The Impact of Early Positive Results on a Mathematics and Science Partnership: The Experience of the Institute for Chemistry Literacy Through Computational Science

After one year of implementation, the Institute for Chemistry Literacy through Computational Science, an NSF Mathematics and Science Partnership Institute Project led by the University of Illinois at Urbana-Champaign’s Department of Chemistry, College of Medicine, and National Center for Supercomputing Applications, experienced statistically significant gains in chemistry content knowledge among students of the rural high school teachers participating in its intensive, year-round professional development course, compared to a control group. The project utilizes a two-cohort, delayed-treatment, random control trial, quasi-experimental research design with the second cohort entering treatment one year following the first. The three-year treatment includes intensive two-week summer institutes, occasional school year workshops and year-round, on-line collaborative lesson development, resource sharing, and expert support. The means of student pre-test scores for Cohort I (η=963) and Cohort II (η=862) teachers were not significantly different. The mean gain (difference between pre-test and post-test scores) after seven months in the classroom for Cohort I was 9.8 percentage points, compared to 6.7 percentage points for Cohort II. This statistically significant difference (p\u3c.001) represented an effect size of .25 standard deviation units, and indicated unusually early confirmation of treatment effects. When post-tests were compared, Cohort I students scored significantly higher than Cohort II and supported the gain score differences. The impact of these results on treatment and research plans is discussed. concentrating on the effect of lessening rural teachers’ isolation and increasing access to tools to facilitate learning

A new way to see inside black holes

Black holes are real astrophysical objects, but their interiors are hidden and can only be "observed" through mathematics. The structure of rotating black holes is typically illustrated with the help of special coordinates. But any such coordinate choice necessarily results in a distorted view, just as the choice of projection distorts a map of the Earth. The truest way to depict the properties of a black hole is through quantities that are coordinate-invariant. We compute and plot all the independent curvature invariants of rotating, charged black holes for the first time, revealing a landscape that is much more beautiful and complex than usually thought.Comment: 4 pages, 3 figures, published in Bridges Baltimore 2015: Mathematics, Music, Art, Architecture, Culture (Phoenix, AZ: Tessellations Publishing, 2015), 479-482. Revised to fix a referenc

Stabilization of large space structures by linear reluctance actuators

Application of magnetic forces are considered for stabilization of vibrations of flexible space structures. Three electromagnetic phenomena are studied, such as: (1) magnetic body force; (2) reluctance torque; and (3) magnetostriction, and their application is analyzed for stabilization of a beam. The magnetic body force actuator uses the force that exists between poles of magnets. The reluctance actuator is configured in such a way that the reluctance of the magnetic circuit will be minimum when the beam is straight. Any bending of the beam increases the reluctance and hence generates a restoring torque that reduces bending. The gain of the actuator is controlled by varying the magnetizing current. Since the energy density of a magnetic device is much higher compared to piezoelectric or thermal actuators, it is expected that the reluctance actuator will be more effective in controlling the structural vibrations

Fractional Chemotaxis Diffusion Equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page

Abundances of Disk Planetary Nebulae in M31 and the Radial Oxygen Gradient

We have obtained spectra of 16 planetary nebulae in the disk of M31 and determined the abundances of He, N, O, Ne, S and Ar. Here we present the median abundances and compare them with previous M31 PN disk measurements and with PNe in the Milky Way. We also derive the radial oxygen gradient in M31, which is shallower than that in the Milky Way, even accounting for M31's larger disk scale length.Comment: 2 pages, 1 figure, 1 table, to appear in the proceedings of IAU Symposium No. 283, Planetary Nebulae: An Eye to the Futur

ELSA: An Integrated, Semi-Automated Nebular Abundance Package

We present ELSA, a new modular software package, written in C, to analyze and manage spectroscopic data from emission-line objects. In addition to calculating plasma diagnostics and abundances from nebular emission lines, the software provides a number of convenient features including the ability to ingest logs produced by IRAF's splot task, to semi-automatically merge spectra in different wavelength ranges, and to automatically generate various data tables in machine-readable or LaTeX format. ELSA features a highly sophisticated interstellar reddening correction scheme that takes into account temperature and density effects as well as He II contamination of the hydrogen Balmer lines. Abundance calculations are performed using a 5-level atom approximation with recent atomic data, based on R. Henry's ABUN program. Improvements planned in the near future include use of a three-region ionization model, similar to IRAF's nebular package, error propagation, and the addition of ultraviolet and infrared line analysis capability. Detailed documentation for all aspects of ELSA are available at http://www.williams.edu/Astronomy/research/PN .Comment: 2 pages, contributed paper, IAU Symp. 234, Planetary Nebulae in Our Galaxy and Beyon