytically vary the mixture composition to optimize cycle performance.
Date: January 1984
Creator: Ash, J. E.
Partner: UNT Libraries Government Documents Department

Stirling-Engine Thermodynamic Analysis: a Users Guide to SEAM1

Description: This report provides background and procedural information for the use of a general-purpose Stirling-engine analysis code developed at Argonne National Laboratory and available through the National Energy Software Center. Different engine configurations are easily specified, or the user may make use of provided data for existing engines, both kinematic and free piston. The code models heat transfer and fluid mechanics throughout the engine and accounts for system energy flows and losses. Good agreement is shown between code predictions and experimental measurements. The present analysis method was chosen for fast execution and useful information on energy flows in the system. A description is provided of the code structure that is intended to accept different analysis modules that can provide improved system modeling or optimization capability.
Date: September 1982
Creator: Heames, T. J.; Uherka, D. J.; Zabel, J. C. & Daley, J. G.
Partner: UNT Libraries Government Documents Department

Chemical Engineering Division Reactor Fuels and Materials Chemistry Research : July 1976-September 1977

Description: This report describes research and development activities conducted in support of fast-reactor programs during the period July 1976 - September 1977. Reactor safety studies were directed primarily toward obtaining high-temperature physical property data for use in reactor safety analyses. Spectrographic data and an oxygen-potential model were used to calculate thermodynamic properties applicable to the equations of state of uranium-plutonium dioxide and uranium dioxide. Work was continued on the compilation of standard sets of property data on reactor fuels and materials. The viscosity of molten aluminum and the thermal diffusivity of molten uranium dioxide were measured as functions of temperature. Modeling and chemical-interaction studies related to post-accident heat removal were conducted. The efforts in sodium technology supported the LMFBR program. Studies were conducted to explore the feasibility of upgrading the quality of commercial-grade sodium and sodium from decommissioned reactors to provide new sources of reactor-grade sodium.
Date: July 1978
Creator: Cafasso, F. A.; Leibowitz, L.; McPheeters, C. C. & Johnson, C. E.
Partner: UNT Libraries Government Documents Department

Contributions to the Data on Theoretical Metallurgy: [Part] 7. The Thermodynamic Properties of Sulphur and its Inorganic Compounds

Description: Report issued by the Bureau of Mines discussing the thermodynamic properties of sulfur, and its inorganic compounds. As stated in the introduction, "the present bulletin has as its primary purpose the correlation of the thermodynamic properties of elementary sulfur and its inorganic compounds and the presentation, after careful consideration of all available information, of a self-consistent system of thermodynamic relationships for these substances" (p. 1). This report includes tables.
Date: 1937
Creator: Kelley, K. K.
Partner: UNT Libraries Government Documents Department

Contributions to the Data on Theoretical Metallurgy: [Part] 7. The Thermodynamic Properties of Sulphur and its Inorganic Compounds

Description: Report issued by the Bureau of Mines over studies on the thermodynamics of sulphur. As stated in the introduction, "the present bulletin has as its primary purpose the correlation of the thermodynamic properties of elementary sulphur and its inorganic compounds and the presentation, after careful consideration of all available information, of a self-consistent system of thermodynamic relationships for these substances" (p. 1). This report includes tables.
Date: 1937
Creator: Kelley, K. K.
Partner: UNT Libraries Government Documents Department