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

First-principles thermodynamic modeling of lanthanum chromate perovskites

Tendencies toward local atomic ordering in (A,A′)(B,B′)O_(3−δ) mixed composition perovskites are modeled to explore their influence on thermodynamic, transport, and electronic properties. In particular, dopants and defects within lanthanum chromate perovskites are studied under various simulated redox environments. (La_(1−x),Sr_x)(Cr_(1−y),Fe_y)O_(3−δ) (LSCF) and (La_(1−x),Sr_x)(Cr_(1−y),Ru_y)O_(3−δ) (LSCR) are modeled using a cluster expansion statistical thermodynamics method built upon a density functional theory database of structural energies. The cluster expansions are utilized in lattice Monte Carlo simulations to compute the ordering of Sr and Fe(Ru) dopant and oxygen vacancies (Vac). Reduction processes are modeled via the introduction of oxygen vacancies, effectively forcing excess electronic charge onto remaining atoms. LSCR shows increasingly extended Ru-Vac associates and short-range Ru-Ru and Ru-Vac interactions upon reduction; LSCF shows long-range Fe-Fe and Fe-Vac interaction ordering, inhibiting mobility. First principles density functional calculations suggest that Ru-Vac associates significantly decrease the activation energy of Ru-Cr swaps in reduced LSCR. These results are discussed in view of experimentally observed extrusion of metallic Ru from LSCR nanoparticles under reducing conditions at elevated temperature

First-principles thermodynamic modeling of atomic ordering in yttria-stabilized zirconia

Yttria-stabilized zirconia YSZ is modeled using a cluster expansion statistical thermodynamics method built upon a density-functional theory database. The reliability of cluster expansions in predicting atomic ordering is explored by comparing with the extensive experimental database. The cluster expansion of YSZ is utilized in lattice Monte Carlo simulations to compute the ordering of dopant and oxygen vacancies as a function of concentration. Cation dopants show a strong tendency to aggregate and vacate significantly sized domains below 9 mol % Y_2O_3, which is likely important for YSZ aging processes in ionic conductivity. Evolution of vibrational and underlying electronic properties as a function of Y doping is explored

Multi-fuel rotary engine for general aviation aircraft

Design studies of advanced multifuel general aviation and commuter aircraft rotary stratified charge engines are summarized. Conceptual design studies were performed at two levels of technology, on advanced general aviation engines sized to provide 186/250 shaft kW/hp under cruise conditions at 7620 (25000 m/ft) altitude. A follow on study extended the results to larger (2500 hp max.) engine sizes suitable for applications such as commuter transports and helicopters. The study engine designs were derived from relevant engine development background including both prior and recent engine test results using direct injected unthrottled rotary engine technology. Aircraft studies, using these resultant growth engines, define anticipated system effects of the performance and power density improvements for both single engine and twin engine airplanes. The calculated results indicate superior system performance and 27 to 33 percent fuel economy improvement for the rotary engine airplanes as compared to equivalent airframe concept designs with current baseline engines. The research and technology activities required to attain the projected engine performance levels are also discussed

Observation of the Purcell effect in high-index-contrast micropillar

We have fabricated pillar microcavity samples with Bragg mirrors consisting of alternate layers of GaAs and Aluminium Oxide. Compared to the more widely studied GaAs/AlAs micropillars these mirrors can achieve higher reflectivities with fewer layer repeats and reduce the mode volume. We have studied a number of samples containing a low density of InGaAs/GaAs self assembled quantum dots in a cavity and here report observation of a three fold enhancement in the radiative lifetime of a quantum dot exciton state due to the Purcell effect

Oxide-apertured microcavity single-photon emitting diode

We have developed a microcavity single-photon source based on a single quantum dot within a planar cavity in which wet-oxidation of a high-aluminium content layer provides lateral confinement of both the photonic mode and the injection current. Lateral confinement of the optical mode in optically pumped structures produces a strong enhancement of the radiative decay rate. Using microcavity structures with doped contact layers, we demonstrate a single-photon emitting diode where current may be injected into a single dot

Thermomechanical characterization of Hastelloy-X under uniaxial cyclic loading

In most high-temperature engineering applications, components are subjected to complex combinations of thermal and mechanical loading during service. A number of viscoplastic constitutive models were proposed which potentially can provide mathematical descriptions of material response under such conditions. Implementation of these models into large finite element codes such as MARC has already resulted in much improved inelastic analysis capability for hot-section aircraft engine components. However, a number of questions remain regarding the validity of methods adopted in characterizing these constitutive models for particular high-temperature materials. One area of concern is that the majority of experimental data available for this purpose are determined under isothermal conditions. This is in contrast to service conditions which, as noted above, almost always involve some form of thermal cycling. The obvious question arises as to whether a constitutive model characterized using an isothermal data base can adequately predict material response under thermomechanical conditions. An experimental program was initiated within the HOST program to address this particular concern. The results of the most recent isothermal and thermomechanical experiments are described

Jet Investigations Using the Radial Moment

We define the radial moment, , for jets produced in hadron-hadron collisions. It can be used as a tool for studying, as a function of the jet transverse energy and pseudorapidity, radiation within the jet and the quality of a perturbative description of the jet shape. We also discuss how non-perturbative corrections to the jet transverse energy affect .Comment: 14 pages, LaTeX, 6 figure

An approximate isoperimetric inequality for r-sets

10 pages10 pages10 pages10 pagesWe prove a vertex-isoperimetric inequality for [n]^(r), the set of all r-element subsets of {1,2,...,n}, where x,y \in [n]^(r) are adjacent if |x \Delta y|=2. Namely, if \mathcal{A} \subset [n]^(r) with |\mathcal{A}|=\alpha {n \choose r}, then the vertex-boundary b(\mathcal{A}) satisfies |b(\mathcal{A})| \geq c\sqrt{\frac{n}{r(n-r)}} \alpha(1-\alpha) {n \choose r}, where c is a positive absolute constant. For \alpha bounded away from 0 and 1, this is sharp up to a constant factor (independent of n and r).The research of the first author was supported by EPSRC grant EP/G056730/1; the research of the third author was supported in part by ERC grant 239696 and EPSRC grant EP/G056730/1