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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Direct Calculation Of Configurational Entropy: Pair Correlation Functions And Disorder, Clifton C. Sluss
Direct Calculation Of Configurational Entropy: Pair Correlation Functions And Disorder, Clifton C. Sluss
Doctoral Dissertations
Techniques such as classical molecular dynamics [MD] simulation provide ready access to the thermodynamic data of model material systems. However, the calculation of the Helmholtz and Gibbs free energies remains a difficult task due to the tedious nature of extracting accurate values of the excess entropy from MD simulation data. Thermodynamic integration, a common technique for the calculation of entropy requires numerous simulations across a range of temperatures. Alternative approaches to the direct calculation of entropy based on functionals of pair correlation functions [PCF] have been developed over the years. This work builds upon the functional approach tradition by extending …
Linked-Cluster Expansions For Lattice Spin Models, Yuyi Wan
Linked-Cluster Expansions For Lattice Spin Models, Yuyi Wan
Honors Theses
Similar to various series expansions that are used to approximate mathematical func- tions, the linked-cluster expansion is an approximation method that allows us to approach the actual values of a very large physical system’s different physical quan- tities by systematically studying smaller systems embedded in this larger system. The main concept in linked-cluster expansion, weight, represents the additional con- tribution to a certain physical quantity by increasing the system size by one unit. These weights are used to eventually build up the result on a larger system. In our case, we focus on the partition function, a quantity that can …
Some Results On A Class Of Functional Optimization Problems, David Rushing Dewhurst
Some Results On A Class Of Functional Optimization Problems, David Rushing Dewhurst
Graduate College Dissertations and Theses
We first describe a general class of optimization problems that describe many natu- ral, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances of these problems in statistical physics, facility allocation, and machine learning. A dynamic description and statement of a partial inverse problem follow. When attempting to optimize the state of a system governed by the generalized equipartitioning princi- ple, it is vital to understand the nature of the governing probability distribution. We show that optimiziation for the incorrect probability distribution can have catas- trophic results, e.g., …
Quantum Groups And Knot Invariants, Greg A. Hamilton
Quantum Groups And Knot Invariants, Greg A. Hamilton
Honors Theses
Knot theory arguably holds claim to the title of the mathematical discipline with the most unusually diverse applications. A knot can be defined topologically as an embedding of S1 in R3. Naturally, two knots are topologically equivalent if one cannot be smoothly deformed into the other. The question of whether two knots are equivalent is highly non-trivial, and so the question of knot invariants used to distinguish knots has occupied knot theorists for over a century. Knot theory has found application in statistical mechanics [1], symbolic logic and set theory [2], quantum fi theory [3], quantum computing [4], etc. …
Theoretical Investigations Of Gas Sorption And Separation In Metal-Organic Materials, Tony Pham
Theoretical Investigations Of Gas Sorption And Separation In Metal-Organic Materials, Tony Pham
USF Tampa Graduate Theses and Dissertations
Metal--organic frameworks (MOFs) are porous crystalline materials that are synthesized from rigid organic ligands and metal-containing clusters. They are highly tunable as a number of different structures can be made by simply changing the organic ligand and/or metal ion. MOFs are a promising class of materials for many energy-related applications, including H2 storage and CO2 capture and sequestration. Computational studies can provide insights into MOFs and the mechanism of gas sorption and separation. Theoretical studies on existing MOFs are performed to determine what structural characteristics leads to favorable gas sorption mechanisms. The results from these studies can provide …
Spatiotemporally Periodic Driven System With Long-Range Interactions, Owen Dale Myers
Spatiotemporally Periodic Driven System With Long-Range Interactions, Owen Dale Myers
Graduate College Dissertations and Theses
It is well known that some driven systems undergo transitions when a system parameter is changed adiabatically around a critical value. This transition can be the result of a fundamental change in the structure of the phase space, called a bifurcation. Most of these transitions are well classified in the theory of bifurcations. Among the driven systems, spatiotemporally periodic (STP) potentials are noteworthy due to the intimate coupling between their time and spatial components. A paradigmatic example of such a system is the Kapitza pendulum, which is a pendulum with an oscillating suspension point. The Kapitza pendulum has the strange …
Theoretical And Numerical Studies Of Phase Transitions And Error Thresholds In Topological Quantum Memories, Pejman Jouzdani
Theoretical And Numerical Studies Of Phase Transitions And Error Thresholds In Topological Quantum Memories, Pejman Jouzdani
Electronic Theses and Dissertations
This dissertation is the collection of a progressive research on the topic of topological quantum computation and information with the focus on the error threshold of the well-known models such as the unpaired Majorana, the toric code, and the planar code. We study the basics of quantum computation and quantum information, and in particular quantum error correction. Quantum error correction provides a tool for enhancing the quantum computation fidelity in the noisy environment of a real world. We begin with a brief introduction to stabilizer codes. The stabilizer formalism of the theory of quantum error correction gives a well-defined description …
Deriving The Density Of States For Granular Contact Forces, Philip Metzger
Deriving The Density Of States For Granular Contact Forces, Philip Metzger
Electronic Theses and Dissertations
The density of single grain states in static granular packings is derived from first principles for an idealized yet fundamental case. This produces the distribution of contact forces P_f(f) in the packing. Because there has been some controversy in the published literature over the exact form of the distribution, this dissertation begins by reviewing the existing empirical observations to resolve those controversies. A method is then developed to analyze Edwards' granular contact force probability functional from first principles. The derivation assumes Edwards' flat measure -- a density of states (DOS) that is uniform within the metastable regions of phase space. …
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Statistical Mechanics Of Farey Fraction Spin Chain Models, Jan Fiala
Electronic Theses and Dissertations
This thesis considers several statistical models defined on the Farey fractions. Two of these models, considered first, may be regarded as "spin chains", with long-range interactions, another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle-Perron-F'robenius operator), which is defined using the maps (presentation functions) generating the Farey "tree". The spectrum of this operator was completely determined by Prellberg. It follows that all these models have a second-order phase transition with a specific …