Modeling Course-Based Undergraduate Research Experiences: An Agenda for Future Research and Evaluation

Course-based undergraduate research experiences (CUREs) are being championed as scalable ways of involving undergraduates in science research. Studies of CUREs have shown that participating students achieve many of the same outcomes as students who complete research internships. However, CUREs vary widely in their design and implementation, and aspects of CUREs that are necessary and sufficient to achieve desired student outcomes have not been elucidated. To guide future research aimed at understanding the causal mechanisms underlying CURE efficacy, we used a systems approach to generate pathway models representing hypotheses of how CURE outcomes are achieved. We started by reviewing studies of CUREs and research internships to generate a comprehensive set of outcomes of research experiences, determining the level of evidence supporting each outcome. We then used this body of research and drew from learning theory to hypothesize connections between what students do during CUREs and the outcomes that have the best empirical support. We offer these models as hypotheses for the CURE community to test, revise, elaborate, or refute. We also cite instruments that are ready to use in CURE assessment and note gaps for which instruments need to be developed.Howard Hughes Medical InstituteScience and Mathematics Educatio

Extensions of Johnson's and Morita's homomorphisms that map to finitely generated abelian groups

We extend each higher Johnson homomorphism to a crossed homomorphism from the automorphism group of a finite-rank free group to a finite-rank abelian group. We also extend each Morita homomorphism to a crossed homomorphism from the mapping class group of once-bounded surface to a finite-rank abelian group. This improves on the author's previous results [Algebr. Geom. Topol. 7 (2007):1297-1326]. To prove the first result, we express the higher Johnson homomorphisms as coboundary maps in group cohomology. Our methods involve the topology of nilpotent homogeneous spaces and lattices in nilpotent Lie algebras. In particular, we develop a notion of the "polynomial straightening" of a singular homology chain in a nilpotent homogeneous space.Comment: 34 page

Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.Comment: 14 pages, 8 figure

A quasi-pure Bose-Einstein condensate immersed in a Fermi sea

We report the observation of co-existing Bose-Einstein condensate and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the 7Li condensate is quasi-pure and in thermal contact with a 6Li Fermi gas. The lowest common temperature is 0.28 muK = 0.2(1) T_C = 0.2(1) T_F where T_C is the BEC critical temperature and T_F the Fermi temperature. Behaving as an ideal gas in the radial trap dimension, the condensate is one-dimensional.Comment: 4 pages, 5 figure

Geometric quantization of Hamiltonian actions of Lie algebroids and Lie groupoids

We construct Hermitian representations of Lie algebroids and associated unitary representations of Lie groupoids by a geometric quantization procedure. For this purpose we introduce a new notion of Hamiltonian Lie algebroid actions. The first step of our procedure consists of the construction of a prequantization line bundle. Next, we discuss a version of K\"{a}hler quantization suitable for this setting. We proceed by defining a Marsden-Weinstein quotient for our setting and prove a ``quantization commutes with reduction'' theorem. We explain how our geometric quantization procedure relates to a possible orbit method for Lie groupoids. Our theory encompasses the geometric quantization of symplectic manifolds, Hamiltonian Lie algebra actions, actions of families of Lie groups, foliations, as well as some general constructions from differential geometry.Comment: 40 pages, corrected version 11-01-200

Isotopic difference in the heteronuclear loss rate in a two-species surface trap

We have realized a two-species mirror-magneto-optical trap containing a mixture of $^{87}$Rb ($^{85}$Rb) and $^{133}$Cs atoms. Using this trap, we have measured the heteronuclear collisional loss rate $\beta_{Rb-Cs}'$ due to intra-species cold collisions. We find a distinct difference in the magnitude and intensity dependence of $\beta_{Rb-Cs}'$ for the two isotopes $^{87}$Rb and $^{85}$Rb which we attribute to the different ground-state hyperfine splitting energies of the two isotopes.Comment: 4 pages, 2 figure

Fluorescence measurements of expanding strongly-coupled neutral plasmas

We report new detailed density profile measurements in expanding strongly-coupled neutral plasmas. Using laser-induced fluorescence techniques, we determine plasma densities in the range of 10^5 to 10^9/cm^3 with a time resolution limit as small as 7 ns. Strong-coupling in the plasma ions is inferred directly from the fluorescence signals. Evidence for strong-coupling at late times is presented, confirming a recent theoretical result.Comment: submitted to PR

Fundamental noise limitations to supercontinuum generation in microstructure fiber

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50 % for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schroedinger equation, finding good quantitative agreement over a range of input pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input pulse shot noise and the spontaneous Raman scattering down the fiber.Comment: 16 pages with 6 figure

From interacting particle systems to random matrices

In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This means that the scaling exponents do not uniquely determine the large time surface statistics, but one has to further divide into subclasses. Some of the fluctuation laws were first discovered in random matrix models. Moreover, the limit process for curved limit shape turned out to show up in a dynamical version of hermitian random matrices, but this analogy does not extend to the case of symmetric matrices. Therefore the connections between growth models and random matrices is only partial.Comment: 18 pages, 8 figures; Contribution to StatPhys24 special issue; minor corrections in scaling of section 2.