Computational micro-flow with spectral element method and high Reynolds number flow with discontinuous Galerkin Finite Element Method

In this dissertation, two numerical methods with high order accuracy, Spectral Element Method (SEM) and Discontinuous Galerkin Finite Element Method (DG-FEM), are chosen to solve problems in Computational Fluid Dynamics (CFD). The merits of these two methods will be discussed and utilized in different kinds of CFD problems. The simulations of the micro-flow systems with complex geometries and physical applications will be presented by SEM. Moreover, the numerical solutions for the Hyperbolic Flow will be obtained by DG-FEM. By solving problems with these two methods, the differences between them will be discussed as well. Compressible Navier-Stokes equations with Electro-osmosis body force and slip boundary conditions are solved to simulate two independent models. The third order Adams-Bashforth method on time splitting, and up to the eighth order SEM on space analysis are utilized in our cases of the electro-osmosis flow (EOF). To solve the body force caused by EOF, simplification of the Poisson-Boltzmann is discussed in details. Results show that SEM can clearly simulate the electric double layers in EOF. Compared with the finite element method, which uses h-refinement to increase resolution, SEM has obvious advantages by using hp-refinement. The other case for SEM is the simulations of drug delivery through the micro needle. The drug flowing inside the needle is treated as a micro-flow system with complex geometry, while the process of drug fluxing in human skin is developed as in the case of CFD problem in porous media. Incompressible Navier-Stokes equations and Darcy-Brinkman equations are solved to simulate the drug flowing inside the needle and diffusing in human skin, respectively. Results are compared with COMSOL simulation, experimental data, and numerical solutions from Smoothed Particle Hydrodynamics (SPH). The high order DG-FEM method is chosen to do research on Hyperbolic Flow

Bioinformatics study of mammalian MRNA polydenylation

Messenger RNA polyadenylation is one of the key post-transcriptional events in mammalian cells, which have influences on many aspects of mRNA metabolism. Several human diseases have been shown to associate with abnormal polyadenylation, highlighting the importance of this process. The availability of the complete sequence of human and mouse genomes, together with their gene expression data provides valuable resources to study mRNA polyadenylation on a system level. This dissertation addresses the following issues of mammalian mRNA polyadenylation through bioinformatics approaches: (1) the extensive documentation of several key aspects of polyadenylation sites in humans and mice on a genomic level; (2) the evaluation of whether polyadenylation is an evolutionarily conserved cellular process between human and mouse ortholog genes; (3) the tissue-specificity of the regulation of alternative polyadenylation in humans and mice; (4) the development of a novel approach to use SAGE data to study polyadenylation. A database is built to comprehensively document mappings of poly(A) sites in humans and mice genome-wide. About 54% of human genes and 32% of mouse genes are shown that can undergo alternative polyadenylation. Conservation studies show that polyadenylation configurations are highly conserved in humans and mice. In addition, Gene Ontology studies identified certain functional groups of genes associated with different types of polyadenylation configurations. Furthermore, tissue-specific usage of alternative poly(A) sites is observed. Microarray data analysis and sequence analysis identified certain trans-acting factors and cis-regulatory elements that might be responsible for such regulation of alternative polyadenylation. Finally, a novel approach to use SAGE data to study alternative polyadenylation is developed and demonstrated. The results presented provide important insights into the mechanism of mRNA polyadenylation and a genomic view of the regulation of gene expression by alternative polyadenylation in mammals

Hidden Terminal-Aware Contention Resolution with an Optimal Distribution

Achieving low-power operation in wireless sensor networks with high data load or bursty traffic is challenging. The hidden terminal problem is aggravated with increased amounts of data in which traditional backoff-based contention resolution mechanisms fail or induce high latency and energy costs. We analyze and optimize Strawman, a receiver-initiated contention resolution mechanism that copes with hidden terminals. We propose new techniques to boost the performance of Strawman while keeping the resolution overhead small. We finally validate our improved mechanism via experiments