Fixed block configuration GDDs with block size 6 and (3, r)-regular graphs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Most of the definitions used in the thesis will be defined, and we provide a basic survey of topics in graph theory and design theory pertinent to the topics studied in this thesis. In Chapter 2, we are concerned with the study of fixed block configuration group divisible designs, GDD(n; m; k; λ1; λ2). We study those GDDs in which each block has configuration (s; t), that is, GDDs in which each block has exactly s points from one of the two groups and t points from the other. Chapter 2 begins with an overview of previous results and constructions for small group size and block sizes 3, 4 and 5. Chapter 2 is largely devoted to presenting constructions and results about GDDs with two groups and block size 6. We show the necessary conditions are sufficient for the existence of GDD(n, 2, 6; λ1, λ2) with fixed block configuration (3; 3). For configuration (1; 5), we give minimal or nearminimal index constructions for all group sizes n ≥ 5 except n = 10, 15, 160, or 190. For configuration (2, 4), we provide constructions for several families ofGDD(n, 2, 6; λ1, λ2)s. Chapter 3 addresses characterizing (3, r)-regular graphs. We begin with providing previous results on the well studied class of (2, r)-regular graphs and some results on the structure of large (t; r)-regular graphs. In Chapter 3, we completely characterize all (3, 1)-regular and (3, 2)-regular graphs, as well has sharpen existing bounds on the order of large (3, r)- regular graphs of a certain form for r ≥ 3. Finally, the appendix gives computational data resulting from Sage and C programs used to generate (3, 3)-regular graphs on less than 10 vertices.

Implementation of porous silicon technology for a fluidic flow-through optical sensor for pH measurements

This work presents an innovative integration of sensing and nano-scaled fluidic actuation in the combination of pH sensitive optical dye immobilization with the electro-osmotic phenomena in polar solvents like water for flow-through pH measurements. These flow-through measurements are performed in a flow-through sensing device (FTSD) configuration that is designed and fabricated at MTU. A relatively novel and interesting material, through-wafer mesoporous silica substrates with pore diameters of 20 -200 nm and pore depths of 500 µm are fabricated and implemented for electro-osmotic pumping and flow-through fluorescence sensing for the first time. Performance characteristics of macroporous silicon (> 500 µm) implemented for electro-osmotic pumping include, a very large flow effciency of 19.8 µLmin-1V-1 cm-2 and maximum pressure effciency of 86.6 Pa/V in comparison to mesoporous silica membranes with 2.8 µLmin-1V-1cm-2 flow effciency and a 92 Pa/V pressure effciency. The electrical current (I) of the EOP system for 60 V applied voltage utilizing macroporous silicon membranes is 1.02 x 10-6A with a power consumption of 61.74 x 10-6 watts. Optical measurements on mesoporous silica are performed spectroscopically from 300 nm to 1000 nm using ellipsometry, which includes, angularly resolved transmission and angularly resolved reflection measurements that extend into the infrared regime. Refractive index (n) values for oxidized and un-oxidized mesoporous silicon sample at 1000 nm are found to be 1.36 and 1.66. Fluorescence results and characterization confirm the successful pH measurement from ratiometric techniques. The sensitivity measured for fluorescein in buffer solution is 0.51 a.u./pH compared to sensitivity of ~ 0.2 a.u./pH in the case of fluorescein in porous silica template. Porous silica membranes are efficient templates for immobilization of optical dyes and represent a promising method to increase sensitivity for small variations in chemical properties. The FTSD represents a device topology suitable for application to long term monitoring of lakes and reservoirs. Unique and important contributions from this work include fabrication of a through-wafer mesoporous silica membrane that has been thoroughly characterized optically using ellipsometry. Mesoporous silica membranes are tested as a porous media in an electro-osmotic pump for generating high pressure capacities due to the nanometer pore sizes of the porous media. Further, dye immobilized mesoporous silica membranes along with macroporous silicon substrates are implemented for continuous pH measurements using fluorescence changes in a flow-through sensing device configuration. This novel integration and demonstration is completely based on silicon and implemented for the first time and can lead to miniaturized flow-through sensing systems based on MEMS technologies.

Regulation of woody plant development by auxin and polar auxin transport

Auxin is a key regulator in plant growth and development. This dissertation examines the role of auxin and polar auxin transport in woody growth and development. Strategies of promoter reporter system, microarray expression analysis, transgenic modification, physiological assays, anatomical analysis, and histochemical/biochemical assays were employed to improve our understanding of auxin study in Populus. The results demonstrate various aspects of auxin regulation on shoot growth, root development, wood formation, and gravitropism in woody tissues. We describe the behavior of the DR5 reporter system for measuring auxin concentrations and response in stably transformed Populus trees. Our study shows that DR5 reporter system can be efficiently used in Populus to study auxin biology at a cellular resolution. We investigated the global gene expression in responding to auxin in Populus root. The results revealed groups of IBA up- and down- regulated genes involved in various biological processes including cell wall modification, root growth and lateral root formation, transporter activity and hormone crosstalk. We also verify two of the identified genes' function by transgenic modification in Populus, which encode auxin efflux carrier PtPIN9 and transcription factor PtERF72. We investigated the role of PtPIN9 in woody growth and development, especially in wood formation and gravitropic response in woody stem. We found that overexpressing PtPIN9 enhanced several growth parameters while suppression of PtPIN9 has inhibited tension wood formation. Our results show that PIN9 and other members from PIN family could be possible useful tools for increasing biomass productivity, wood quality, or in modifying plant form.