Rice University Graduate Electronic Theses and Dissertations
http://hdl.handle.net/1911/8299
2018-12-11T14:13:52ZSpace–Time Interface-Tracking Computations with Contact Between Solid Surfaces
http://hdl.handle.net/1911/103780
Space–Time Interface-Tracking Computations with Contact Between Solid Surfaces
To address the computational challenges associated with contact between moving solid surfaces, such as those in cardiovascular fluid–structure interaction (FSI), parachute FSI, and flapping-wing aerodynamics, we introduce a space–time (ST) interface-tracking method that can deal with topology change (TC). In cardiovascular FSI, our primary target is heart valves. The method is a new version of the Deforming-Spatial-Domain/Stabilized ST (DSD/SST) method, and we call it ST-TC. It includes a master–slave system that maintains the connectivity of the "parent" mesh when there is contact between the moving interfaces. It is an efficient, practical alternative to using unstructured ST meshes, but without giving up on the accurate representation of the interface or consistent representation of the interface motion. We explain the method with conceptual examples and present 2D and 3D test computations with models representative of the classes of problems we are targeting.
2014-04-25T00:00:00ZGold nanorods: Synthesis, structural manipulation, and self -assembly
http://hdl.handle.net/1911/103752
Gold nanorods: Synthesis, structural manipulation, and self -assembly
This work describes methods for the synthesis, structural manipulation, and self-assembly of one-dimensional gold nanostructures. The thesis begins with an efficient technique for the synthesis and separation of gold nanorods from a complex mixture, which has been a long standing challenge in the field of inorganic nanocrystals. The key aspect of our approach is the combination of partial oxidative dissolution and gravitational sedimentation of gold nanostructures. In addition, the length of nanorods can be tuned using reversible elongation and shortening of rods when Au (I) and Au (III) ions are used, respectively. The synthesis of extremely long gold nanowires measuring up to ∼25 µm was accomplished by this novel synthetic approach. The width of gold nanowires can also be precisely controlled by adjusting the concentration of Au (I) ions in the growth solution. This thesis also describes a procedure for the large scale synthesis of gold nanorods. The gram quantity of nearly monodisperse single crystalline nanorods was synthesized by slow reduction of Au (I) ions on the surface of pre-formed gold nanorods. This results in the amplification of nanorods without the formation of any undesirable shapes. Finally, the surface functionalization technique described in this thesis allows for the synthesis of polymer-functionalized gold nanorods. Our investigation revealed their unique ability to undergo spontaneous self-organization into ring-like superstructures. This process is templated by water microdroplets which condense from the air when a volatile organic solvent evaporates. This self-assembly does not require any lithographic technique and can organize millions of gold nanorods into rings in a matter of seconds.
2009-01-01T00:00:00ZNumerical solutions of matrix equations arising in model reduction of large-scale linear -time -invariant systems
http://hdl.handle.net/1911/103751
Numerical solutions of matrix equations arising in model reduction of large-scale linear -time -invariant systems
This thesis presents and analyzes new algorithms for matrix equations arising from model reduction of linear-time-invariant (LTI) systems. Such systems arise in a variety of areas, especially in circuit simulation. When an integrated circuit has millions of devices, performing a full-system simulation can be infeasible due to the time required for the nonlinear solver to compute the solution of large linearized systems. Model reduction becomes indispensable since model reduction techniques aim to produce low-dimensional systems that capture the same response characteristics as the originals while enabling substantial improvement in simulation time and resulting in greatly reduced storage requirements. One of the crucial physical features of LTI systems in circuit simulation is passivity, which is essential to preserve during model reduction. Passivity preserving model reduction using the invariant subspace method in conjunction with positive real balancing for LTI systems provides an error bound and involves the solution of two Riccati equations. The contributions of this thesis are fourfold. First, a generalization of the invariant subspace method for passivity preserving model reduction is presented for LTI systems in descriptor form. Second, two iterative algorithms to compute the solution of the two algebraic Riccati equations are derived. Even though these two iterative algorithms have been in existence, the thesis introduces them here in addition with specific conditions on LTI systems for their convergence. At each step of either iteration, a pair of Lyapunov equations result. The thesis next investigates a parameter free ADI-like (PFADI) method for the solution of the Lyapunov equation. This PFADI method involves the solution of the Sylvester equation at each step, and its computational complexity depends on how efficiently the solution of the Sylvester equation is obtained. The final part of the thesis is devoted to the study of two techniques to solve the Sylvester equation. The first technique is to obtain the solution of the Sylvester equation via that of an invariant subspace problem. The thesis presents a complete analysis and an efficient algorithm to compute the optimal real shift for the Cayley transformation used in the invariant subspace technique. The analysis is then generalized for multiple optimal real shift selection for the ADI technique for the solution of the Sylvester equation.
2009-01-01T00:00:00ZGivenness and explanation: A phenomenological response to naturalist accounts in religious studies
http://hdl.handle.net/1911/103750
Givenness and explanation: A phenomenological response to naturalist accounts in religious studies
This dissertation contributes to ongoing scholarship regarding the phenomenology of religion by engaging it with debates in Religious Studies between naturalist methodologies, which reduce religious experience to social-scientific terms, and descriptive methodologies, which argue religious experience cannot be explained in nonreligious terms lest we lose that which is religious about the experience. I propose that in the phenomenology of Jean-Luc Marion, specifically in his phenomenology of revelation, we find a methodology that avoids the reductionism of the naturalist method while still explaining religion in a manner that avoids the apologetics associated with descriptive accounts of religion.
2009-01-01T00:00:00Z