Fractional-order operators: Boundary problems, heat equations

The first half of this work gives a survey of the fractional Laplacian (and related operators), its restricted Dirichlet realization on a bounded domain, and its nonhomogeneous local boundary conditions, as treated by pseudodifferential methods. The second half takes up the associated heat equation with homogeneous Dirichlet condition. Here we recall recently shown sharp results on interior regularity and on $L_p$-estimates up to the boundary, as well as recent H\"older estimates. This is supplied with new higher regularity estimates in $L_2$-spaces using a technique of Lions and Magenes, and higher $L_p$-regularity estimates (with arbitrarily high H\"older estimates in the time-parameter) based on a general result of Amann. Moreover, it is shown that an improvement to spatial $C^\infty$-regularity at the boundary is not in general possible.Comment: 29 pages, updated version, to appear in a Springer Proceedings in Mathematics and Statistics: "New Perspectives in Mathematical Analysis - Plenary Lectures, ISAAC 2017, Vaxjo Sweden

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

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

Ultracompact microinterferometer-based fiber Bragg grating interrogator on a silicon chip

We report an interferometer-based multiplexed fiber Bragg grating (FBG) interrogator using silicon photonic technology. The photonic-integrated system includes the grating coupler, active and passive interferometers, interferometers, a 12-channel wavelength-division-multiplexing (WDM) filter, and Ge photodiodes, all integrated on a 6x8 mm2 silicon chip. The system also includes optical and electric interfaces to a printed board, which is connected to a real-time electronic board that actively performs the phase demodulation processing using a multitone mixing (MTM) technique. The device with active demodulation, which uses thermally-based phase shifters, features a noise figure of σ  =  0.13 pm at a bandwidth of 700 Hz, which corresponds to a dynamic spectral resolution of 4.9 fm/Hz1/2. On the other hand, the passive version of the system, based on a 90º-hybrid coupler, features a noise figure of σ  =  2.55 pm at a bandwidth of 10 kHz, also showing successful detection of a 42 kHz signal when setting the bandwidth to 50 kHz. These results demonstrate the advantage of integrated photonics, which allows the integration of several systems with different demodulation schemes in the same chip and guarantees easy scalability to a higher number of ports without increasing the dimensions or the cost

Liquid crystals in focus

Liquid Crystal lenses may be used for imaging or projection systems, in portable devices and vision correction in head-mounted devices. There are many types of LC lenses with tunable focal length, but only few have achieved practical importance, due to their small size or due to their limited focusing capability. The three most important classes of LC lenses with variable focus are lenses with curved surfaces, flat gradient index lenses and composite lenses. Fresnel lenses, included in flat gradient lenses, achieve better aperture size (1-2 cm) in thin cells and fast response, but they are on-off lenses or they have a complicated multilevel electrode structures to achieve different focal power. In this work we present a novel approach to make tunable LC Fresnel lenses, with a very simple electrode structure