Browsing by Subject "Continuum"
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Item Complexity of atriodic continua(Texas Tech University, 2009-05) Kennaugh, Christopher T.; Lewis, Wayne; Byerly, Robert E.; Gelca, RazvanThis dissertation investigates the relative complexity between a continuum and its proper subcontinua, in particular, providing examples of atriodic n-od-like continua. Let X be a continuum and n be an integer greater than or equal to three. If X is homeomorphic to an inverse limit of simple-n-od graphs with simplicial bonding maps and is simple-(n-1)-od-like, it is shown that the bonding maps can be simplicially factored through a simple-(n-1)-od. This implies, in particular, that X is homeomorphic to an inverse limit of simple-(n-1)-od graphs with simplicial bonding maps. This factoring is subsequently used to show that a specific inverse limit of simple-n-ods with simplicial bonding maps, having the property of every proper nondegenerate subcontinuum being an arc, is not simple-(n-1)-od-like.Item Expansive homeomorphisms and indecomposable subcontinua(Texas Tech University, 1998-08) Mouron, Christopher G.It is the goal of this dissertation to classify which continua admit expansive homeomorphisms and which do not. Plykin's attractors [12] and the dyadic solenoid [16]are examples of continua that admit an expansive homeomorphism. Both of these continua have the property of being indecomposable. A continuum is decomposable if it is the union of two proper subcontinuum. A continuum is indecomposable if it is not decomposable. Indecomposable continua are created by stretching and bending arcs an infinite number of times back and forth. Intuitively, it appears that in order to have expansiveness, the subset of the continuum between points that are close to each other would have to be continually stretched in order to move points away from each other. However, because of compactness, some folding or wrapping must also occur. Every known continuum that admits an expansive homeomorphism has an indecomposable subcontinuum. Thus, one of the major questions in this-area is "If X admits an expansive homeomorphism, must X contain a nondegenerate indecomposable subcontinuum?". However, it is known that X being indecomposable is not necessary. For example, it will be shown later that there exists an expansive homeomorphism of the solenoid that contains a fixed point. If we attach two solenoids at that fixed point, the resulting space will admit an expansive homeomorphism and be decomposable. However, the resulting space will clearly contain subcontinua that are indecomposable.Item Quantifying electrostatic fields at protein interfaces using classical electrostatics calculations(2015-08) Ritchie, Andrew William; Webb, Lauren J.; Elber, Ron; Fast, Walter; Henkelman, Graeme; Ren, PengyuThe functional aspects of proteins are largely dictated by highly selective protein- protein and protein-ligand interactions, even in situations of high structural homology, where electrostatic factors are the major contributors to selectivity. The vibrational Stark effect (VSE) allows us to measure electrostatic fields in complex environments, such as proteins, by the introduction of a vibrational chromophore whose vibrational absorption energy is linearly sensitive to changes in the local electrostatic field. The works presented here seek to computationally quantify electrostatic fields measured via VSE, with the eventual goal of being able to quantitatively predict electrostatic fields, and therefore Stark shifts, for any given protein-interaction. This is done using extensive molecular dynamics in the Amber03 and AMOEBA force fields to generate large ensembles the GTPase Rap1a docked to RalGDS and [superscript p]²¹Ras docked to RalGDS. We discuss how side chain orientations contribute to the differential binding of different mutations of Rap1a binding to RalGDS, where it was found that a hydrogen-bonding pocket is disrupted by the mutation of position 31 from lysine to glutamic acid. We then show that multi-dimensional umbrella sampling of the probe orientations yields a wider range of accessible structures, increasing the quality of the ensembles generated. A large variety of methods for calculating electrostatic fields are presented, with Poisson- Boltzmann electrostatics yielding the most consistent, reliable results. Finally, we explore using AMOEBA for both ensemble-generation as well as the electrostatic description of atoms for field calculations, where early results suggest that the electrostatic field due to the induce dipole moment of the probe is responsible for predicting qualitatively correct Stark shifts.