Lattice models, cylinder partition functions, and the affine coxeter element

The partition functions of the affine Pasquier models on the cylinder are calculated in the continuum limit. The partition functions of the models based upon the Â(_n) cycle graphs are first found from the appropriate Coulomb-gas equivalence. Their relationship with the D(_n) and Ề(_6,7,8) models is established by constructing an affine analogue to the classical intertwiners using a Temperley-Lieb algebraic equivalence. From this relationship, each of the partition functions is constructed. We write our results in terms of 'generating polynomials' establishing explicitly the precise operator content of the conformally invariant continuum field theories. A numerical study is undertaken to establish the validity of the partition functions as calculated. We conclude that the partition functions calculated are correct. The partition functions are further studied and the connection with the McKay correspondence established. We establish a simple form for the partition functions in terms of degenerate c = 1 Virasoro characters and Chebychev polynomials of the second kind. From this, we establish the role within the partition functions played by the affine Coxeter element, a particular member of the Weyl group associated with the defining graph of the model. Some of the resulting consequences of this role are explored

The Incidence of Low-Metallicity Lyman-Limit Systems at z~3.5: Implications for the Cold-Flow Hypothesis of Baryonic Accretion

Cold accretion is a primary growth mechanism of simulated galaxies, yet observational evidence of "cold flows" at redshifts where they should be most efficient ($z=2$-4) is scarce. In simulations, cold streams manifest as Lyman-limit absorption systems (LLSs) with low heavy-element abundances similar to those of the diffuse IGM. Here we report on an abundance survey of 17 H I-selected LLSs at $z=3.2$-4.4 which exhibit no metal absorption in SDSS spectra. Using medium-resolution spectra obtained at Magellan, we derive ionization-corrected metallicities (or limits) with a Markov-Chain Monte Carlo sampling that accounts for the large uncertainty in $N_{\rm HI}$ measurements typical of LLSs. The metal-poor LLS sample overlaps with the IGM in metallicity and is best described by a model where $71^{+13}_{-11}\%$ are drawn from the IGM chemical abundance distribution. These represent roughly half of all LLSs at these redshifts, suggesting that 28-40$\%$ of the general LLS population at $z\sim3.7$ could trace unprocessed gas. An ancillary sample of ten LLSs without any a priori metal-line selection is best fit with $48^{+14}_{-12}\%$ of metallicities drawn from the IGM. We compare these results with regions of a moving-mesh simulation; the simulation finds only half as many baryons in IGM-metallicity LLSs, and most of these lie beyond the virial radius of the nearest galaxy halo. A statistically significant fraction of all LLSs have low metallicity and therefore represent candidates for accreting gas; large-volume simulations can establish what fraction of these candidates actually lie near galaxies and the observational prospects for detecting the presumed hosts in emission.Comment: 19 pages, 17 figures; Submitted to ApJ; Corrected figure 16

Influence of substrate miscut angle on surface morphology and luminescence properties of AlGaN

The influence of substrate miscut on Al0.5Ga0.5 N layers was investigated using cathodoluminescence (CL) hyperspectral imaging and secondary electron imaging in an environmental scanning electron microscope. The samples were also characterized using atomic force microscopy and high resolution X-ray diffraction. It was found that small changes in substrate miscut have a strong influence on the morphology and luminescence properties of the AlGaN layers. Two different types are resolved. For low miscut angle, a crack-free morphology consisting of randomly sized domains is observed, between which there are notable shifts in the AlGaN near band edge emission energy. For high miscut angle, a morphology with step bunches and compositional inhomogeneities along the step bunches, evidenced by an additional CL peak along the step bunches, are observed

Exploration of Directed Self Assembly Polymers

Directed Self Assembly (DSA) is an attractive alternative to 193i and multiple patterning. Various polymers were investigated to find the possible structures that can be created with them. Previous research was used to determine the process used. Two surface treatments, a polymer brush and hexamethyldisilazane (HMDS) were used to help the polymers phase separate into their respective structure. The first polymer a polystyrene (PS) block polydimethylsiloxane (PDMS) resulted in de-wetting and film non-uniformity that prevented measurement. The second polymer a PS block polyethylene oxide (PEO) resulted in crystallization if the PEO ratio was too high at 40% mole. When the PEO ratio was low enough at 29% mole and on a PS brush polymer via holes 30 nm in diameter were found using phase imaging on an Atomic Force Microscope (AFM). Repeat samples of the via holes de-wetted from the surface likely due to surface contamination preventing the brush polymer from adhering to the surface

Personalized body segment inertia parameters using 3D body scanner images

XV International Symposium on 3-D Analysis of Human Movement, MANCHESTER, ROYAUME-UNI, 03-/07/2018 - 06/07/2018Personalized values of Body Segment Inertia Parameters (BSIP) are necessary to perform dynamic analysis of human movement (e.g. trajectory of the whole body centre of mass trajectory for stability analysis, joint torques / muscular forces estimations, etc.). BSIPs are usually estimated using regressions derived from anthropometric tables (AT) [1]. However, these tables are usually not adapted to atypical populations (children, elderly, obese persons, individuals with prostheses, etc.) that are classically of interest. An alternative consists in estimating BSIPs from segments' volumes assuming a uniform density. This alternative is of growing interest as: 1) it would be suitable even for populations with atypical body mass repartition; 2) 3D body shapes acquisition has recently became easier and cheaper thanks to the developments of low-cost 3D scanners [2]. However, there are still some issues to makes this measurement (3D point cloud of the external shape) usable in the context of movement analysis with minimal intervention. The main issue is the segmentation of the whole body external shape into body segments with relevant local coordinate systems (LCS) and anatomical landmarks (AL) [3]