We study a system of spatially discrete FitzHugh-Nagumo equations, which are nonlinear differential-difference equations on an infinite one-dimensional lattice. These equations are used as a model of impulse propagation in nerve cells. We employ McKean's caricature of the cubic as our nonlinearity, which allows us to reduce the nonlinear problem into a linear inhomogeneous problem. We find exact solutions for standing waves, which are steady states of the system. We derive formulas for all 1-pulse solutions. We determine the range of parameter values that allow for the existence of standing waves. We use numerical methods to demonstrate the stability of our solutions and to investigate the relationship between the existence of standing waves and propagation failure of traveling waves.

In this work we investigate the reaction propagation velocity of aluminum and copper oxide Metastable Intermolecular Composites (MIC's). All samples were deposited in a magnetron sputtering system using 2 aluminum targets and 2 copper targets. The copper is sputtered in an oxygen rich environment in order to obtain copper oxide rich films. Three different layer structures are used for various measurements that are composed of alternating 20 layer pairs, 30 layer pairs, and 40 layer pairs. All layer pairs maintain a constant total thickness of 3.2 microns. Each layer structure can be prepared independent of a substrate and is measured with the use of photodiodes or with direct device contact. Aluminum and copper oxide structures have potential use as propellants and additives to explosives, thus, accurate propagation velocity or burn rate measurements are important. The developed measurement system for burn rate measurements of Al/CuO MIC's can achieve and accuracy of 0.1 m/s. In order to determine the velocity limiting characteristics, MIC's on glass and silicon substrates were measured as well as free standing Al/CuO MIC's. Separate burn rate measurement devices were created in order to handle the variety of substrates. In addition, the ignition energy of the Al/CuO MIC was studied to further characterize the samples. This was done using both voltage and current probes of a reacting sample. Rutherford backscattering spectroscopy (RBS) was used for sample composition calibration. The pre- and post-reaction Al/CuO MIC's were also characterized by transmission electron microscopy (TEM).

Standing support is often used in conjunction with underground retreat mining. Knowledge of the load-displacement behavior of a standing support and loading induced by the mine opening is critical proper support selection. The NIOSH STOP database contains load-displacement laboratory test data for most commonly used standing supports. Hydraulic load cells currently used to measure in-situ loading of standing supports have exhibited leakage under load, producing irregularities within the dataset. An improved hydraulic load cell eliminates leakage and produces more consistent data. / Master of Science / In retreat mining of a traditional room and pillar or longwall mining operation standing support is utilized. The standing support is comprised over various types of systems, wood timbers, wood cribs, pumpable supports and metal supports. These standing supports help aid in the recovery of the reserves and/or maintain ventilation through the mining excavation. National Institute for Occupational Safety and Health (NIOSH) Support Technology Optimization Program (STOP) has a database of laboratory testing on load displacement used on various standing supports. To relate this laboratory testing to in-situ load of standing support hydraulic load cells have been introduced. The hydraulic load cells design is a thin metal bladder filled with fluid that is placed on the top or bottom of the standing support. These hydraulic load cells have exhibited inconsistencies due to leakage under load, producing irregularities within the dataset. To achieve a reliable dataset on active standing supports it is vital that current load-measuring devices needs to be re-evaluated and redesigned.

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Prediction of the clip reactions of a standing seam roof in a metal building under dynamic loading is of great interest because currently static uplift tests are the standard for determining the design load capacity. The use of a static test to replicate a dynamic loading leads to a great amount of debate because clearly a standing seam roof visually behaves very different under the two different types of loads. This leads to the question of whether a static test accurately replicates the magnitude of loads that the roof clips would feel under a dynamic wind load. This study uses a magnetic suspension uplift loading for the simulation of wind tunnel data in comparison with the ASTM E-1592 ?Standard Test Method for Structural Performance of Sheet Metal Roof and Siding Systems by Uniform Static Air Pressure Difference? test to determine clip reactions. An approximate finite element model is also utilized to verify the validity of the experimentally acquired clip reactions to form another comparison.

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