The Euler characteristic of the Whitehead automorphism group of a free product

A combinatorial summation identity over the lattice of labelled hypertrees is established that allows one to gain concrete information on the Euler characteristics of various automorphism groups of free products of groups.Comment: 19 pages, 3 figures, to appear in Trans. Amer. Math. So

Combinatorial conditions that imply word-hyperbolicity for 3-manifolds

Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piecewise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The proof involves a mixture of computer computation and techniques from small cancellation theory.Comment: (21 pages) To appear in Topolog

Digital radar receiver design based on highly efficient bandpass sampling FPGA architecture

Thesis (M.S.)--University of Oklahoma, 2009.Includes bibliographical references (leaves 62-64).As digital electronics become faster and more efficient, it becomes possible to move the analog/digital interface in a radar downconversion system further towards the antenna. Instead of digitizing radar echoes at the end of the down-conversion process, digital logic can perform the same operations previously performed by analog components. Taking full advantage of this opportunity will result in a more highly integrated and reconfigurable design. By removing unnecessary analog components, the error from component variability and noise injected into the signal of interest is reduced, the size of the receiver and the power required for operation is minimized, and the overall cost of the system can be lowered. This research is focused on employing software defined radio concepts for weather observation, thus creating a low-cost digital radar receiver at the University of Oklahoma for use in radar projects as a way of obviating the need for commmercial radar receivers, which can be many times more expensive. Software-defined radio techniques, such as bandpass sampling, are used to achieve a high data processing bandwidth and oversampling ratio with the smallest logic resource utilization. Two novel digital receiver designs are discussed in this thesis. A prototype compact single-channel digital receiver based on a 14-bit analog-to-digital converter and a hand-solderable Xilinx FPGA was built and tested both in the laboratory and at the National Weather Radar Testbed (NWRT). Building on the lessons learned from testing the single-channel digital radar receiver, a second digital receiver was designed for expanded capabilities. Through the utilization of a low-power, simultaneous-sampling eight channel ADC with high-speed serial data links and a cost-efficient FPGA with integrated DSP slices, eight data channels can be digitized, processed and transferred at the same time in a compact form factor. An ethernet interface has been included which allows for a scalable control channel so that the digital receiver's operations can be quickly modified. This also makes it possible to remotely change the firmware of the FPGA in seconds, without the need for physical access. Development of host computer platforms to store and process each digital receiver's output are also discussed

Gas Bubbles Emerging from a Submerged Granular Bed

This fluid dynamics video was submitted to the Gallery of Fluid Motion for the 2009 APS Division of Fluid Dynamics Meeting in Minneapolis, Minnesota. In this video we show some results from a simple experiment where air was injected by a single nozzle at known constant flow rates in the bottom of a granular bed submerged in water. The injected air propagates through the granular bed in one of two modes. Mode 1 emergence involves small discrete bubbles taking tortuous paths through the interstitial space of the bed. Multiple small bubbles can be emitted from the bed in an array of locations at the same time during Mode 1 emergence. Mode 2 emergence involves large discrete bubbles locally fluidizing the granular bed and exiting the bed approximately above the injection site. Bead diameter, bead density, and air flow rate were varied to investigate the change in bubble release behavior at the top of the granular bed. This system is a useful model for methane seeps in lakes. Methane bubbles are released from the decomposition of organic matter in the lake bed. The initial size of the bubble determines how much of the gas is absorbed into the lake and how much of the gas reaches the surface and is released into the atmosphere. The size and behavior of the emerging bubbles may also affect the amount of vertical mixing occurring in the lake, as well as the mixing from the lake bed into the benthic layer.Comment: 2009 APS DFD Gallery of Fluid Motion Submissio