Deterministic Solutions for a Step-growth Polymerization

Chain topology, including branch node, chain link and cross-link dynamics that contribute to the number of elastically active strands and junctions, are calculated using purely deterministic derivations. Solutions are not coupled to population density distributions. An eigenzeit transformation assists in the conversion of expressions derived by chemical reaction principles from time to conversion space, yielding transport phenomena type expressions where the rate of change in the molar concentrations of branch nodes with respect to conversion is expressed as functions of the fraction of reactive sites on precursors and reactants. Analogies are hypothesized to exist in cross-linking space that effectively distribute branch nodes with i reacted moieties between cross-links having j bonds extending to the gel. To obtain solutions, reacted sites on nodes or links with finite chain extensions are examined in terms of stoichiometry associated with covalent bonding. Solutions replicate published results based on Miller and Macosko’s recursive procedure and results obtained from truncated weighted sums of population density distributions as suggested by Flory.

An Investigation of Wild Bee Diversity and Abundance in Plots Managed by The Nature Conservancy in South-Central Nebraska and of Beneficial Arthropods Associated with Native Nebraska Flora

Insect pollination is an essential ecosystem service, and bees are the principal pollinators of wild and cultivated plants. Habitat management and enhancement are a proven way to encourage wild bee populations, providing them with food and nesting resources. I examined bee diversity and abundance in plots managed by The Nature Conservancy near Wood River, NE. The plots were seeded with 2 seed mixes at 2 seeding rates: high diversity mix at the recommended rate, high diversity mix double the recommended rate, Natural Resources Conservation Service (NRCS) conservation planting (CP) 25 mix at one-half the recommended rate, and NRCS CP25 mix at the recommended rate. I measured wild bee abundance and diversity, and established a database of wild bees associated with the plots. I also compared genus richness and abundance among the plots using and aerial net and blue vane traps to collect bees. Significant differences were not observed in genus richness and diversity among the plots; however, plot size and the ability of blue vane traps to draw bees from a long distance may have influenced my results. In 2008, 15 genera and 95 individual bees were collected using an aerial net and in 2009, 32 genera and 6,103 individual bees were collected using blue vane traps. I also studied the beneficial insects associated with native Nebraska flora. Seventeen species of native, perennial flora were established in 3 separate plots located in eastern Nebraska. I transplanted four plants of each species in randomized 0.61 m x 0.61 m squares of a 3.05 m x 9.14 m plot. Arthropods were sampled using a modified leaf blower/vacuum. Insects and other arthropods were identified to family and organized into groups of predators, parasites, pollinators, herbivores, and miscellaneous. Associations between plant species and families of beneficial arthropods (predators, parasites, and pollinators) were made. Pycnanthemum flexuosum Walter attracted significantly more beneficial arthropod families than 7 other species of plants tested. Dalea purpurea Vent and Liatris punctata Hook also attracted significantly fewer beneficial arthropod families than 4 other species of plants tested. In total, 31 predator, 11 parasitic, 4 pollinator, 31 herbivore, and 10 miscellaneous families of arthropods were recorded.