A Collaborative Approach: Two Perspectives

This article is a story of collaboration between a principal, Baek Chong, and the mathematics coach, Megan Farrelly. This article shows both perspectives: Baek\u27s thoughts are written in regular typeface, whereas Megan\u27s perspective is italicized. Both educators work at Mark Twain Middle School in Fairfax County Public Schools in Virginia which has nearly 900 seventh- and eighth-grade students. Twain Middle School serves a diverse population, of which about 35% of the students arc on free or reduced lunch, 15% receive special education services, 14% receive English language services, and 40% of the students are in the advanced academics program

Ultrafast and octave-spanning optical nonlinearities from strongly phase-mismatched cascaded interactions

Cascaded nonlinearities have attracted much interest, but ultrafast applications have been seriously hampered by the simultaneous requirements of being near phase-matching and having ultrafast femtosecond response times. Here we show that in strongly phase-mismatched nonlinear frequency conversion crystals the pump pulse can experience a large and extremely broadband self-defocusing cascaded Kerr-like nonlinearity. The large cascaded nonlinearity is ensured through interaction with the largest quadratic tensor element in the crystal, and the strong phase-mismatch ensures an ultrafast nonlinear response with an octave-spanning bandwidth. We verify this experimentally by showing few-cycle soliton compression with noncritical cascaded second-harmonic generation: Energetic 47 fs infrared pulses are compressed in a just 1-mm long bulk lithium niobate crystal to 17 fs (under 4 optical cycles) with 80% efficiency, and upon further propagation an octave-spanning supercontinuum is observed. Such ultrafast cascading is expected to occur for a broad range of pump wavelengths spanning the near- and mid-IR using standard nonlinear crystals.Comment: resubmitted, revised version, accepted for Phys. Rev. Let

Perturbation theory of constraints - Application to a lithium hydride calculation

Constraint perturbation calculations for ground state of lithium hydride molecul

Isovector channel of quark-meson-coupling model and its effect on symmetry energy

The non-relativistic approximation of the quark-meson-coupling model has been discussed and compared with the Skyrme-Hartree-Fock model which includes spin exchanges. Calculations show that the spin-exchange interaction has important effect on the descriptions of finite nuclei and nuclear matter through the Fock exchange. Also in the quark-meson-coupling model, it is the Fock exchange that leads to a nonlinear density-dependent isovector channel and changes the density-dependent behavior of the symmetry energy.Comment: 20 pages, 9 figures and 1 table, accepted for publication in Nuclear Physics

Antiproton-Proton Channels in J/psi Decays

The recent measurements by the BES Collaboration of J/psi decays into a photon and a proton-antiproton pair indicate a strong enhancement at the proton-antiproton threshold not observed in the decays into a neutral pion and a proton-antiproton pair. Is this enhancement due to a proton-antiproton quasi-bound state or a baryonium? A natural explanation follows from a traditional model of proton-antiproton interactions based on G-parity transformation. The observed proton-antiproton structure is due to a strong attraction in the 1S0 state, and possibly to a near-threshold quasi-bound state in the 11S0 wave.Comment: 6 pages, 5 figures. The antiproton-proton pair being in isospin one in the J/Psi decay into neutral pion-antiproton-proton, the antiproton-proton 1P1 and 3S1 waves have been replaced by the 31P1 and 33S1 ones and Figs. 1 and 2 have been replaced accordingly. Conclusions are unchanged. Most of the content of the paper is published in Phys. Rev. C72, 011001 (2005

Laser Mode Bifurcations Induced by PT\mathcal{PT}-Breaking Exceptional Points

A laser consisting of two independently-pumped resonators can exhibit mode bifurcations that evolve out of the exceptional points (EPs) of the linear system at threshold. The EPs are non-Hermitian degeneracies occurring at the parity/time-reversal ($\mathcal{PT}$) symmetry breaking points of the threshold system. Above threshold, the EPs become bifurcations of the nonlinear zero-detuned laser modes, which can be most easily observed by making the gain saturation intensities in the two resonators substantially different. Small pump variations can then switch abruptly between different laser behaviors, e.g. between below-threshold and $\mathcal{PT}$-broken single-mode operation.Comment: 4 pages, 3 figure

UV-enhanced sacrificial layer stabilised graphene oxide hollow fibre membranes for nanofiltration

Graphene oxide (GO) membranes have demonstrated great potential in gas separation and liquid filtration. For upscale applications, GO membranes in a hollow fibre geometry are of particular interest due to the high-efficiency and easy-assembly features at module level. However, GO membranes were found unstable in dry state on ceramic hollow fibre substrates, mainly due to the drying-related shrinkage, which has limited the applications and post-treatments of GO membranes. We demonstrate here that GO hollow fibre membranes can be stabilised by using a porous poly(methyl methacrylate) (PMMA) sacrificial layer, which creates a space between the hollow fibre substrate and the GO membrane thus allowing stress-free shrinkage. Defect-free GO hollow fibre membrane was successfully determined and the membrane was stable in a long term (1200 hours) gas-tight stability test. Post-treatment of the GO membranes with UV light was also successfully accomplished in air, which induced the creation of controlled microstructural defects in the membrane and increased the roughness factor of the membrane surface. The permeability of the UV-treated GO membranes was greatly enhanced from 0.07 to 2.8 L m(−2) h(−1) bar(−1) for water, and 0.14 to 7.5 L m(−2) h(−1) bar(−1) for acetone, with an unchanged low molecular weight cut off (~250 Da)