Generalized shuffles related to Nijenhuis and TD-algebras

Shuffle and quasi-shuffle products are well-known in the mathematics literature. They are intimately related to Loday's dendriform algebras, and were extensively used to give explicit constructions of free commutative Rota-Baxter algebras. In the literature there exist at least two other Rota-Baxter type algebras, namely, the Nijenhuis algebra and the so-called TD-algebra. The explicit construction of the free unital commutative Nijenhuis algebra uses a modified quasi-shuffle product, called the right-shift shuffle. We show that another modification of the quasi-shuffle product, the so-called left-shift shuffle, can be used to give an explicit construction of the free unital commutative TD-algebra. We explore some basic properties of TD-operators and show that the free unital commutative Nijenhuis algebra is a TD-algebra. We relate our construction to Loday's unital commutative dendriform trialgebras, including the involutive case. The concept of Rota-Baxter, Nijenhuis and TD-bialgebras is introduced at the end and we show that any commutative bialgebra provides such objects.Comment: 20 pages, typos corrected, accepted for publication in Communications in Algebr

Revealing large-scale homogeneity and trace impurity sensitivity of GaAs nanoscale membranes

III-V nanostructures have the potential to revolutionize optoelectronics and energy harvesting. For this to become a reality, critical issues such as reproducibility and sensitivity to defects should be resolved. By discussing the optical properties of MBE grown GaAs nanomembranes we highlight several features that bring them closer to large scale applications. Uncapped membranes exhibit a very high optical quality, expressed by extremely narrow neutral exciton emission, allowing the resolution of the more complex excitonic structure for the first time. Capping of the membranes with an AlGaAs shell results in a strong increase of emission intensity but also to a shift and broadening of the exciton peak. This is attributed to the existence of impurities in the shell, beyond MBE-grade quality, showing the high sensitivity of these structures to the presence of impurities. Finally, emission properties are identical at the sub-micron and sub-millimeter scale, demonstrating the potential of these structures for large scale applications.Comment: just accepted in Nano Letters, http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.7b0025

A high flux source of cold strontium atoms

We describe an experimental apparatus capable of achieving a high loading rate of strontium atoms in a magneto-optical trap operating in a high vacuum environment. A key innovation of this setup is a two dimensional magneto-optical trap deflector located after a Zeeman slower. We find a loading rate of 6x10^9/s whereas the lifetime of the magnetically trapped atoms in the 3P2 state is 54s.Comment: 12 pages, 16 figure

Three-dimensional imaging and detection efficiency performance of orthogonal coplanar CZT strip detectors

We report on recent three-dimensional imaging performance and detection efficiency measurements obtained with 5 mm thick prototype CdZnTe detectors fabricated with orthogonal coplanar anode strips. In previous work, we have shown that detectors fabricated using this design achieve both very good energy resolution and sub-millimeter spatial resolution with fewer electronic channels than are required for pixel detectors. As electron-only devices, like pixel detectors, coplanar anode strip detectors can be fabricated in the thickness required to be effective imagers for photons with energies in excess of 500 keV. Unlike conventional double-sided strip detectors, the coplanar anode strip detectors require segmented contacts and signal processing electronics on only one surface. The signals can be processed to measure the total energy deposit and the photon interaction location in three dimensions. The measurements reported here provide a quantitative assessment of the detection capabilities of orthogonal coplanar anode strip detectors

Strong light-matter coupling in bulk GaN-microcavities with double dielectric mirrors fabricated by two different methods

Two routes for the fabrication of bulk GaN microcavities embedded between two dielectric mirrors are described, and the optical properties of the microcavities thus obtained are compared. In both cases, the GaN active layer is grown by molecular beam epitaxy on (111) Si, allowing use of selective etching to remove the substrate. In the first case, a three period Al0.2Ga0.8N / AlN Bragg mirror followed by a lambda/2 GaN cavity are grown directly on the Si. In the second case, a crack-free 2,mu m thick GaN layer is grown, and progressively thinned to a final thickness of lambda. Both devices work in the strong coupling regime at low temperature, as evidenced by angle-dependent reflectivity or transmission experiments. However, strong light-matter coupling in emission at room temperature is observed only for the second one. This is related to the poor optoelectronic quality of the active layer of the first device, due to its growth only 250 nm above the Si substrate and its related high defect density. The reflectivity spectra of the microcavities are well accounted for by using transfer matrix calculations. (C) 2010 American Institute of Physics. [doi:10.1063/1.3477450

Multiscale nature of hysteretic phenomena: Application to CoPt-type magnets

We suggest a workable approach for the description of multiscale magnetization reversal phenomena in nanoscale magnets and apply it to CoPt-type alloys. We show that their hysteretic properties are governed by two effects originating at different length scales: a peculiar splitting of domain walls and their strong pinning at antiphase boundaries. We emphasize that such multiscale nature of hysteretic phenomena is a generic feature of nanoscale magnetic materials.Comment: 4 pages (revtex 4), 2 color EPS figure

Mixable Shuffles, Quasi-shuffles and Hopf Algebras

The quasi-shuffle product and mixable shuffle product are both generalizations of the shuffle product and have both been studied quite extensively recently. We relate these two generalizations and realize quasi-shuffle product algebras as subalgebras of mixable shuffle product algebras. As an application, we obtain Hopf algebra structures in free Rota-Baxter algebras.Comment: 14 pages, no figure, references update

SEM-EDS analyses of small craters in stardust aluminium foils: implications for the Wild-2 dust distribution

Implications for the Wild-2 dust distribution of the statistical results obtained by SEM-EDS from nearly 300 impact craters on aluminium foils of the Stardust sample tray assembly