Elliptic Selberg integrals and conformal blocks

We present an elliptic version of Selberg's integral formula.Comment: 13 page

Effective Training Methods for Deans and Administrative Managers of Virginia Western Community College

The purpose of this study was to determine the most effective delivery methods for training deans and administrative managers to be better communicators and morale boosters at Virginia Western Community College for continued professional development and create better office morale

Modeling Stromatolite Formation with Diffusion-Limited Aggregation

Stromatolites, microbialites, and other microbially induced sedimentary structures exist in the rock record as far back as 3.6 billion years ago and continue to form in the present day. Better characterizing these structures and better understanding how they form is crucial in distinguishing these biosignatures from similar, abiotic structures, which can help us to understand the conditions of early Earth and early Mars. To that end, I have modified DLA 3D EXT, an open-source stromatolite modeling program, to more closely reflect the process of microbial trapping-and-binding by filamentous microbes in a calcite-precipitating hot spring system. This modified program includes a field of upright spikes that can trap incoming particles and sediment. I simulated stromatolites forming with different spike heights, spike spacings, and stickiness. To quantify these stromatolites’ morphologies, I obtained the fractal dimension and lacunarity of a section of each resulting structure. I found that stickiness affects morphology as measured by both fractal dimension and lacunarity. This may help us better distinguish true stromatolites from abiotic imposters

Modeling space-time correlations of velocity fluctuations in wind farms

An analytical model for the streamwise velocity space-time correlations in turbulent flows is derived and applied to the special case of velocity fluctuations in large wind farms. The model is based on the Kraichnan-Tennekes random sweeping hypothesis, capturing the decorrelation in time while including a mean wind velocity in the streamwise direction. In the resulting model, the streamwise velocity space-time correlation is expressed as a convolution of the pure space correlation with an analytical temporal decorrelation kernel. Hence, the spatio-temporal structure of velocity fluctuations in wind farms can be derived from the spatial correlations only. We then explore the applicability of the model to predict spatio-temporal correlations in turbulent flows in wind farms. Comparisons of the model with data from a large eddy simulation of flow in a large, spatially periodic wind farm are performed, where needed model parameters such as spatial and temporal integral scales and spatial correlations are determined from the large eddy simulation. Good agreement is obtained between the model and large eddy simulation data showing that spatial data may be used to model the full temporal structure of fluctuations in wind farms.Comment: Submitted to Wind Energ