Browsing by Subject "Computational"
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Item A computational model for the diffusion coefficients of DNA with applications(2010-05) Li, Jun, 1977-; Gonzalez, Oscar, 1968-; Demkowicz, Leszek F.; Makarov, Dmitrii E.; Rodin, Gregory J.; van de Geijn, Robert A.The sequence-dependent curvature and flexibility of DNA is critical for many biochemically important processes. However, few experimental methods are available for directly probing these properties at the base-pair level. One promising way to predict these properties as a function of sequence is to model DNA with a set of base-pair parameters that describe the local stacking of the different possible base-pair step combinations. In this dissertation research, we develop and study a computational model for predicting the diffusion coefficients of short, relatively rigid DNA fragments from the sequence and the base-pair parameters. We focus on diffusion coefficients because various experimental methods have been developed to measure them. Moreover, these coefficients can also be computed numerically from the Stokes equations based on the three-dimensional shape of the macromolecule. By comparing the predicted diffusion coefficients with experimental measurements, we can potentially obtain refined estimates of various base-pair parameters for DNA. Our proposed model consists of three sub-models. First, we consider the geometric model of DNA, which is sequence-dependent and controlled by a set of base-pair parameters. We introduce a set of new base-pair parameters, which are convenient for computation and lead to a precise geometric interpretation. Initial estimates for these parameters are adapted from crystallographic data. With these parameters, we can translate a DNA sequence into a curved tube of uniform radius with hemispherical end caps, which approximates the effective hydrated surface of the molecule. Second, we consider the solvent model, which captures the hydrodynamic properties of DNA based on its geometric shape. We show that the Stokes equations are the leading-order, time-averaged equations in the particle body frame assuming that the Reynolds number is small. We propose an efficient boundary element method with a priori error estimates for the solution of the exterior Stokes equations. Lastly, we consider the diffusion model, which relates our computed results from the solvent model to relevant measurements from various experimental methods. We study the diffusive dynamics of rigid particles of arbitrary shape which often involves arbitrary cross- and self-coupling between translational and rotational degrees of freedom. We use scaling and perturbation analysis to characterize the dynamics at time scales relevant to different classic experimental methods and identify the corresponding diffusion coefficients. In the end, we give rigorous proofs for the convergence of our numerical scheme and show numerical evidence to support the validity of our proposed models by making comparisons with experimental data.Item Computational, theoretical investigation of materials for a sustainable energy future(2016-08) Stauffer, Shannon Kaylie; Henkelman, Graeme; Mullins, Charles B; Crooks, Richard; Hwang, Gyeong; Milliron, DeliaOver the past several decades there has been significant progress in electronic structure theory, statistical sampling algorithms and computational resources which can be leveraged to calculate fundamental properties of materials and estimate rates of relevant chemical reactions. In the following dissertation, I use computational methods to address the materials problem of a sustainable energy future. Energy storage technologies have played a vital role in the mobile-technology revolution and the transition to utilize more sustainable energy sources; however improvements to the energy density, charge/discharge rate, and safety of rechargeable batteries are needed to realize the ambitious goals of fully electric vehicles and on-grid storage in areas with intermittent, renewable power sources. Li-ion batteries, in general, have a potential to fulfill these demands. In the following work, a new, high energy density electrode material with little capacity loss is considered. Additionally, the complex interaction between an electrode/electrolyte model system is considered in a potential dependent computational framework. Having a sustainable energy future also means utilizing energy-efficient processing in industrial scale applications. Separation processes use roughly 12% of all energy consumed in the United States due to energy-intensive thermal separation techniques. A final study looks at an alloy catalysts for the separation of ethylene from ethane/ethylene mixtures. A unique selectivity property was discovered that may help design catalysts to replace thermal separation of gases.Item Diagonal plus low rank approximation of matrices for solving modal frequency response problems(2010-12) Vargas, David Antonio; Bennighof, Jeffrey Kent, 1960-; Sirohi, JayantIf a structure is composed mainly of one material but contains a small amount of a second material, and if these two materials have significantly different levels of structural damping, this can increase the cost of solving the modal frequency response problem substantially. Even if the rank of the contribution to the finite element structural damping matrix from the second material is very low, the matrix becomes fully populated when transformed to the modal representation. As a result, the complex-valued modal matrix that represents the structure’s stiffness and structural damping is both full rank, because of the diagonal part contributed by the stiffness, and fully populated, because of off-diagonal imaginary terms contributed by the second material’s structural damping. Solving the modal frequency response problem at many frequencies requires either the factorization of a coefficient matrix at every frequency, or the solution of a complex symmetric eigenvalue problem associated with the modal stiffness/structural damping matrix. The cost of both of these approaches is proportional to the cube of the number of modes included in the analysis. This cost could be reduced greatly if the damping properties of the structure were handled carefully in modeling the structure, but in practical computation of the modal frequency response, the information that could potentially reduce the computational cost is often unavailable. This thesis explores the possibilities of obtaining a representation of the complex modal stiffness/structural damping matrix as a diagonal matrix plus a matrix of minimal rank. An algorithm for computing a “diagonal plus low rank” (DPLR) representation is developed, along with an iterative algorithm for using an inexact DPLR approximation in the solution of the modal frequency response problem. The behavior of these algorithms is investigated on several example problems.Item Fatigue behavior of post-installed shear connectors used to strengthen continuous non-composite steel bridge girders(2016-08) Ghiami Azad, Amir Reza; Engelhardt, Michael D.; Williamson, Eric B., 1968-; Helwig, Todd A; Jirsa, James O; Taleff, Eric MMany older bridges in Texas are constructed with floor systems consisting of a concrete slab over steel girders. A potentially economical means of strengthening these floor systems is to connect the existing concrete slab and steel girders using post-installed shear connectors to change the behavior of the beam from non-composite to partially-composite. Since fatigue is one of the main concerns in designing bridges, investigating the fatigue properties of these post-installed shear connectors becomes crucial. Results from direct-shear testing show that post-installed shear connectors have a better fatigue life compared to conventional welded shear studs. However, based on currently available data from direct-shear tests, fatigue life of post-installed shear connectors is still inadequate for economical retrofit in some cases. Furthermore, it is unclear if direct-shear tests provide an appropriate means of evaluating fatigue performance. The objective of this dissertation is to develop new and more accurate approaches for evaluating the fatigue characteristics of post-installed shear connectors. This objective is addressed through large-scale beam fatigue tests and computational studies. The focus of the work is on evaluating fatigue life of shear connectors based on both slip and stress demands.Item Logos Ex Machina: A reasoned approach toward Cancer(2012-05) Avila, Andrew; Gollahon, Lauren; Strauss, Richard E.; Rice, Sean H.; Butler, Boyd; Watson, RichardLimitations in our current ability to integrate a diverse spectrum of genetic information in an effort to elucidate the underlying causes of cancer has spawned the need for a novel cancer modeling approach. Public repositories of biological pathways and gene expression experiments were combined in order to provide a systems biology approach toward cancer. Furthermore, by unifying these sources of knowledge, the ability to predict expression levels of unmeasured genes was developed. This technique was then applied to a variety of cancer types in order to resolve commonalities between heretofore divergent (or disparate) cancers. The results generated in this manner revealed characteristics that challenge the current prevailing paradigm of cancer. Specifically, the predicted results, according to the Somatic Mutation Theory of Cancer, of a significant upregulation of oncogenes and a significant downregulation of tumor suppressor genes was not found. In contrast, it was found that oncogenes were significantly downregulated and tumor suppressor genes were upregulated among the cancers examined. Furthermore, the results demonstrate the differential expression, in cancer cells, of genes involved in the cellular differentiation and wound healing processes. These results were used as a springboard to develop a novel oncogenesis hypothesis, named Umbracesis. In short, the Umbracesis hypothesis proposes that disruption of the wound healing process via carcinogens, occurs in such a way as to prevent organismic homeostasis from being recovered or prevent full re-differentiation of dedifferentiated cells. The former concept is implicated in inflammatory cancers. Whereas the latter concept, is implicated in cancers that show characteristics associated with embryonic tissues. It was concluded, that the instrumental use of the modeling approach, developed within this study, has implications beyond cancer and may be of use within other areas of biomedical concern.Item Transport in higher dimensional phase spaces(2016-12) Curry, Christopher Timothy; Morrison, Philip J.; Horton, Jr., Claude W; Hazeltine, Richard; Matzner, Richard; Gamba, IreneWe use a four dimensional symplectic mapping, the coupled cubic-quadratic map, to provide evidence of Arnol’d Diffusion in phase space. We use the method of frequency analysis for dynamical systems to demonstrate the existence of regular orbits, and show that these orbits enclose weakly chaotic orbits which escape in finite time around the tori. A new collocation method for frequency analysis is employed by adapting it to allow for higher precision results. Arbitrary precision numerics are used to obtain highly accurate orbits for long timescales, and the adapted frequency method is used to obtain highly accurate frequencies of the mapping. We review the method of frequency analysis, demonstrate its effectiveness and accuracy in determining frequencies and finding tori in simple systems and low-dimensional mappings, and extend the results to higher dimensions. In the four dimensional mapping, we find several regular orbits with irrational frequency ratios, indicating the existence of tori in the phase space, as well as interior orbits that escape around these tori.