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Articles 3091 - 3120 of 3436

Full-Text Articles in Physical Sciences and Mathematics

Unfolding Of The Period-Two Bifurcation In A Fiber Laser Pumped With Two Modulation Tones, Scott Glasgow, T. C. Newell, A. Gavrielides, V. Kovanis, D. Sukow, T. Erneux Dec 1997

Unfolding Of The Period-Two Bifurcation In A Fiber Laser Pumped With Two Modulation Tones, Scott Glasgow, T. C. Newell, A. Gavrielides, V. Kovanis, D. Sukow, T. Erneux

Faculty Publications

The effect of a small second frequency component on a pump modulated neodymium fiber laser is investigated experimentally and theoretically. This term, whose frequency is exactly half the primary driver, incites an unfolding of the attractor. It breaks the period two pitchfork bifurcation and splits the period one orbit. The modification of the bifurcation diagram is studied analytically by employing a map derived from the class B laser rate equations. We determine specific conditions and scaling laws for this phenomenon. Our analytical predictions are in good agreement with recorded experimental data.

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System For Electron Paramagnetic Resonance Measurements At High Pressure And Low Temperature, Ke Huang, Daniel L. Decker, H. Mark Nelson, J. Dean Barnett Oct 1997

System For Electron Paramagnetic Resonance Measurements At High Pressure And Low Temperature, Ke Huang, Daniel L. Decker, H. Mark Nelson, J. Dean Barnett

Faculty Publications

Major improvements have been made on the sensitive high pressure electron paramagnetic resonance (EPR) system developed previously in 1978 at this laboratory. These changes allow low temperature measurements and provide a more stable signal. The high pressure EPR cell is placed inside a vacuum chamber to provide thermal isolation, so that the system may be cooled by a closed cycle refrigerator to temperatures between 45 and 60 K, depending on the energy input to the modulation coil. The combination of high pressure and low temperature greatly expands the thermodynamic range over which EPR measurements can be made. An improved and …

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A Fluid In Contact With A Semipermeable Surface: Second-Order Integral Equation Approach, Douglas Henderson, Pawel Bryk, Stefan Sokolowski Aug 1997

A Fluid In Contact With A Semipermeable Surface: Second-Order Integral Equation Approach, Douglas Henderson, Pawel Bryk, Stefan Sokolowski

Faculty Publications

An integral equation approach for a binary hard-sphere mixture interacting with a planar semipermeable wall (membrane) is formulated by using the second-order nonuniform or pair Ornstein–Zernike equation as well as the usual singlet Ornstein–Zernike equation. The results of the pair theory are compared with those obtained from the singlet theory and with computer simulation data. The pair approach is more accurate than the singlet theory.

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Grand Canonical Monte Carlo And Modified Singlet Integral Equations For The Density Profile Of A Yukawa Fluid Near A Planar Wall, Douglas Henderson, Wilmer Olivares-Rivas, Leo Degreve, Jacqueline Quintana May 1997

Grand Canonical Monte Carlo And Modified Singlet Integral Equations For The Density Profile Of A Yukawa Fluid Near A Planar Wall, Douglas Henderson, Wilmer Olivares-Rivas, Leo Degreve, Jacqueline Quintana

Faculty Publications

Results for the density profile for Yukawa molecules near a hard wall and an exponential attractive wall are presented for Grand Canonical Monte Carlo (GCMC) simulations, for the singlet hypernetted chain (HNC) integral equation and for a modified version of the Lovett–Mou–Buff–Wertheim (LMBW-1) which uses the exact contact value theorem. The results of the standard singlet HNC are quite poor. If the LMBW equation is modified (but still using the bulk direct correlation function) the results at high temperature become reasonable. However, the results at low temperatures, close to the bulk coexistence curve, are only a partial improvement. The contact …

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Damped Diocotron Quasi-Modes Of Non-Neutral Plasmas And Inviscid Fluids, S. Neil Rasband, Ross L. Spencer Jan 1997

Damped Diocotron Quasi-Modes Of Non-Neutral Plasmas And Inviscid Fluids, S. Neil Rasband, Ross L. Spencer

Faculty Publications

Computations of damped diocotron oscillations (quasi-modes) are described for non-neutral plasmas and inviscid fluids. The numerical method implements a suggestion made by Briggs, Daugherty, and Levy some 25 years ago [Phys. Fluids 13, 421 (1970)] to push the branch line that forms the continuum into the complex w-plane by solving the mode equation in the complex r-plane. For the special case of power-law density profiles the calculation finds the same quasi-mode frequencies found recently by Corngold [Phys. Plasmas 2, 620 (1995)]. It is found that the feature of the continuum eigenfunctions which indicates the presence of a nearby quasi-mode is …

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Faster Ray Tracing Using Adaptive Grids, Thomas W. Sederberg, Krysztof S. Klimaszewski Jan 1997

Faster Ray Tracing Using Adaptive Grids, Thomas W. Sederberg, Krysztof S. Klimaszewski

Faculty Publications

A new hybrid approach is presented which outperforms the regular grid technique in scenes with highly irregular object distributions by a factor of hundreds, and combined with an area interpolator, by a factor of thousands. Much has been said about scene independence of different acceleration techniques and the alleged superiority of one approach over another. Several theoretical and practical studies conducted in the past have led to the same conclusion: a space partitioning method that allows the fastest rendering of one scene often fails with another. Specialization may be the answer. This has always been pursued, consciously or not, in …

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On The Dynamic Behaviour Of A Thermoviscoelastic Body In Frictional Contact With A Rigid Obstacle, Kenneth Kuttler, K. T. Andrews, M. Shillor Jan 1997

On The Dynamic Behaviour Of A Thermoviscoelastic Body In Frictional Contact With A Rigid Obstacle, Kenneth Kuttler, K. T. Andrews, M. Shillor

Faculty Publications

We consider the dynamic behaviour of a thermoviscoelastic body which may come into frictional contact with a rigid obstacle. The frictional contact is modelled by general contact and friction laws which include as special cases the power law normal compliance condition and the corresponding generalization of Coulomb's law of dry friction. The stress-strain constitutive relation is assumed to be of Kelvin-Voigt type and the frictional heat generation on the contact surface is taken into account. In this setting we establish the existence of a solution to a weak version of the energy-elasticity system which consists of a parabolic equation coupled …

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Improved Heterogeneous Distance Functions, Tony R. Martinez, D. Randall Wilson Jan 1997

Improved Heterogeneous Distance Functions, Tony R. Martinez, D. Randall Wilson

Faculty Publications

Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values between nominal attribute values, but it largely ignores continuous attributes, requiring discretization to map continuous values into nominal values. This paper proposes three new heterogeneous distance functions, called the Heterogeneous Value Difference Metric (HVDM), the Interpolated Value Difference Metric (IVDM), and the Windowed Value Difference Metric (WVDM). These new distance functions are designed to handle applications with nominal attributes, continuous attributes, or both. In experiments on 48 applications …

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Procedurally Rational Decision-Making And Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling Oct 1996

Procedurally Rational Decision-Making And Control, Richard L. Frost, Michael A. Goodrich, Wynn C. Stirling

Faculty Publications

Substantive rationality requires a decision-maker to be a utility maximizer; under this paradigm, the decision is paramount, and not dependent on the computational process used to obtain it. Procedural rationality is dependent on the method used to make the decision; reasonableness of the procedure is paramount. Well-formed problems are amenable to substantive rationality; ill-formed problems are not, but are amenable to procedural rationality. To qualify as being procedurally rational, a methodology must possess a sound epistemological basis, it must be amenable to a formal design synthesis procedure, and it must be consistent with substantive rationality. Epistemic utility theory forms the …

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A Fertility Channel Model For Post-Correction Of Continuous Speech Recognition, Eric K. Ringger, James F. Allen Oct 1996

A Fertility Channel Model For Post-Correction Of Continuous Speech Recognition, Eric K. Ringger, James F. Allen

Faculty Publications

We have implemented a post-processor called SPEECHPP to correct word-level errors committed by an arbitrary speech recognizer. Applying a noisy-channel model, SPEECHPP uses a Viterbi beam-search that employs language and channel models. Previous work demonstrated that a simple word-for-word channel model was sufficient to yield substantial incieases in word accuracy. This paper demonstrates that some improvements in word accuracy result from augmenting the channel model with an account of word fertility in the channel. This work further demonstrates that a modern continuous speech recognizer can be used in "black-box" fashion for robustly recognizing speech for which the recognizer was not …

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Structural Phase Transition And Tc Distribution In Hf-Doped Lamno3 Investigated Using Perturbed-Angular-Correlation Spectroscopy, William E. Evenson, David D. Allred, Gary L. Catchen Aug 1996

Structural Phase Transition And Tc Distribution In Hf-Doped Lamno3 Investigated Using Perturbed-Angular-Correlation Spectroscopy, William E. Evenson, David D. Allred, Gary L. Catchen

Faculty Publications

Using perturbed-angular-correlation (PAC) spectroscopy, via the Hf-->Ta probe, we have measured Mn-site electric-field gradients (EFG's) at Ta nuclei in ceramic samples of LaMnO3. Two crystallographic phases coexist over a temperature interval of ≈16 K near the orthorhombic-to-rhombohedral transition at ≈724 K, which shows a thermal hysteresis of ≈1.7±0.2 K. Concurrently, in the two phases, we determined the temperature dependence of the EFG parameters, Vzz, ƞ, and δ, and the ratio of the probe concentrations A1/A2. To explain the apparent coexistence of two phases in this weakly first-order transition, we present a model that assumes a spatial distribution of Tc …

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Robust Optimization Using Training Set Evolution, Tony R. Martinez, Dan A. Ventura Jun 1996

Robust Optimization Using Training Set Evolution, Tony R. Martinez, Dan A. Ventura

Faculty Publications

Training Set Evolution is an eclectic optimization technique that combines evolutionary computation (EC) with neural networks (NN). The synthesis of EC with NN provides both initial unsupervised random exploration of the solution space as well as supervised generalization on those initial solutions. An assimilation of a large amount of data obtained over many simulations provides encouraging empirical evidence for the robustness of Evolutionary Training Sets as an optimization technique for feedback and control problems.

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A Robust System For Natural Spoken Dialogue, Eric K. Ringger, James F. Allen, Bradford W. Miller, Teresa Sikorski Jun 1996

A Robust System For Natural Spoken Dialogue, Eric K. Ringger, James F. Allen, Bradford W. Miller, Teresa Sikorski

Faculty Publications

This paper describes a system that leads us to believe in the feasibility of constructing natural spoken dialogue systems in task-oriented domains. It specifically addresses the issue of robust interpretation of speech in the presence of recognition errors. Robustness is achieved by a combination of statistical error post-correction, syntactically- and semantically-driven robust parsing, and extensive use of the dialogue context. We present an evaluation of the system using time-to-completion and the quality of the final solution that suggests that most native speakers of English can use the system successfully with virtually no training.

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Heterogeneous Radial Basis Function Networks, Tony R. Martinez, D. Randall Wilson Jun 1996

Heterogeneous Radial Basis Function Networks, Tony R. Martinez, D. Randall Wilson

Faculty Publications

Radial Basis Function (RBF) networks typically use a distance function designed for numeric attributes, such as Euclidean or city-block distance. This paper presents a heterogeneous distance function which is appropriate for applications with symbolic attributes, numeric attributes, or both. Empirical results on 30 data sets indicate that the heterogeneous distance metric yields significantly improved generalization accuracy over Euclidean distance in most cases involving symbolic attributes.

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A Brief Introduction To Formal Methods, Paul E. Black, Kelly M. Hall, Michael D. Jones, Trent N. Larson, Phillip J. Windley May 1996

A Brief Introduction To Formal Methods, Paul E. Black, Kelly M. Hall, Michael D. Jones, Trent N. Larson, Phillip J. Windley

Faculty Publications

As hardware designs grow in size and complexity, current design methods are proving less adequate. Current methods for specification, design, and test are typically empirical or informal, that is, they are based on experience and argument. Formal methods are solidly based on mathematical logic systems and precise rules of inference. Formal methods offer a discipline which complements current methods so designers can successfully meet the demand for high performance systems. Formal methods covers a broad and diverse set of techniques aimed at improving computer correctness. This paper explains the role of specifications and implementation models in formal methods, and different …

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Error Correction Via A Post-Processor For Continuous Speech Recognition, Eric K. Ringger, James F. Allen May 1996

Error Correction Via A Post-Processor For Continuous Speech Recognition, Eric K. Ringger, James F. Allen

Faculty Publications

This paper presents a new technique for overcoming several types of speech recognition errors by post-processing the output of a continuous speech recognizer. The post-processor output contains fewer errors, thereby making interpretation by higher-level modules, such as a parser, in a speech understanding system more reliable. The primary advantage to the post-processing approach over existing approaches for overcoming SR errors lies in its abilityto introduce options that are not available in the SR module’s output. This work provides evidence for the claim that a modern continuous speech recognizer can be used successfully in “black-box” fashion for robustly interpreting spontaneous utterances …

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Simulations Of Electrostatic Modes Of Non-Neutral Plasmas With Small Aspect Ratio In A Penning Trap, Grant W. Mason, Ross L. Spencer, Jonathan A. Bennett May 1996

Simulations Of Electrostatic Modes Of Non-Neutral Plasmas With Small Aspect Ratio In A Penning Trap, Grant W. Mason, Ross L. Spencer, Jonathan A. Bennett

Faculty Publications

The dependence on induced charge, experimental geometry, and temperature of electrostatic modes in very low aspect ratio non-neutral plasmas in a Penning trap is considered. The modes are of interest as non-destructive diagnostics of the shape of the plasmas. These investigations include equilibrium calculations of plasma shapes and profiles at finite temperature and particle-in-cell simulations of axisymmetric modes. The results of the simulations are compared to the zero-temperature theory by Dubin [Phys. Rev. Lett. 66, 2076 (1991)] taken to first-order in the aspect ratio and to experimental measurements by Weimer et al. [Phys. Rev. A 49, 3842 (1994)]. In general, …

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Compressing Semi-Structured Text Using Hierarchical Phrase Identifications, Dan R. Olsen Jr., Craig G. Nevill-Manning, Ian H. Witten Apr 1996

Compressing Semi-Structured Text Using Hierarchical Phrase Identifications, Dan R. Olsen Jr., Craig G. Nevill-Manning, Ian H. Witten

Faculty Publications

The structure of this paper is as follows. We begin by identifying some characteristics of semi-structured text that have special relevance to data compression. We then give a brief account of a particular large textual database, and describe a compression scheme that exploits its structure. In addition to providing compression, the system gives some insight into the structure of the database. Finally we show how the hierarchical grammar can be generalized, first manually and then automatically, to yield further improvements in compression performance.

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Nature Among The Mormons: An Ecocritical Approach To Mormon Literature, Gail D. Ballard Jan 1996

Nature Among The Mormons: An Ecocritical Approach To Mormon Literature, Gail D. Ballard

Theses and Dissertations

Increasingly, environmentalists have focused on Judeo-Christian tradition as the cause of Western culture's ecological crisis. It is the purpose of this paper to examine the charges against Judeo-Christian tradition and to show how the revealed doctrines of The Church of Jesus Christ of Latter-day Saints provide possible solutions to environmental challenges. The resulting Latter-day Saint environmental paradigm will be superimposed on selected Mormon literature to determine how effectively the doctrines taught by Church authorities filtered into popular Mormon culture.

Despite the inspired teachings of Latter-day Saint prophets, Mormons remain unimpressive in their environmental practices. My research will show that while …

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A New High Pressure Sapphire Nuclear Magnetic Resonance Cell, Shi Bai, Craig M. Taylor, Charles L. Mayne, Ronald J. Pugmire, David M. Grant Jan 1996

A New High Pressure Sapphire Nuclear Magnetic Resonance Cell, Shi Bai, Craig M. Taylor, Charles L. Mayne, Ronald J. Pugmire, David M. Grant

Faculty Publications

A new version of a single-crystal sapphire high pressure nuclear magnetic resonance (NMR) cell is described that is capable of controlling the sample pressure independent of the temperature. A movable piston inside the cell adjusts and controls the sample pressure from ambient conditions to 200 atm within plus or minus 0.3 atm. The linewidth at half-height for a 13C spectrum of carbon dioxide at 15degrees C and 57.8 atm is found to be 0.5 Hz. The carbon dioxide gas/liquid phase transition is clearly observed by measuring 13C chemical shifts as the sample pressure approaches equilibrium. The time required for this …

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Model Equations From Gyrokinetic Theory For A Non-Neutral Plasma To Include Temperature Effects And Applications To A Plasma Of Infinite Length, S. Neil Rasband Jan 1996

Model Equations From Gyrokinetic Theory For A Non-Neutral Plasma To Include Temperature Effects And Applications To A Plasma Of Infinite Length, S. Neil Rasband

Faculty Publications

Gyrokinetic equations are derived for applications to non-neutral plasmas in constant, straight magnetic fields wherein E X B drift velocities are of the same order as thermal velocities. The ratio of the E X B rotation frequency to the cyclotron frequency and the ratio of the gyroradius to a plasma scale length are assumed to be of order epsilon and terms are retained in the gyrokinetic expansion to second order to include finite-Larmor-radius (FLR) effects. A mode equation is obtained for a non-neutral plasma in the infinite-length approximation. The singularities of this equation are compared and contrasted with the familiar …

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High-Sensitivity Absorption Spectroscopy In Fe Ii, Scott D. Bergeson, K. L. Mullman, J. E. Lawler Jan 1996

High-Sensitivity Absorption Spectroscopy In Fe Ii, Scott D. Bergeson, K. L. Mullman, J. E. Lawler

Faculty Publications

We report the first measurements of UV oscillator strengths (ƒ-values) in Fe II from a high-sensitivity absorption experiment developed at the University of Wisconsin. The accuracy of our measurements is demonstrated by our reproducing well-known ƒ-value ratios in Fe I and Fe II. The first laboratory ƒ-value measurement of the 160.845 nm transition in Fe II is presented and compared to values in the literature. While this paper focuses on Fe II, the high-sensitivity absorption method that we have developed is applicable to essentially every element in the periodic table, for both neutral and ionized species, over a broad range …

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Branching Fractions And Oscillator Strengths For Fe Ii Transitions From The 3d6(5D)4p Subconfiguration, Scott D. Bergeson, K. L. Mullman, M. E. Wickliffe, J. E. Lawler Jan 1996

Branching Fractions And Oscillator Strengths For Fe Ii Transitions From The 3d6(5D)4p Subconfiguration, Scott D. Bergeson, K. L. Mullman, M. E. Wickliffe, J. E. Lawler

Faculty Publications

New experimental branching fractions and transition probabilities are reported for 56 transitions in Fe II. The branching fractions are measured with a Fourier transform spectrometer and also with a high-resolution grating spectrometer on a n optically thin hollow cathode discharge. Highly accurate experimental radiative lifetimes from the recent literature provide the normalization required to convert our branching fractions into absolute transition probabilities. Results are compared with experimental and theoretical values in the literature. Our new transition probabilities will establish the absolute scale for relative absorption oscillator strengths of vacuum ultraviolet lines measured using a new high-sensitivity absorption experiment at the …

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Observation Of Beam-Induced Changes In The Polarization Of Balmer-Α Radiation Emitted Following Beam--Tilted-Foil Transmission, Wang Qi, David D. Allred, Larry V. Knight, Douglas L. Harper, Royal G. Albridge, Norman H. Tolk Dec 1995

Observation Of Beam-Induced Changes In The Polarization Of Balmer-Α Radiation Emitted Following Beam--Tilted-Foil Transmission, Wang Qi, David D. Allred, Larry V. Knight, Douglas L. Harper, Royal G. Albridge, Norman H. Tolk

Faculty Publications

Measurements of the circular polarization of Balmer-α radiation emitted by excited hydrogen atoms, following the transmission of (20-50)-keV protons through thin, tilted amorphous carbon foils, exhibit markedly unexpected behavior as a function of exposure of the foil to the proton beam. Specifically, the circular polarization changes from an initially well understood tilt-angle dependence to a behavior which, for low tilt angles, gives the opposite handedness of circular polarization from that predicted. In addition, the degree of alignment, indicated by the linear Stokes parameter M/I, is enhanced also as a function of dose. These changes in the tilt-angle dependence of the …

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A Provably Convergent Dynamic Training Method For Multi-Layer Perceptron Networks, Timothy L. Andersen, Tony R. Martinez Sep 1995

A Provably Convergent Dynamic Training Method For Multi-Layer Perceptron Networks, Timothy L. Andersen, Tony R. Martinez

Faculty Publications

This paper presents a new method for training multi-layer perceptron networks called DMP1 (Dynamic Multilayer Perceptron 1). The method is based upon a divide and conquer approach which builds networks in the form of binary trees, dynamically allocating nodes and layers as needed. The individual nodes of the network are trained using a genetic algorithm. The method is capable of handling real-valued inputs and a proof is given concerning its convergence properties of the basic model. Simulation results show that DMP1 performs favorably in comparison with other learning algorithms.

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An Integrated Framework For Learning And Reasoning, Christophe G. Giraud-Carrier, Tony R. Martinez Aug 1995

An Integrated Framework For Learning And Reasoning, Christophe G. Giraud-Carrier, Tony R. Martinez

Faculty Publications

Learning and reasoning are both aspects of what is considered to be intelligence. Their studies within AI have been separated historically, learning being the topic of machine learning and neural networks, and reasoning falling under classical (or symbolic) AI. However, learning and reasoning are in many ways interdependent. This paper discusses the nature of some of these interdependencies and proposes a general framework called FLARE, that combines inductive learning using prior knowledge together with reasoning in a propositional setting. Several examples that test the framework are presented, including classical induction, many important reasoning protocols and two simple expert systems.

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Surface Intersection Loop Destruction, Thomas W. Sederberg, Alan K. Zundel Jul 1995

Surface Intersection Loop Destruction, Thomas W. Sederberg, Alan K. Zundel

Faculty Publications

The intersection curve between two surface patches consists of one or more connected components or branches. Each component can be classified as either an open branch, with endpoints on at least one patch boundary, or as a closed loop.

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Numerical Calculation Of Axisymmetric Electrostatic Modes For Cold Finite-Length Non-Neutral Plasmas, Johnny K. Jennings, Ross L. Spencer, K. C. Hansen Jul 1995

Numerical Calculation Of Axisymmetric Electrostatic Modes For Cold Finite-Length Non-Neutral Plasmas, Johnny K. Jennings, Ross L. Spencer, K. C. Hansen

Faculty Publications

A numerical calculation of mode frequencies for cold, non-neutral plasmas is reported. The numerical method can be applied to any axisymmetric plasma shape in a trap. Here, it is used to study axisymmetric electrostatic modes in a long conducting cylinder. These modes were previously studied by Prasad and O'Neil [Phys. Fluids 26, 665 (1983)] and by Dubin [Phys. Rev. Lett. 66, 2076 (1991)]. In contrast to Dubin's calculation, the effects of a nearby cylindrical wall, including its influence on the shape of the plasma equilibrium, are considered. It is found that for plasmas with aspect ratios (length divided by diameter) …

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Hodographs And Normals Of Rational Curves And Surfaces, Thomas W. Sederberg, Takafumi Saito, Guo-Jin Wang Jun 1995

Hodographs And Normals Of Rational Curves And Surfaces, Thomas W. Sederberg, Takafumi Saito, Guo-Jin Wang

Faculty Publications

Derivatives and normals of rational Bézier curves and surface patches are discussed. A non-uniformly scaled hodograph of a degree m x n tensor-product rational surface, which provides correct derivative direction but not magnitude, can be written as a degree (2m - 2) x 2n or 2m x (2n - 2) vector function in polynomial Bézier form. Likewise, the scaled normal direction is degree (3m - 2) x(3n - 2). Efficient methods are developed for bounding these directions and the derivative magnitude.

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New Optical Cell Design For Laser Flash Photolysis Studies In Supercritical Fluids, Steven R. Goates, Milton L. Lee, Qin Ji, Edward M. Eyring, Rudi Van Eldik, Kedika Bal Reddy Jan 1995

New Optical Cell Design For Laser Flash Photolysis Studies In Supercritical Fluids, Steven R. Goates, Milton L. Lee, Qin Ji, Edward M. Eyring, Rudi Van Eldik, Kedika Bal Reddy

Faculty Publications

A high-pressure optical cell has been designed that achieves an effective separation between the chemical sample and the pressurizing medium and system. This design limits possible sample contamination and catalytic effects under supercritical fluid sample conditions. Laser flash photolysis experiments were carried out on molybdenum hexacarbonyl dissolved in supercritical CO2. The thermal ring closure reaction of the species Mo(CO)5L, where L is 2,2- bipyridine was found to proceed at rates comparable to those measured previously in liquid benzene or toluene. Much larger activation volumes were found for the reaction in supercritical CO2 than in liquid toluene.

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