Diffraction from visible lattice points and k-th power free integers

We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settles previous speculation on the exact nature of the diffraction in this situation, see math-ph/9903046 and references therein. Using similar methods we show the same result for the 1-dimensional set of k-th power free integers with k at least 2. Of special interest is the fact that neither of these sets is a Delone set --- each has holes of unbounded inradius. We provide a careful formulation of the mathematical ideas underlying the study of diffraction from infinite point sets.Comment: 45 pages, with minor corrections and improvements; dedicated to Ludwig Danzer on the occasion of his 70th birthda

Using Videoconferencing to Establish and Maintain a Social Presence in Online Learning Environments

For 30 years, the educational administration program faculty at Fort Hays State University (FHSU) followed a traditional face-to-face (F2F) on campus approach to course delivery

Escape tactics used by bluegills and fathead minnows to avoid predation by tiger muskellunge

To explain why esocids prefer cylindrical, soft-rayed prey over compressed, spiny-rayed prey, we quantified behavioral interaction between tiger muskellunge (F1 hybrid of male northern pike Esox lucius and female muskellunge E. masquinongy) and fathead minnows (Pimephales promelas) and bluegills (Lepomis macrochirus). Tiger muskellunge required four times as many strikes and longer pursuits to capture bluegills than fathead minnows. Tiger muskellunge attacked each prey species differently; fathead minnows were grasped at midbody and bluegills were attacked in the caudal area. Each prey species exhibited different escape tactics. Fathead minnows remained in open water and consistently schooled; bluegills dispersed throughout the tank and sought cover by moving to corners and edges. Due to their antipredatory behavior (dispersing, cover seeking, and remaining motionless) and morphology (deep body and spines), bluegills were less susceptible to capture by tiger muskellunge than were fathead minnows.Funding for this project was provided by the Federal Aid in Fish Restoration Act under Dingell-Johnson Project F-57-R

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Performance of a Pilot-Scale Air Sparged Continuous Flow Reactor and Hydrocyclone for Struvite Precipitation and Removal from Liquid Swine Manure

The objective of this research was to test a pilot-scale air sparged tank reactor (ASTR) and the ASTR in combination with a hydrocyclone (called the pilot-scale ASTR-hydrocyclone system) on two swine manure slurries for struvite-based (MgNH4PO4-6H2O) phosphorus removal and recovery. The pilot-scale ASTR system operated at flow rates of 80 to 115 L/min and was based on the bench-scale design from Shepherd et al. (2007). The ASTR effluent was processed using a hydrocyclone separator for struvite separation and total phosphorus (TP) recovery. The pilot-scale ASTR-hydrocyclone system provided a 92% reduction of dissolved reactive phosphorus (DRP) in manure slurry from a swine finishing facility concrete storage tank and a 91% reduction of DRP in manure slurry collected from a swine finishing facility deep-pit under floor collection system. The pilot-scale ASTR-hydrocyclone system removed 18% of TP in swine manure from a concrete storage tank and 9% to 14% of TP in swine manure slurry from a deep-pit under floor collection system. The low TP recovery was attributed to the hydrocyclones inability to provide effective struvite separation as operated. Full-scale economics and implementation of the tested struvite-based phosphorus removal is discussed. A case study of a typical Iowa deep-pit swine production facility (10,000 head/year) indicated that the annual cost of struvite-based phosphorus removal using this system would be approximately $8.88/finished pig or$0.035/L manure slurry treated ($ 0.134/gal). This cost often exceeds producer\u27s profit margins; this indicates that struvite-based phosphorus removal using this ASTR-hydrocyclone system in swine finisher manure slurries is not currently economically viable

Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces

Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his 65th birthda