Social and Political Dimensions of Identity

We study the interior regularity of solutions to the Dirichlet problem Lu = g in Omega, u = 0 in R-nOmega, for anisotropic operators of fractional type Lu(x) = integral(+infinity)(0) dp integral(Sn-1) da(w) 2u(x) - u(x + rho w) - u(x - rho w)/rho(1+2s). Here, a is any measure on Sn-1 (a prototype example for L is given by the sum of one-dimensional fractional Laplacians in fixed, given directions). When a is an element of C-infinity(Sn-1) and g is c(infinity)(Omega), solutions are known to be C-infinity inside Omega (but not up to the boundary). However, when a is a general measure, or even when a is L-infinity(s(n-1)), solutions are only known to be C-3s inside Omega. We prove here that, for general measures a, solutions are C1+3s-epsilon inside Omega for all epsilon > 0 whenever Omega is convex. When a is an element of L-infinity(Sn-1), we show that the same holds in all C-1,C-1 domains. In particular, solutions always possess a classical first derivative. The assumptions on the domain are sharp, since if the domain is not convex and the measure a is singular, we construct an explicit counterexample for which u is not C3s+epsilon for any epsilon > 0 - even if g and Omega are C-infinity

H^s versus C^0-weighted minimizers

We study a class of semi-linear problems involving the fractional Laplacian under subcritical or critical growth assumptions. We prove that, for the corresponding functional, local minimizers with respect to a C^0-topology weighted with a suitable power of the distance from the boundary are actually local minimizers in the natural H^s-topology.Comment: 15 page

High density bimodal parts by three dimensional printing

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1998.Includes bibliographical references (p. 102-103).Three Dimensional Printing (3DP) is a rapid prototyping process that allows for the fabrication of injection molding tooling from computer generated models. Due to market demands for harder, more robust tooling, improving the material properties and the geometric control of 3DP parts has been a necessary goal of the project. One path to accomplishing this task is to increase the green density of the 3DP compact prior to sintering. To accomplish this goal, the printing of fine, sub-micron Titanium Carbide slurries into a large powder bed to create a dense bimodal compact was investigated. Experiments performed demonstrated that a uniform, defect free microstructure could be obtained by appropriately selecting 3DP process parameters. By spreading 4 mil layers, and double printing, sample coupons with estimated green densities of up to 83% were obtained. In addition, the effect of varying either the bimodal concentrations or the relative particle sizes, on fine porosity in 3DP parts after infiltration was studied. Three bimodal ceramic-metal material systems, each based on Titanium Carbide and subsequently infiltrated with a copper-nickel-manganese alloy, were also developed. The first system, a bimodal system of large TiC and fine TiC powders exhibits good dimensional control (net shrinkage of 0.2%) and age-hardening properties (up to 43 HRC). The second system, a bimodal system of large Stainless Steel and fine TiC powders, is characterized by modest dimensional control (less than 2%), but does not exhibit any age-hardening behavior. The third system developed, a bimodal system of large Molybdenum powders and fine TiC powders, can be hardened up to 25 HRC with a 12 hour 400°C treatment.by Akan E. Oton.S.M

Frozen-hydrated chromatin from metaphase chromosomes has an interdigitated multilayer structure

Cryo-electron tomography and small-angle X-ray scattering were used to investigate the chromatin folding in metaphase chromosomes. The tomographic 3D reconstructions show that frozen-hydrated chromatin emanated from chromosomes is planar and forms multilayered plates. The layer thickness was measured accounting for the contrast transfer function fringes at the plate edges, yielding a width of similar to 7.5 nm, which is compatible with the dimensions of a monolayer of nucleosomes slightly tilted with respect to the layer surface. Individual nucleosomes are visible decorating distorted plates, but typical plates are very dense and nucleosomes are not identifiable as individual units, indicating that they are tightly packed. Two layers in contact are similar to 13 nm thick, which is thinner than the sum of two independent layers, suggesting that nucleosomes in the layers interdigitate. X-ray scattering of whole chromosomes shows a main scattering peak at similar to 6 nm, which can be correlated with the distance between layers and between interdigitating nucleosomes interacting through their faces. These observations support a model where compact chromosomes are composed of many chromatin layers stacked along the chromosome axis

Local regularity for fractional heat equations

We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$. Proofs combine classical abstract regularity results for parabolic equations with some new local regularity results for the associated elliptic problems.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0756

Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings

This paper was published in OPTICS LETTERS and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OL.36.002104. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law[EN] Single-wall carbon nanotube deposition on the cladding of optical fibers has been carried out to fabricate an all-fiber nonlinear device. Two different nanotube deposition techniques were studied. The first consisted of repeatedly immersing the optical fiber into a nanotube supension, increasing the thickness of the coating in each step. The second deposition involved wrapping a thin film of nanotubes around the optical fiber. For both cases, interaction of transmitted light through the fiber core with the external coating was assisted by the cladding mode resonances of a tilted fiber Bragg grating. Ultrafast nonlinear effects of the nanotube-coated fiber were measured by means of a pump-probe pulses experiment. © 2011 Optical Society of America.This work was financially supported by the European Commission under the FP7 EURO-FOS Network of Excellence (ICT-2007-2-224402), the Ministerio de Educación y Ciencia SINADEC project (TEC2008-06333), and the Natural Sciences and Engineering Research Council of Canada (NSERC). The work of G. E. Villanueva was supported by the Ministerio de Educación y Ciencia Formación de Profesorado Universitario programs. The work of P. Pérez-Millán was supported by the Juan de la Cierva program, JCI-2009-05805.Villanueva Ibáñez, GE.; Jakubinek, M.; Simard, B.; Oton Nieto, CJ.; Matres Abril, J.; Shao, L.; Pérez Millán, P.... (2011). Linear and nonlinear optical properties of carbon nanotube-coated single-mode optical fiber gratings. Optics Letters. 36(11):2104-2106. https://doi.org/10.1364/OL.36.002104S210421063611Sakakibara, Y., Rozhin, A. G., Kataura, H., Achiba, Y., & Tokumoto, M. (2005). Carbon Nanotube-Poly(vinylalcohol) Nanocomposite Film Devices: Applications for Femtosecond Fiber Laser Mode Lockers and Optical Amplifier Noise Suppressors. Japanese Journal of Applied Physics, 44(4A), 1621-1625. doi:10.1143/jjap.44.1621Chow, K. K., Yamashita, S., & Song, Y. W. (2009). A widely tunable wavelength converter based on nonlinear polarization rotation in a carbon-nanotube-deposited D-shaped fiber. Optics Express, 17(9), 7664. doi:10.1364/oe.17.007664Set, S. Y., Yaguchi, H., Tanaka, Y., & Jablonski, M. (2004). Ultrafast Fiber Pulsed Lasers Incorporating Carbon Nanotubes. IEEE Journal of Selected Topics in Quantum Electronics, 10(1), 137-146. doi:10.1109/jstqe.2003.822912Chow, K. K., Tsuji, M., & Yamashita, S. (2010). Single-walled carbon-nanotube-deposited tapered fiber for four-wave mixing based wavelength conversion. Applied Physics Letters, 96(6), 061104. doi:10.1063/1.3304789Chow, K. K., & Yamashita, S. (2009). Four-wave mixing in a single-walled carbon-nanotube-deposited D-shaped fiber and its application in tunable wavelength conversion. Optics Express, 17(18), 15608. doi:10.1364/oe.17.015608Choi, S. Y., Rotermund, F., Jung, H., Oh, K., & Yeom, D.-I. (2009). Femtosecond mode-locked fiber laser employing a hollow optical fiber filled with carbon nanotube dispersion as saturable absorber. Optics Express, 17(24), 21788. doi:10.1364/oe.17.021788Chan, C.-F., Chen, C., Jafari, A., Laronche, A., Thomson, D. J., & Albert, J. (2007). Optical fiber refractometer using narrowband cladding-mode resonance shifts. Applied Optics, 46(7), 1142. doi:10.1364/ao.46.001142Kingston, C. T., Jakubek, Z. J., Dénommée, S., & Simard, B. (2004). Efficient laser synthesis of single-walled carbon nanotubes through laser heating of the condensing vaporization plume. Carbon, 42(8-9), 1657-1664. doi:10.1016/j.carbon.2004.02.020Jakubinek, M. B., Johnson, M. B., White, M. A., Guan, J., & Simard, B. (2010). Novel Method to Produce Single-Walled Carbon Nanotube Films and Their Thermal and Electrical Properties. Journal of Nanoscience and Nanotechnology, 10(12), 8151-8157. doi:10.1166/jnn.2010.3014Vallaitis, T., Koos, C., Bonk, R., Freude, W., Laemmlin, M., Meuer, C., … Leuthold, J. (2008). Slow and fast dynamics of gain and phase in a quantum dot semiconductor optical amplifier. Optics Express, 16(1), 170. doi:10.1364/oe.16.00017

A Light Calibration System for the ProtoDUNE-DP Detector

A LED-based fiber calibration system for the ProtoDUNE-Dual Phase (DP) photon detection system (PDS) has been designed and validated. ProtoDUNE-DP is a 6x6x6 m3 liquid argon time-projection-chamber currently being installed at the Neutrino Platform at CERN. The PDS is based on 36 8-inch photomultiplier tubes (PMTs) and will allow triggering on cosmic rays. The system serves as prototype for the PDS of the final DUNE DP far detector in which the PDS also has the function to allow the 3D event reconstruction on non-beam physics. For this purpose an equalized PMT response is desirable to allow using the same threshold definition for all PMT groups, simplifying the determination of the trigger efficiency. The light calibration system described in this paper is developed to provide this and to monitor the PMT performance in-situ.Comment: 15 pages, 5 figure

Isolation of ‘Candidatus Nitrosocosmicus franklandus’, a novel ureolytic soil archaeal ammonia oxidiser with tolerance to high ammonia concentration

Acknowledgements The authors would like to thank Mr Kevin Mackenzie and Mrs Gillian Milne (University of Aberdeen) for technical support with scanning electron microscopy, and Dr Robin Walker for access to the Woodlands Field experimental plots at the SRUC,Craibstone Estate, Aberdeen. Funding This work was financially supported by Natural Environmental Research Council (standard grants NE/I027835/1 and NE/L006286/1 and fellowship NE/J019151/1), EC Marie Curie ITN NORA, Grant Agreement No. 316472, the AXA Research Fund and the Centre for Genome Enabled Biology and Medicine, University of Aberdeen.Peer reviewedPublisher PD