Innovative Opportunities for Elementary and Middle School Teachers to Maintain Currency in Mathematics and Science: A Community College-School System Partnership

Since 1992 the Manassas Campus of Northern Virginia Community College – in response to requests from local school systems – has developed four innovative methods of assisting elementary, secondary and middle school teachers to enhance their content knowledge in science and mathematics, as well as integrate curriculum units for classroom presentation. These methods are based on the assumptions that: - While teachers at this level have fundamental understanding of math and science, if they wish to incorporate new concepts or technologies from these fields, graduate level content courses are generally beyond their background level. - Community College faculty can often provide a bridge that connects advanced content in science and mathematics with the applications that can be adapted to elementary/middle school curriculum. - Presenting content to a mixed audience of teachers from K-8 allows teachers to see how content can be adapted to grade levels above and below. - Content delivery methods must be interactive and must be responsive to the multiple demands on these teachers’ time. This requires flexibility in scheduling and course requirements

Application of projection algorithms to differential equations: boundary value problems

The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary valued problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well-suited to parallelization. We explore the stability of the method by applying it to several examples of BVPs, including cases where the traditional Newton's method fails

Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics

The dependence of inter-particle correlations on the orientation of particle relative-momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real cartesian harmonics. Mathematical properties of the lesser-known cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regarding to determining angular features of emission regions is investigated. The considered final-state effects include identity interference and strong and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.Comment: 32 pages 10 figure

The influence of defects of the fatigue resistance of butt and girth welds in A106B steel

This three-phase study was directed at developing a fitness for service defect acceptance criteria for welds with defect indications. The study focussed on A106 Gr. B steel pipe. The first phase involved a literature search and critical review to develop the preliminary acceptance criteria to the extent permitted by the data. The second phase developed data for flat plate, wall segment, and vessel specimens containing artificial or natural planar or volumetric defects. The final phase developed acceptance criteria from the test data

Energetic Consistency and Momentum Conservation in the Gyrokinetic Description of Tokamak Plasmas

Gyrokinetic field theory is addressed in the context of a general Hamiltonian. The background magnetic geometry is static and axisymmetric, and all dependence of the Lagrangian upon dynamical variables is in the Hamiltonian or in free field terms. Equations for the fields are given by functional derivatives. The symmetry through the Hamiltonian with time and toroidal angle invariance of the geometry lead to energy and toroidal momentum conservation. In various levels of ordering against fluctuation amplitude, energetic consistency is exact. The role of this in underpinning of conservation laws is emphasised. Local transport equations for the vorticity, toroidal momentum, and energy are derived. In particular, the momentum equation is shown for any form of Hamiltonian to be well behaved and to relax to its magnetohydrodynamic (MHD) form when long wavelength approximations are taken in the Hamiltonian. Several currently used forms, those which form the basis of most global simulations, are shown to be well defined within the gyrokinetic field theory and energetic consistency.Comment: RevTeX 4, 47 pages, no figures, revised version updated following referee comments (discussion more strictly correct/consistent, 4 references added, results unchanged as they depend on consistency of the theory), resubmitted to Physics of Plasma

Ultraviolet/X-ray variability and the extended X-ray emission of the radio-loud broad absorption line quasar PG 1004+130

We present the results of recent Chandra, XMM-Newton, and Hubble Space Telescope observations of the radio-loud (RL), broad absorption line (BAL) quasar PG 1004+130. We compare our new observations to archival X-ray and UV data, creating the most comprehensive, high signal-to-noise, multi-epoch, spectral monitoring campaign of a RL BAL quasar to date. We probe for variability of the X-ray absorption, the UV BAL, and the X-ray jet, on month-year timescales. The X-ray absorber has a low column density of $N_{H}=8\times10^{20}-4\times10^{21}$ cm$^{-2}$ when it is assumed to be fully covering the X-ray emitting region, and its properties do not vary significantly between the 4 observations. This suggests the observed absorption is not related to the typical "shielding gas" commonly invoked in BAL quasar models, but is likely due to material further from the central black hole. In contrast, the CIV BAL shows strong variability. The equivalent width (EW) in 2014 is EW=11.24$\pm$0.56 \AA, showing a fractional increase of $\Delta EW / \langle EW \rangle$=1.16$\pm$0.11 from the 2003 observation, 3183 days earlier in the rest-frame. This places PG 1004+130 among the most highly variable BAL quasars. By combining Chandra observations we create an exposure 2.5 times deeper than studied previously, with which to investigate the nature of the X-ray jet and extended diffuse X-ray emission. An X-ray knot, likely with a synchrotron origin, is detected in the radio jet ~8 arcsec (30 kpc) from the central X-ray source with a spatial extent of ~4 arcsec (15 kpc). No similar X-ray counterpart to the counterjet is detected. Asymmetric, non-thermal diffuse X-ray emission, likely due to inverse Compton scattering of Cosmic Microwave Background photons, is also detected.Comment: 15 pages, 7 figures, 3 tables. Accepted for publication in Ap

Correlation length scalings in fusion edge plasma turbulence computations

The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence computations. Scalings by density gradient length, collisionality, plasma beta, and by an imposed shear flow are considered. It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.Comment: Submitted to "Plasma Physics and Controlled Fusion

Magnification as a Tool in Weak Lensing

Weak lensing surveys exploit measurements of galaxy ellipticities. These measurements are subject to errors which degrade the cosmological information that can be extracted from the surveys. Here we propose a way of using the galaxy data themselves to calibrate the measurement errors. In particular, the cosmic shear field, which causes the galaxies to appear elliptical, also changes their sizes and fluxes. Information about the sizes and fluxes of the galaxies can be added to the shape information to obtain more robust information about the cosmic shear field. The net result will be tighter constraints on cosmological parameters such as those which describe dark energy.Comment: 4 pages, 2 figure