Browsing by Subject "Entropy"
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Item Abstraction, representation, and entropy(2012-05) Payzant, Marcus Ray, 1982-; Mutchler, Leslie; Petersen, BradleyThe following graduate report is an overview of my artistic endeavors spanning the past three years at the University of Texas at Austin. While at UT, I have concentrated on making paintings that focus on the relationship between abstraction, representation, and entropy. Using banal, often overlooked cultural objects as subject matter, I paint ambiguous scenes that teeter between disintegration and formation. Representations of banal detritus within an ambiguous natural space become a metaphor for memory, culture, and life and death alluding to unseen forces and, ultimately, a lack of control. Using a combination of random and deliberate decisions, I aim to create a commentary about the unpredictable yet conformist aspects of the world in which we participate.Item Connecting asymmetric time evolution to the dynamical irreversibility of open quantum systems(2012-08) Bryant, Peter William; Böhm, Arno, 1936-; Dicus, Duane; Odell, Edward; Reichl, Linda; Sitz, GregOne consequence of a quantum theory in which resonances are mathematically unified with decaying states is an asymmetry in time evolution, even for closed quantum mechanical systems. This time asymmetry is different from the environmentally induced, dynamical irreversibility that is experienced only by open quantum systems and that is quantified by an increase in entropy. To investigate the connection between time asymmetry and dynamical irreversibility, we study open systems within a time asymmetric theory. We find that, when using a time asymmetric theory for open systems, one must relax the assumption that measurements are perfectly repeatable. To treat this problem, we develop a framework in which one can incorporate the interference from multiple environmental systems affecting a single experiment. We also study a kinematic effect of indistinguishability that affects only open systems, and we show how it leads to a monotonic increase in entropy without requiring an active measurement. Finally, within our framework we develop two models that reproduce for open systems the expected and observed phenomena. One is a model of photons scattering inefficiently from a beam splitter. The other is a model of systems undergoing Rabi oscillations and suffering environmental interference. We find that the kinematic effect of indistinguishability can explain for such systems the generally measured Excitation Induced Dephasing, which has previously been treated dynamically.Item Cooling atomic ensembles with Maxwell's demon(2011-08) Bannerman, Stephen Travis; Raizen, Mark G.; Berk, Herbert L.; Brodbelt, Jennifer S.; Ditmire, Todd; Reichl, Linda E.This dissertation details the development and implementation of novel experimental techniques for cooling neutral atoms. Based on a method first proposed by Maxwell in a nineteenth century thought experiment, these techniques reduce the entropy of an ensemble by allowing unidirectional transmission through a barrier and thus compressing the ensemble without doing work or increasing its temperature. Because of their general nature, these techniques are much more broadly applicable than traditional laser and evaporative cooling methods, with the potential to cool the vast majority of the periodic table and even molecules. An implementation that cools in one dimension is demonstrated for an ensemble of magnetically trapped rubidium atoms which are irreversibly transferred to a gravito-optical trap. Analysis of the experimental results confirms that phase-space is completely compressed in one dimension. The results also indicate that the overall cooling performance is limited only by the dynamics of atoms in the magnetic trap and may be improved with a more ergodic system. Three-dimensional cooling may be accomplished with a modified technique which substitutes a radio-frequency-dressed magnetic trap for the gravito-optical trap. Application of this technique to atomic hydrogen and progress toward building an experimental apparatus are discussed.Item Discontinuous Galerkin Finite Element Method for the Nonlinear Hyperbolic Problems with Entropy-Based Artificial Viscosity Stabilization(2012-07-16) Zingan, Valentin NikolaevichThis work develops a discontinuous Galerkin finite element discretization of non- linear hyperbolic conservation equations with efficient and robust high order stabilization built on an entropy-based artificial viscosity approximation. The solutions of equations are represented by elementwise polynomials of an arbitrary degree p > 0 which are continuous within each element but discontinuous on the boundaries. The discretization of equations in time is done by means of high order explicit Runge-Kutta methods identified with respective Butcher tableaux. To stabilize a numerical solution in the vicinity of shock waves and simultaneously preserve the smooth parts from smearing, we add some reasonable amount of artificial viscosity in accordance with the physical principle of entropy production in the interior of shock waves. The viscosity coefficient is proportional to the local size of the residual of an entropy equation and is bounded from above by the first-order artificial viscosity defined by a local wave speed. Since the residual of an entropy equation is supposed to be vanishingly small in smooth regions (of the order of the Local Truncation Error) and arbitrarily large in shocks, the entropy viscosity is almost zero everywhere except the shocks, where it reaches the first-order upper bound. One- and two-dimensional benchmark test cases are presented for nonlinear hyperbolic scalar conservation laws and the system of compressible Euler equations. These tests demonstrate the satisfactory stability properties of the method and optimal convergence rates as well. All numerical solutions to the test problems agree well with the reference solutions found in the literature. We conclude that the new method developed in the present work is a valuable alternative to currently existing techniques of viscous stabilization.Item Essential physics for fuel cycle modeling(2011-12) Scopatz, Anthony Michael; Schneider, Erich A.; Biegalski, Steven; Landsberger, Sheldon; Deinert, Mark; Yim, Man-SungNuclear fuel cycles (NFC) are the collection of interconnected processes which generate electricity through nuclear power. Due to the high degree of coupling between components even in the simplest cycles, the need for a dynamic fuel cycle simulator and analysis framework arises. The work presented herein develops essential physics models of nuclear power reactors and incorporate them into a NFC simulation framework. First, a one-energy group reactor model is demonstrated. This essential physics model is then to simulate a sampling fuel cycles which are perturbations of well known base-case cycles. Because the NFC may now be simulated quickly, stochastically modeling many fuel cycle realizations dramatically expands the parameter space which may be analyzed. Finally, a multigroup reactor model which incorporates spectral changes as a function of burnup is presented to increase the fidelity of the original one-group reactor. These methods form a suite of modeling technologies which reach from the lowest levels (individual components) to the highest (inter-cycle comparisons). Prior to the development of this model suite, such broad-ranging analysis had been unrealistic to perform. The work here thus presents a new, multi-scale approach to fuel cycle system design.Item Generic Properties of Actions of F_n(2011-10-21) Hitchcock, James MitchellWe investigate the genericity of measure-preserving actions of the free group Fn, on possibly countably infinitely many generators, acting on a standard probability space. Specifically, we endow the space of all measure-preserving actions of Fn acting on a standard probability space with the weak topology and explore what properties may be verified on a comeager set in this topology. In this setting we show an analog of the classical Rokhlin Lemma. From this result we conclude that every action of Fn may be approximated by actions which factor through a finite group. Using this finite approximation we show the actions of Fn, which are rigid and hence fail to be mixing, are generic. Combined with a recent result of Kerr and Li, we obtain that a generic action of Fn is weak mixing but not mixing. We also show a generic action of Fn has sigma-entropy at most zero. With some additional work, we show the finite approximation result may be used to that show for any action of Fn, the crossed product embeds into the tracial ultraproduct of the hyperfinite II1 factor. We conclude by showing the finite approximation result may be transferred to a subspace of the space of all topological actions of Fn on the Cantor set. Within this class, we show the set of actions with sigma-entropy at most zero is generic.Item The governing cycle and the dynamics of new majority formation(2009-12) Nichols, Curtis William; Tulis, Jeffrey; Burnham, Walter D; Shaw, Daron; Buchanan, Bruce; Levinson, SanfordIn this dissertation I advance a new, regime style, governing cycle theory to account for the constitutional origins and political dynamics of new majority formation. It is these periodic attempts to reorder politics and overcome conditions of entropy that I argue best account for the broad contours of American political development. Using a historical institutional approach, I argue that the U.S. Constitution’s durable separation of powers design interacts with America’s two party system to unintentionally structure political conflict in ways that makes it almost impossible for anyone to address the inevitable build up of entropy in the political system. Recurrently, this challenges partisan leaders to renew politics via the formation of a new governing majority. Partisan leaders accomplish this goal by completing three tasks: 1) shifting the main axis of partisan conflict; 2) assembling a new majority coalition that allows for effective control of federal governing institutions; and, 3) locking-in partisan priorities and advantage through institutionalization of a new governing regime. Through case study analysis, I demonstrate that the dynamics of new governing majority formation can play out in either a straightforward or a protracted manner depending on whether or not partisan leaders initially succeed or fail to accomplish these tasks. This leads to new interpretations of the crucial “System of 1896” and “Reagan Revolution” cases, which allows me to argue for the superiority of my new cyclical theory and to conclude that the governing cycle contains the American polity’s best opportunity to reorder and revitalize itself.Item Image resizing with maximum entropy algorithm(Texas Tech University, 2005-12) Kao, Pingli B.; Nutter, Brian; Mitra, Sunanda; Karp, TanjaSubsampling technologies are frequently applied to resize digital images into a lower resolution for the purpose of preservation and transmission for photography, scientific analysis, and Internet applications. Image subsampling methods should be analyzed for color distortion and retention of usable details from the original image. However, the interpolation-based resizing methods change the color information and attenuate a specific range of high-frequency components of which the human visual system makes significant use. The proposed maximum entropy algorithm provides that, after an image goes through a lossy channel, here called subsampling, informative pixels are retained by analyzing the neighboring pixels. The selected pixels are represented directly in the output image, and color information is therefore preserved. From subjective observation and object evaluation using the entropy, contrast, and PSNR, the maximum entropy algorithm effectively maintains important features and color information and demonstrates better performance than the interpolation-based methods in some applications. Furthermore, the computational expense is suitable for real-time implementation due to the geometrically limited areas and simple arithmetic.Item Image resizing with maximum entropy algorithm(2005-12) Kao, Pingli B.; Nutter, Brian; Mitra, Sunanda; Karp, TanjaSubsampling technologies are frequently applied to resize digital images into a lower resolution for the purpose of preservation and transmission for photography, scientific analysis, and Internet applications. Image subsampling methods should be analyzed for color distortion and retention of usable details from the original image. However, the interpolation-based resizing methods change the color information and attenuate a specific range of high-frequency components of which the human visual system makes significant use. The proposed maximum entropy algorithm provides that, after an image goes through a lossy channel, here called subsampling, informative pixels are retained by analyzing the neighboring pixels. The selected pixels are represented directly in the output image, and color information is therefore preserved. From subjective observation and object evaluation using the entropy, contrast, and PSNR, the maximum entropy algorithm effectively maintains important features and color information and demonstrates better performance than the interpolation-based methods in some applications. Furthermore, the computational expense is suitable for real-time implementation due to the geometrically limited areas and simple arithmetic.Item Integrated Drought Modeling For Texas Under Climate Change Impact With Implications For Water Resources Planning(2014-12-02) Rajsekhar, DeepthiDrought is a deficiency in the hydro climatic variable of interest that is experienced for an extended period of time. In many parts of the world, it is a normal, recurring feature of climate and is therefore inevitable. Adequate monitoring and planning is required for effective mitigation of droughts. The study area for this research is Texas, which has been a consistently drought prone state. There has been at least one serious drought in one part of the state or the other during every decade of the twentieth century. This trend is likely to increase in the coming years due to the effect of global warming and climate change. Taking into account the importance of water management under conditions of extreme climate, this study focuses on enhancing various aspects of drought modeling. The major goals include the development of an efficient means to quantify multiple physical forms of drought, formulation of scientifically robust drought planning regions, integrated multivariate hazard and vulnerability assessment under climate change impact, understanding the causal factors that might trigger a drought event in future, and development of an effective interface to convey the research results to decision makers. These goals were designed to bridge the gaps existing in the current drought research, which even though substantial, still fails to address some of the issues. The goals are addressed by developing a new multivariate drought index, use of copula to build the dependence structure of drought properties and subsequent plotting of multivariate risk maps, development of Drought Hazard Index (DHI) and Drought Vulnerability Index (DVI) for integrated risk analysis under climate change impact, and use of Directional Information Transfer (DIT) for grouping of homogeneous drought regions. A novel transfer entropy approach is adopted to analyze the cause-effect relationship between various hydro-climatic variables and drought properties, thus identifying the prominent future drought triggers. Finally, an efficient drought Decision Support System (DSS) is developed to convey the research results to decision makers through a number of statistical techniques and effective visualization. Ultimately, the study aims at developing a comprehensive framework for better understanding of droughts in Texas which will help decision makers to formulate a more effective adaptation and mitigation strategy in future.Item Numerical approximation of the spectrum of a nonselfadjoint operator governing the vibrations of a nonhomogeneous damped string(Texas Tech University, 2004-08) Busse, Theresa NicoleIn my dissertation, I present the results of numerical investigations of the spectrum of the damped hyperbolic equation involving damping terms, both in the equation and in the boundary conditions. This equation describes the vibrations of a realistic string having distributed (Kevin-Voight) damping and smart material inclusions (self-straining actuators) in the string. The action of the actuators is modeled through specific boundary conditions that involve two independent parameters reflecting the strengths of smart materials. The dissertation has two distinct parts: the first part is devoted to the physical background of vibrational motion, and the second part is devoted to the formulation of a specific problem, presentation, and discussion of the main findings of research. In my dissertation I consider a non standard Strum-Liouville problem. The problem is nonstandard due to two factors, the model incorporates two energy decay mechanisms, i.e., the energy of a string dissipates through the internal friction (Kevin- Voight damping) and through the end points of the string. Many researchers have studied the Strum-Liouville problem for the string equation in the absence of any damping. My problem involves two different types of damping, which makes the problem much more difficult. My particular goals were to investigate the distribution of the eigenfrequencies for the string (in mathematical language, the distribution of the eigenvalues of some linear operator), to analyze dependence on the damping coefficient, and finally to support a well known conjecture in the mathematical community about the multiple eigenfrequencies. In the course of my work, an unexpected discovery was made. I already mentioned, my main goal originally was to support a well known idea concerning the behavior and properties of purely imaginary eigenvalues for the aforementioned Strum-Liouville problem. Since I have a string with energy dissipation, the corresponding spectrum is a countable set of complex points. These points geometrically converge to some horizontal asymptote; these points form a set symmetric with respect to the imaginary axes. It has been assumed tin the mathematical community that with a change in the damping of small steps, the two eigenvalues closest to the imaginary axes would move toward each other, and finally they merge into one double eigenvalue. A minor change in the damping instantly breaks the double eigenvalues into two different simple purely imaginary eigenvalues. A goal of this thesis was to support that idea numerically. Unexpectedly, it was observed that the actual behavior of the two eigenvalues closest to the imaginary axes is totally different from the prediction. Namely, when I change the damping by a very small step (10"^^), for the first dozen steps, the eigenvalues behave as expected: they slowly move in such a way that the distance between them decreases. However, at some moment, those two eigenvalues totally change their behavior and begin moving apart in opposite directions. The movement continues along two branches of a hyperbola like curve until the moment when both eigenvalues reach the imaginary axes. When I continue changes in the damping, the pair of eigenvalues moves along the imaginary axes. So, my calculations show that contrary to the widespread opinion, the eigenvalues never merge to create a multiple one. This interesting and important behavior had not previously been observed. It should be emphasized that in my research I have changed the values of the coefficient that stands for the first order derivative in time of the unknown function {Ut). In the dissertation of R. Plant II [9], the dependence of multiple eigenvalues upon changing the density of the string, i.e., the coefficient standing before the highest derivative in time {Uu)- The fact that R. Plant obtained similar results, validates the importance of the discovery made in this thesis. The results here create more unsolved questions, and opens a rich and exciting area for future research in this area.Item Relating energy use to economic complexity(2015-05) Bond, Stephen Richard; King, Carey Wayne, 1974-Energy is a fundamental requirement for the development of any complex human system. One prevalent view suggests that societal development is a direct result of increased energy use, such that progress occurs mainly during times when a surplus of energy is available. Alternately, anthropologist Joseph Tainter posits that human systems increase in complexity as a means of solving social problems, which requires additional energy use. Tainter's theory, since it implies compulsory increases in resource use, has significant implications for long-term economic sustainability. This thesis is an attempt to provide support, or show a lack thereof, for Tainter's theory. To accomplish this, the concept of entropy, in the context of information theory, is used as an indicator of economic complexity. Economic input-output tables for 40 countries from the World Input Output Database are used to calculate these metrics, on an annual basis between 1995 and 2011. Several model boundaries, on both the global and country scales, are used to select the data for these calculations. The results are compared to energy consumption and production data from the U.S. Energy Information Administration. This thesis presents the results of this comparison in the context of quantifying Tainter's theory of the linkage between energy and complexity.Item Seasonal Precipitation Variability and Its Impact on Vegetation Dynamics under Climate Change and Aridity Spectra of the Southwest United States Ecosystems(2015-01-16) Sohoulande Djebou, Dagbegnon ClementThis study combines hydro-climatological and biological components for addressing variability in precipitation and vegetation patterns under climate change. We explore the marginal and interactive effects of vegetation and atmospheric variables in order to better understand the plausible changes in terrestrial hydrological processes. We target the southwest United States, known for its diversified ecosystem and depleting water resources. Specifically, we employ an entropy-based disorder index to address precipitation variability and evaluate the marginal effect of watershed topography. Results show that the variability gradually increases westward. We concluded a significant watershed topography effect, which suggests that hilly reliefs have a stabilizing effect on seasonal precipitation variability in time and space. We conclude the necessity to include watershed topography information in climate model parameterizations. However, the implication of a spatial precipitation gradient raises questions regarding vegetation dynamics. In order to understand these dynamics, we analyze the inclusion of precipitation variability in conjunction with the Normalized Difference Vegetation Index (NDVI) during the growing season. We identify three climatic regions based on the United Nations Aridity Index (AI): a relatively humid region with AI?0.65, an intermediate region with 0.50?AI<0.65, and a relatively dry region with AI<0.50. We target four types of vegetation covers: deciduous forest, shrubland, pasture, and grassland. We conclude significant positive trends in the NDVI series for both relatively humid and intermediate climatic regions. In the arid region, we find distinct responses to precipitation for perennial vegetation versus annual vegetation types. The magnitude of these responses tends to increase with environmental aridity. Later we apply the entropy theory to investigate the joint inclusion of precipitation, soil moisture, and temperature in vegetation dynamics analysis. Results reveal trends toward maximum entropy; however, the variable precipitation remained particularly determinant from a marginal point of view. We use a probabilistic approach to analyze the climate change impact on future precipitation patterns. We conclude significant drifts in seasonal precipitation regimes and a meaningful spatial weight. Finally, we emphasize the plausible implications of our findings for future water management. Nevertheless, we suggest further studies on the topic particularly at a global scale.Item Structure, thermodynamics and dynamics of confined and supercooled liquids(2007-05) Mittal, Jeetain; Truskett, Thomas Michael, 1973-Static measures such as density and entropy, which are intimately connected to structure, have featured prominently in modern thinking about the dynamics of the liquid state. In this dissertation, we explore the connections between self-diffusivity, density, available space, and excess entropy in two non-trivial problems in liquid state theory, confined and supercooled liquids. We present exact simulation data for the relationship between self-diffusivity and excess entropy for a wide range of simple of simple fluids (i.e. hard-sphere, Lennard-Jones and square-well) confined to pores with a variety of different sizes and fluid-wall interations. Our main finding is that, at a given temperature, self-diffusivity of the confined fluids collapses onto the bulk behavior when plotted versus excess entropy. In other words, the only information required to "predict" the implications of confinement for the single-particle dynamics is the bulk fluid behavior at a given temperature and the excess entropy of the confined fluid. This should prove practically useful given that the bulk behavior is well known for these fluid systems, and the excess entropy of the confined fluids can be readily estimated from classical density functional theory. We also show that the self-diffusivity of the confined fluids approximately collapses onto the data for the corresponding bulk fluid when plotted versus the average packing fraction (which is based on total, rather than center accessible volume). For continuous interaction potentials such as Lennard-Jones, calculation of effective packing fraction requires knowledge of both the number density of the fluid and a temperature-dependent Boltzmann diameter associated with the repulsive part of the interparticle interactions. We suggest a way to calculate this effective diameter, which to a very good approximation, collapse the temperature- and density-dependent data for the self-diffusivity of the bulk Lennard-Jones fluid onto hard-sphere fluid data plotted versus the fluid's effective packing fraction. Finally, we found that the self-diffusivities of several model systems in their supercooled state also scale exponentially not only with the excess entropy, but also with the two-body contribution to the excess entropy obtained from the pair correlation function of the fluid. The latter observation is particularly interesting because it provides direct evidence of a quantitative link between the dynamics and the average structural order of supercooled liquids. Whether such a connection could indeed be discovered is part of a long-standing question in the study of liquids.