This paper is the result of a study of the power method to find dominant eigenvalues of square matrices. It introduces ideas basic to the study and shows the development of the power method for the most well-behaved matrices possible, and it explores exactly which other types of matrices yield to the power method. The paper also discusses a type of matrix typically considered impossible for the power method, along with a modification of the power method which works for this type of matrix. It gives an overview of common extensions of the power method. The appendices contain BASIC versions of the power method and its modification.

Molten carbonate fuel cell system is a leading candidate for the utility power generation because of its high efficiency for fuel to AC power conversion, capability for an internal reforming, and a very low environmental impact. However, the performance of the molten carbonate fuel cell is limited by the oxygen reduction reaction and the cell life time is limited by the stability of the cathode material. An elucidation of oxygen reduction reaction in molten alkali carbonate is essential because overpotential losses in the molten carbonate fuel cell are considerably greater at the oxygen cathode than at the fuel anode. Oxygen reduction on a fully-immersed gold electrode in a lithium carbonate melt was investigated by electrochemical impedance spectroscopy and cyclic voltammetry to determine electrode kinetic and mass transfer parameters. The dependences of electrode kinetic and mass transfer parameters on gas composition and temperature were examined to determine the reaction orders and the activation energies. The results showed that oxygen reduction in a pure lithium carbonate melt occurs via the peroxide mechanism. A mass transfer parameter, D{sub O}{sup 1/2}C{sub O}, estimated by the cyclic voltammetry concurred with that calculated by the EIS technique. The temperature dependence of the exchange current density and …

We present data from our study of a device known as the inverse free electron laser. First, numerical simulations were performed to optimize the design parameters for an experiment that accelerates electrons in the presence of an undulator by stimulated absorption of radiation. The Columbia free electron laser (FEL) was configured as an auto-accelerator (IFELA) system; high power (MW`s) FEL radiation at {approximately}1.65 mm is developed along the first section of an undulator inside a quasi-optical resonator. The electron beam then traverses a second section of undulator where a fraction of the electrons is accelerated by stimulated absorption of the 1.65 mm wavelength power developed in the first undulator section. The second undulator section has very low gain and does not generate power on its own. We have found that as much as 60% of the power generated in the first section can be absorbed in the second section, providing that the initial electron energy is chosen correctly with respect to the parameters chosen for the first and second undulators. An electron momentum spectrometer is used to monitor the distribution of electron energies as the electrons exit the IFELA. We have found; using our experimental parameters, that roughly 10% of …

A divergence correction is conventionally applied to zero-offset data in an effort to preserved amplitude information. The conventional divergence correction compensates for the geometrical spreading of a point source in a horizontally layered medium where velocity varies with depth only. The dip-dependent divergence correction extends the conventional correction for improved amplitude processing of dipping beds. The dip-dependent divergence correction is computed by dynamic ray tracing, and applied to stacked data using a dip decomposition technique. This correction decreases amplitudes relative to the conventional correction for steep dips and late times. In a data example from the Gulf of Mexico, the conventional correction over- amplified the reflection off a salt dome flank by a factor of 1.6. High amplitudes near salt flanks are also associated with the presence of hydrocarbons. Applying the dip-dependent divergence correction ensures that ``bright spots`` are not due to over-amplification of steep dips by the conventional correction. In areas like the Gulf of Mexico, where the velocity function varies primarily with depth, and steep beds are commonplace, the dip-dependent divergence correction is an inexpensive way to improve the amplitude information in seismic images.

Stability of a cylindrical pore under the influence of surface energy is important for porous silicon (PS) processing in the integrated circuit industry. Once the zig-zag cylindrical pores of porous silicon or oxidized porous silicon (OPS) are unstable and breakup into rows of isolated spherical pores, oxidation of PS and densification/nitridation of OPS become difficult. Swing to difficulty transport of reactant gas (O{sub 2}, NH{sub 3}) or the trapped gas (for densification of OPS). A first order analysis of the stability of a cylindrical pore or cylinder is considered first. Growth of small sinusoidal perturbations by viscous flow or evaporation/condensation result in dependence of perturbation growth rate on perturbation wavelength. Rapid thermal oxidation (RTO) of porous silicon is proposed as an alternative for the tedious two-step 300 and 800C oxidation process. Transmission electron microscopy, energy dispersive spectroscopy ESCA are used for quality control. Also, rapid thermal nitridation of oxidized porous silicon in ammonia is proposed to enhance OPS resistance to HF solution. Pores breakup of OPS results in a trapped gas problem during densification. Wet helium is proposed as OPS densification ambient gas to shorten densification time. Finally, PS is proposed to be an extrinsic gettering center in silicon wafers. …

Release rates of 15 radionuclides from waste packages expected to result from partitioning and transmutation of Light-Water Reactor (LWR) and Actinide-Burning Liquid-Metal Reactor (ALMR) spent fuel are calculated and compared to release rates from standard LWR spent fuel packages. The release rates are input to a model for radionuclide transport from the proposed geologic repository at Yucca Mountain to the water table. Discharge rates at the water table are calculated and used in a model for transport to the accessible environment, defined to be five kilometers from the repository edge. Concentrations and dose rates at the accessible environment from spent fuel and wastes from reprocessing, with partitioning and transmutation, are calculated. Partitioning and transmutation of LWR and ALMR spent fuel reduces the inventories of uranium, neptunium, plutonium, americium and curium in the high-level waste by factors of 40 to 500. However, because release rates of all of the actinides except curium are limited by solubility and are independent of package inventory, they are not reduced correspondingly. Only for curium is the repository release rate much lower for reprocessing wastes.

A transport model for polymer electrolytes is presented, based on concentrated solution theory and irreversible thermodynamics. Thermodynamic driving forces are developed, transport properties are identified and experiments devised. Transport number of water in Nafion 117 membrane is determined using a concentration cell. It is 1.4 for a membrane equilibrated with saturated water vapor at 25{degrees}C, decreases slowly as the membrane is dehydrated, and falls sharply toward zero as the water content approaches zero. The relation between transference number, transport number, and electroosmotic drag coefficient is presented, and their relevance to water-management is discussed. A mathematical model of transport in a solid-polymer-electrolyte fuel cell is presented. A two-dimensional membrane-electrode assembly is considered. Water management, thermal management, and utilization of fuel are examined in detail. The membrane separators of these fuel cells require sorbed water to maintain conductivity; therefore it is necessary to manage the water content in membranes to ensure efficient operation. Water and thermal management are interrelated. Rate of heat removal is shown to be a critical parameter in the operation of these fuel cells. Current-voltage curves are presented for operation on air and reformed methanol. Equations for convective diffusion to a rotating disk are solved numerically for a consolute …

To enhance the SQUID`s field sensitivity, it is coupled to a flux transformer, a closed superconducting circuit consisting of a pickup loop, to which a signal is applied, connected in series to an input coil, which is inductively coupled to the SQUID. To fabricate an optimal flux transformer, one must use more than one superconducting thin-film layer, each of which is patterned into narrow strips or wires. Some wires from different layers cross, yet remain electrically isolated, to form crossovers, while in other places there must be superconducting contact between wires from different layers. Together, the superconducting wire, superconducting-superconducting contact and the superconducting crossover constitute a superconducting interconnect or multilayer wiring technology. We discuss the development of an interconnect technology involving the high transition temperature ({Tc}) superconductor YBa{sub 2}Cu{sub 3}O{sub 7-x} (YBCO). Because of the need for epitaxial growth there are limits on materials for the insulating layer separating the YBCO films in multilayer structures, and on deposition and patterning techniques. We discuss the use of pulsed laser deposition in conjunction with patterning by shadow masks and later by photolithography to produce interconnects, multiturn input coils, and flux transformers. We also discuss the performance of SQUID magnetometers, in which a …

The measurement of q{sub o} is extremely important for understanding the quantity of matter in our universe. The measurement of q{sub o} using supernovae of type Ia as standard candles is appealing because it requires less modeling than other methods using galaxies. The challenge with using supernovae to measure q{sub o} is in finding enough of them. In order to find supernovas, we have constructed a very popular f/1 camera for the 3.9m Anglo-Australian Telescope. The camera uses reducing optics that put a 17 in. {times} 17 in. field on a 1024 {times} 1024 pixel Thomson CCD. Using this system, we image to 23rd magnitude in five minutes. We have developed a software package that uses image subtraction to find supernovae that are approximately magnitude 22.4 or brighter in these images. One field can be processed every 6.6 minutes on a relatively unloaded VAX 6000-6510. We estimate that this system should find one supernova in every 105--139 images (about two nights of observation on the AAT). Throughout the two years of operation, we observed the equivalent of about four nights with seeing better than two arc seconds. Although we found many candidates, we were unable to confirm any supemovae. The …