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.

Characterization of a Coal Fly Ash-Cement Slurry by the Absolute Foam Index

This dissertation established a standard foam index: the absolute foam index test. This test characterized a wide range of coal fly ash by the absolute volume of air-entraining admixture (AEA) necessary to produce a 15-second metastable foam in a coal fly ash-cement slurry in a specified time. The absolute foam index test was used to characterize fly ash samples having loss on ignition (LOI) values that ranged from 0.17 to 23.3 %wt. The absolute foam index characterized the fly ash samples by absolute volume of AEA, defined as the amount of undiluted AEA solution added to obtain a 15-minute endpoint signified by 15-second metastable foam. Results were compared from several foam index test time trials that used different initial test concentrations to reach termination at selected times. Based on the coefficient of variation (CV), a 15-minute endpoint, with limits of 12 to 18 minutes was chosen. Various initial test concentrations were used to accomplish consistent contact times and concentration gradients for the 15-minute test endpoint for the fly ash samples. A set of four standard concentrations for the absolute foam index test were defined by regression analyses and a procedure simplifying the test process. The set of standard concentrations for the absolute foam index test was determined by analyzing experimental results of 80 tests on coal fly ashes with loss on ignition (LOI) values ranging from 0.39 to 23.3 wt.%. A regression analysis informed selection of four concentrations (2, 6, 10, and 15 vol.% AEA) that are expected to accommodate fly ashes with 0.39 to 23.3 wt.% LOI, depending on the AEA type. Higher concentrations should be used for high-LOI fly ash when necessary. A procedure developed using these standard concentrations is expected to require only 1-3 trials to meet specified endpoint criteria for most fly ashes. The AEA solution concentration that achieved the metastable foam in the foam index test was compared to the AEA equilibrium concentration obtained from the direct adsorption isotherm test with the same fly ash. The results showed that the AEA concentration that satisfied the absolute foam index test was much less than the equilibrium concentration. This indicated that the absolute foam index test was not at or near equilibrium. Rather, it was a dynamic test where the time of the test played an important role in the results. Even though the absolute foam index was not an equilibrium condition, a correlation was made between the absolute foam index and adsorption isotherms. Equilibrium isotherm equations obtained from direct isotherm tests were used to calculate the equilibrium concentrations and capacities of fly ash from 0.17 to 10.5% LOI. The results showed that the calculated fly ash capacity was much less than capacities obtained from isotherm tests that were conducted with higher initial concentrations. This indicated that the absolute foam index was not equilibrium. Rather, the test is dynamic where the time of the test played an important role in the results. Even though the absolute foam index was not an equilibrium condition, a correlation was made between the absolute foam index and adsorption isotherms for fly ash of 0.17 to 10.5% LOI. Several batches of mortars were mixed for the same fly ash type increasing only the AEA concentration (dosage) in each subsequent batch. Mortar air test results for each batch showed for each increase in AEA concentration, air contents increased until a point where the next increase in AEA concentration resulted in no increase in air content. This was maximum air content that could be achieved by the particular mortar system; the system reached its air capacity at the saturation limit. This concentration of AEA was compared to the critical micelle concentration (CMC) for the AEA and the absolute foam index.