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Many data analysis problems can be approached by fitting a probability distribution to the data, but there are few models for distributions of images. By a distribution of images we mean a distribution describing images resulting from some process, for example sub-images selected from mammograms by a computer-aided diagnosis system. Previous attempts to model image probabilities either model the probability of some features of the image or are only suited for modeling images of textures; they seem unsuitable for modeling images of more structured objects. To address this problem we formulate a set of models for probability distributions on image spaces, which we call Hierarchical Image Probability or HIP models. They are hierarchical because they explicitly represent image structure at several length scales, and finer scale structures are conditioned on coarser scales. To make the model tractable we factor the distribution over scale and position. Such factoring would make it impossible to capture long-range correlations that arise from the objects being imaged. To fix this we introduce a further hierarchy of hidden variables whose probabilities also factor over scale and position. Since they are unknown, they must be summed over or marginalized to evaluate the image probability, and the summation reintroduces long-range correlations. We present algorithms for performing this sum and for finding the model parameters with maximum likelihood estimation. We have obtained encouraging preliminary results on the problems of detecting various objects in SAR images, target recognition in optical aerial images, and mass detection in mammograms.

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This talk demonstrates numerous computer systems that teach physics, chemistry, mathematics, medicine or engineering. These systems have resulted in increased student time on task, improved student grades and reduced faculty costs and are used by more than 4,000 students at over 20 universities.

In physics, we have built an electronic homework system which results in improved test and final exam scores, sometimes adding a full letter grade to the student score. Additionally, the weaker students receive the greatest benefit from this system. In chemistry, Web-based homework program includes thirty-five interactive discovery environments that provide guided inquiry, feedback to student responses and tracking of student performance. Intelligent tutors in chemistry provide levels of customized responses to expose students to the depths of chemical reactions. One tutor enables students to directly manipulate images and work with a palette of tools for placing and moving symbols. Tutors have been tested with over 900 students and show positive improvement in final exams. The electronic homework system provides an open architecture allowing for rapid extensions to new departments.

In addition, engineering tutors provide animated 3D tooling solutions of student designs and advice about relative costs. Evaluation demonstrates that these tutors are as effective as several lectures and homework assignments within a traditional classroom setting. A microbiology tutor provides visual support for an entire undergraduate course in molecular biology with rich 3-D animations depicting production of proteins through the interaction of DNA and RNA. A mathematics tutor uses machine learning to individualize problems and hints.

Each demonstrated project has been evaluated for effectiveness and efficiency. The talk will show how technology's impact on leaning has been quantified and that these systems can be of general use on a national scale.

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Results are presented of ALEGRA simulations of the x-ray pulse shape from shot 26 of Sandia's Z machine. ALEGRA is Sandia's multi-dimensional, arbitrary Lagrangian-Eulerian MHD code. Shot 26 produced 180 TW of x-ray power in a 7.5-ns FWHM pulse. This shot was chosen because other MHD codes (MACH II and Darrell Peterson's code from LANL) also have simulated shot 26, thereby providing the opportunity to compare ALEGRA to other codes as well as to data. Discussed in this talk are the effects on x-ray pulse shape of: (i) true void versus plasma fill inside the liner, (ii) differing interface tracking schemes, and (iii) differing levels and models of density perturbations.

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Particle acceleration occuring at or near the time solar flares is common, but it is not so common for high energy particles to reach the Earth's space environment. Solar energetic particles can have very destructive consequences for satellites and astronauts in space; thus, an import question to ask is if a large, destructive proton event will occur in conjuction with a particular solar flare or an associated coronal mass ejection. Acceleration of high energy electrons in flares is generally observed via hard X-ray (bremsstrahlung) and microwave (gyrosychriotron) emissions. In two earlier studies, Kiplinger has found a very high association between an uncommon hard X-ray signature called "progresssive spectral hardening" and interplanetary proton events. Those studies have been been extended from ~330 to more than 700 solar flares observed in hard X-rays by the Solar Maximum Mission (SMM). The results confirm the robustness for the association of progressive spectral hardening with major interplatetary proton events. Some episodes of progressive hardening are also associated with high energy neutrons seen at Earth. Gamma ray lines in flares also result from high energy ion production. A new, ongoing study of all gamma ray line flares seen by SMM compares times of emission of gamma ray lines with occurrences of progressive spectral hardening. These results and their implications will be discussed.

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We have examined the photoelectric charging of dust 90-106 microns in diameter dropped through UV illumination and dropped past a UV illuminated surface having a photoelectron sheath. Experiments are performed in vacuum with illumination from a 1 kW Hg-Xe arc lamp that has a spectrum extending to 200 nm (6.2 eV). We present and compare the photoelectric charging properties of particles composed of zinc, copper, graphite, lunar regolith simulant (JSC-1), and martian regolith simulant (JSC Mars-1). We find that the photoelectric charging properties of the elemental materials are consistent with charging models calculated from the theoretical capacitance and charge on an isolated spherical grain. Dust dropped through UV illumination loses electrons due to photoemission, while dust dropped past an illuminated surface gains electrons from the photoelectron sheath. The photoelectric charging properties of JSC-1 and JSC Mars-1 are more difficult to interpret due to residual charge on the dust. The results suggest that JSC Mars-1 is more susceptible to photoelectric charging than JSC-1. The relation of this work to similar phenomena in the solar system is discussed.

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The period doubling bifurcation process in the two-dimensional area preserving mapping is investigated on the basis of simmetry structure analysis. In particular a case of the period-4 orbits in the standard map has been studied throughly to analyze boundary islands formation around the principal period-4 island, and the onset of the hyperbolic bifurcation without reflection. It is illustrated explicitly that the hyperbolic bifurcation without reflection gives rise to the birth of twin orbits with the periodicity of the mother orbit.

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The effect of poloidally mode coupled, ballooning type electrostatic drift waves on a magnetic island has been studied both analytically and numerically. It has been shown quantitatively that particle orbits become stochastic and their behavior can be a possible candidate for the radial plasma transport across a magnetic island of a tokamak. The transport is significant in that it takes place even when the flux surface is not destroyed. The mechanism of the stochasticity generation is understood as an overlapping of secondary islands caused by resonance between periodic particle motions in the magnetic island and Fourier modes of E x B drift due to the electrostatic drift waves. The diffusion process perpendicular to the island magnetic surface has been shown to follow the Gaussian type and can be influential for the deterioration of the plasma confinement. In addition, local diffusion process in the vicinity of Kolmogorov, Arnold and Moser (KAM) surfaces is discussed.

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Finite-length equilibria occur in a number of intense-beam and plasma applications. Penning traps permit the study of intra-beam collective effects, as the additional freedom gained from having an internal conductor permits greater control over the plasma profile, so that monotonic, but not constant, plasma profiles can be obtained. On the basis that the thermal velocity of background neutrals and the drift velocity of the electrons are much lower than the thermal velocity of the electrons, and the rotation frequency is small compared to the gyrofrequency, the equilibrium equation can be reduced to a self-consistent Poisson equation where the source depends on the potential. We solve for these equilibria using a Gauss-Seidel relaxation method. Our results show the shape of the equilibria for various electrode configurations.

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In 1985 it was shown that linear analysis techniques were inadequate to describe the behavior of the magnetosphere, and so nonlinear studies of the magnetosphere were begun. When a finite dimension for an attractor was found in magnetospheric data it was thought that conclusive proof was found for chaotic behavior. However, later studies found that random noise with a certain frequency spectrum, called colored random or pink noise, could also give a finite result for the correlation dimension. Since then a controversy has been raging as to whether the magnetospheric was chaotic or stochastic. The definition and method for computing the correlation dimension will be discussed as well as the properties of colored random noise. Also to be discussed is how the properties of colored random noise can lead to a test to determine the difference between a colored random noise time series and a time series from ordinary differential equations that are chaotic.

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We study the global stability of charged dust grains orbiting an axisymmetric planet with co-rotating magnetic field. The magnetic field and induced electric field are described in an inertial frame using the magnetic stream function $\Psi$. The combined gravitational, magnetic, and electric forces are modelled by a two dimensional effective potential $U^e(\rho,z)$, parametrized by the conserved angular momentum $\pp$. The critical points of $U^e$ then locate the equilibrium circular orbits, nonequatorial as well as equatorial. The stable equilibria form the nuclei of potential wells, which can contain large populations of dust grains. These potential wells have their own topological structure, so that a particle which loses local stability can still be trapped globally. Explicit Lyapunov stability boundaries are derived for both positive and negative charges in both prograde and retrograde orbits. Thus, radial stability is lost when a critical point of $U^e$ undergoes a ta! ngent bifurcation, while transverse stability is lost via a pitchfork bifurcation. For a given position near a given planet stability depends only on the charge-to-mass ratio $q/m$, which for a spherical dust grain is proportion to $\Phi/a^2$, where $\Phi$ is the ambient plasma potential and $a$ is the grain radius. The results are applied to Saturn and Jupiter.

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The edge and scrape-off-layer (SOL) of a tokamak plasma, while comprising only a few percent of the minor radius, is of great importance in understanding global tokamak confinement and heat deposition on the divertor plates. In this talk, a tutorial introduction to some of the relevant physics governing boundary plasma instabilities and turbulence will be presented, including the use of the collisional fluid Braginskii equations, the role of X-point geometry on wave physics, and the types of modes and instability drives thought to be important. Then, the results of recent work will be presented in which we have identified the curvature-driven resistive X-point mode as the dominant instability of a characteristic L-phase discharge in the DIII-D tokamak. This mode, expected to be a generic L-mode edge/SOL instability, is electromagnetic in the "bad curvature" region, but transitions to an electrostatic mode near the X-point due to the combined effects of resistivity and X-point magnetic shear. Motivated by observations of elevated electron temperature near the X-point, we investigate heating and parallel energy flow induced by the resistive X-point mode. We speculate that energy in the unstable waves flows to and dissipates in the X-point region, heating the electrons. Progress in understanding the nonlinear saturation levels and implications of this mode for perpendicular wave-induced transport will be discussed.

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Landau's prescription for determining the dispersion relation of waves in a collisionless plasma with a given velocity distribution for each species lies at the heart of kinetic plasma theory. However the treatment of damped modes requires the analytic continuation of the distribution functions for complex velocities.

In practical application, velocity distributions are often determined experimentally, or are numerically generated by computer simulations. These general distribution functions cannot be assumed analytic, nor can they necessarily be well-modeled by a superposition of analytic functions (e.g., Maxwellians).

An alternative perspective on the problem of determining the dispersive properties of damped plasma waves will be presented. This method draws a connection between the plasma susceptibility and the convolution (or deconvolution) of the distribution function with simple Lorentzians. This approach lends itself to the numerical determination of the plasma susceptibility for piecewise-analytic distributions that have been subjected to Gaussian smoothing.

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The Penning trap confines plasma of electrons (or ions) by using an electrostatic potential to prevent the escape of particles along magnetic field lines. A modified Penning trap has been constructed which has an azimuthal magnetic field made by wires along the axis. The resulting field is helical and particles execute bounce orbits along helical field lines. Drifts cause a particle path in the +z direction to be at a slightly larger radius than in the -z direction so that the orbit is oval, like a rubber band. Collisions cause a step-wise change in position with a characteristic length determined by the width of the oval rather than the the Larmor radius. Experiments in the new trap allow aspects of transport theory for toroidal devices to be isolated and tested. The first experiment shows that the transport due to electric mobility scales with the width of the oval drift orbit (the "banana width") and not with the Larmor radius.

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Recent advances in available on-board electrical power in satellites has moved plasma propulsion devices from the laboratory to space-based application. In the past year alone more than 80 spacecraft employing some type of plasma propulsion system were flown on commercial vehicles. This talk will present a brief introduction to plasma thrusters including Arcjets, Resisojets, Electrostatic Ion Thrusters, and Magnetoplasmadynamic Thrusters before entering a more detailed analysis of the plasma transport properties in the plume of closed-drift Hall-effect thrusters. The Hall thruster utilizes static crossed electric and magnetic fields to accelerate ionized xenon producing a reactive thrust. The experimental investigation reported utilized in-situ probes to quantify the transport of charged and neutral species in the flowing exhaust plume as well as the construction of a molecular beam mass spectrometer to provide species-dependent measurements of the heavy-particle energy distributions. Among the phenomena discovered was the existence of an anomalous population of ions having apparent acceleration voltages of up to three times that applied to the discharge electrodes. Discussion of such phenomena in the context of charge- and momentum-transfer collisions will be presented.

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Numerical, as opposed to symbolic, differential algebras have a growing number of uses in computational science. These differential algebras can be used for simultaneous calculation of some quantity plus a certain number of its derivatives up to some order in some number of variables. Solving a differential equation for a differential algebra element gives the Taylor series expansion for the transfer map - the solution for initial conditions near some particular initial condition. In recent years, it has been recognized that numerical differential algebras are most easily treated by Object Oriented Programming methods in C++, a language that allows operator overloading. In this talk we will review numerical differential algebras and object oriented programming methods. We then discuss the implementation of numerical differential algebras within C++ and show that by judicious choice of data layout, the effiency of the numerical calculations can be increased by an order of magnitude.

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The effect of poloidally mode coupled, ballooning type electrostatic drift waves on a magnetic island has been studied both analytically and numerically. It has been shown quantitatively that particle orbits become stochastic and their behavior can be a possible candidate for the radial plasma transport across a magnetic island of a tokamak. The transport is significant in that it takes place even when the flux surface is not destroyed. The mechanism of the stochasticity generation is understood as an overlapping of secondary islands caused by resonance between periodic particle motions in the magnetic island and Fourier modes of E x B drift due to the electrostatic drift waves. The diffusion process perpendicular to the island magnetic surface has been shown to follow the Gaussian type and can be influential for the deterioration of the plasma confinement. In addition, local diffusion process in the vicinity of Kolmogorov, Arnold and Moser (KAM) surfaces is discussed.

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The spatiotemporal evolution of stimulated Brillouin scattering (SBS) in homogeneous plasmas and some aspects of the influence that nonlinear and kinetic effects have on the evolution of SBS were studied.

A one-dimensional analytical linear model based on a fluid description of the plasma was initially developed. It was found that the threshold intensity of the absolute instability and the steady-state spatial growth rate of the convective instability are both independent of the scattering angle. However, the saturation time of the convective instability exhibits a strong inverse dependence on the scattering angle.

The basic model was improved by extending the one-dimensional analysis to include two spatial dimensions and time. In order to assess the effects that the finite size of the laser beam has on SBS, wide and narrow laser-beam geometries were considered. Detailed comparison were made between the predictions of a reduced 1D and 2d models, which can be solved and analytically, and the results of 2D numerical simulations.

The influence that nonlinear and kinetic effects have on SBS was investigated by performing particle-in-cell (PIC) simulations. The results of these PIC simulations were compared against fluid simulations, and good agreement was obtained for sufficiently weak laser intensities. When the laser intensity is sufficiently strong for ion trapping to be significant, PIC and fluid simulations differ substantially. The SBS reflectivity is shown to depend sensitively on the frequency mismatch between the light wave used to seed the instability and the incident laser.

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Plasmas, the ionized states of matter, are usually hot and gaseous. However, a sufficiently cold or dense plasma can be liquid or solid. We trap beryllium ions in a Penning trap, and utilize laser cooling to reduce the ion temperature to less than 5 mK. By applying an asymmetric electric field that rotates in the same sense as the ions, we are able to phase-lock the rotation of these plasmas, therefore enabling precise control of the plasma density and shape. The ions freeze into Coulomb crystals, which we have studied through both Bragg diffraction and spatial imaging. The crystals have a rich phase structure, whose features are shared with such diverse systems as neutron star crusts, hard spheres, colloidal suspensions and semiconductor electron bilayers. Plasma modes can be excited with potentials applied to the trap electrodes, and directly imaged by changes in the ion resonance fluorescence produced by Doppler shifts from the coherent velocities of the mode. Enhanced radial transport is observed where modes are resonant with static external perturbations; similarly, the plasma angular momentum can be usefully changed through the deliberate excitation of azimuthally asymmetric modes. Precise control of the plasma's angular momentum and structure is important for possible applications such as frequency standards, quantum computing and antihydogen production.

Reprints are available.

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