A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)

For a right-invariant and controllable driftless system on SU(n), we consider a time-periodic reference trajectory along which the linearized control system generates su(n): such trajectories always exist and constitute the basic ingredient of Coron's Return Method. The open-loop controls that we propose, which rely on a left-invariant tracking error dynamics and on a fidelity-like Lyapunov function, are determined from a finite number of left-translations of the tracking error and they assure global asymptotic convergence towards the periodic reference trajectory. The role of these translations is to avoid being trapped in the critical region of this Lyapunov-like function. The convergence proof relies on a periodic version of LaSalle's invariance principle and the control values are determined by numerical integration of the dynamics of the system. Simulations illustrate the obtained controls for $n=4$ and the generation of the C--NOT quantum gate.Comment: Submitte

Thulium and ytterbium-doped titanium oxide thin films deposited by ultrasonic spray pyrolysis

Thin films of thulium and ytterbium-doped titanium oxide were grown by metal-organic spray pyrolysis deposition from titanium(IV)oxide bis(acetylacetonate), thulium(III) tris(2,2,6,6-tetramethyl-3,5-heptanedionate) and ytterbium(III) tris(acetylacetonate). Deposition temperatures have been investigated from 300{\deg}C to 600{\deg}C. Films have been studied regarding their crystallity and doping quality. Structural and composition characterisations of TiO2:Tm,Yb were performed by electron microprobe, X-ray diffraction and Fourier transform infrared spectroscopy. The deposition rate can reach 0.8 \mum/h. The anatase phase of TiO2 was obtained after synthesis at 400{\deg}C or higher. Organic contamination at low deposition temperature is eliminated by annealing treatments.Comment: 6 pages, 6 figure

The formation of IRIS diagnostics I. A quintessential model atom of Mg II and general formation properties of the Mg II h&k lines

NASA's Interface Region Imaging Spectrograph (IRIS) space mission will study how the solar atmosphere is energized. IRIS contains an imaging spectrograph that covers the Mg II h&k lines as well as a slit-jaw imager centered at Mg II k. Understanding the observations will require forward modeling of Mg II h&k line formation from 3D radiation-MHD models. This paper is the first in a series where we undertake this forward modeling. We discuss the atomic physics pertinent to h&k line formation, present a quintessential model atom that can be used in radiative transfer computations and discuss the effect of partial redistribution (PRD) and 3D radiative transfer on the emergent line profiles. We conclude that Mg II h&k can be modeled accurately with a 4-level plus continuum Mg II model atom. Ideally radiative transfer computations should be done in 3D including PRD effects. In practice this is currently not possible. A reasonable compromise is to use 1D PRD computations to model the line profile up to and including the central emission peaks, and use 3D transfer assuming complete redistribution to model the central depression.Comment: 13 pages, 13 figures, accepted for Ap

The formation of IRIS diagnostics II. The formation of the Mg II h&k lines in the solar atmosphere

NASA's Interface Region Imaging Spectrograph (IRIS) small explorer mission will study how the solar atmosphere is energized. IRIS contains an imaging spectrograph that covers the Mg II h&k lines as well as a slit-jaw imager centered at Mg II k. Understanding the observations requires forward modeling of Mg II h&k line formation from 3D radiation-MHD models. We compute the vertically emergent h&k intensity from a snapshot of a dynamic 3D radiation-MHD model of the solar atmosphere, and investigate which diagnostic information about the atmosphere is contained in the synthetic line profiles. We find that the Doppler shift of the central line depression correlates strongly with the vertical velocity at optical depth unity, which is typically located less than 200 km below the transition region (TR). By combining the Doppler shifts of the h and the k line we can retrieve the sign of the velocity gradient just below the TR. The intensity in the central line depression is anticorrelated with the formation height, especially in subfields of a few square Mm. This intensity could thus be used to measure the spatial variation of the height of the transition region. The intensity in the line-core emission peaks correlates with the temperature at its formation height, especially for strong emission peaks. The peaks can thus be exploited as a temperature diagnostic. The wavelength difference between the blue and red peaks provides a diagnostic of the velocity gradients in the upper chromosphere. The intensity ratio of the blue and red peaks correlates strongly with the average velocity in the upper chromosphere. We conclude that the Mg II h&k lines are excellent probes of the very upper chromosphere just below the transition region, a height regime that is impossible to probe with other spectral lines.Comment: 15 pages, 12 figures, accepted for ApJ, astro-ph abstract shortened to confirm to submission requirement

Ring Width Variation and Heartwood Development in Quercus Faginea

High-value exploitation of endogenous forest species may help in fighting the threat to their sustainability, as is the case for Quercus faginea Lam. (Portuguese oak) for which research is underway to determine the wood potential for high-quality products. Ring widths were measured in 20 trees in two sites in Portugal and within-tree heartwood and sapwood development was determined. The wood shows distinct ring porosity. The mean annual radial growth at dbh was 2.3 and 1.0 mm for the two sites, respectively. Ring width decreased with cambial age, ie 3.1 ± 1.2 mm in the first 10 rings to 1.3 ± 0.8 mm at around 40 yr (site 1). Ring width decreased axially from the tree base upward but the variation was small. The trees showed a relatively high proportion of heartwood, ie 60-70% heartwood for 20-25 cm wood diameters that decreased with height, and followed the stem profile. Heartwood diameter was modeled as a function of stem diameter, to be used for heartwood estimation in standing trees. Sapwood width was relatively constant. Overall the stem quality was found to be good for production of solid wood products regarding ring and heartwood features

Tailoring the thermal Casimir force with graphene

The Casimir interaction is omnipresent source of forces at small separations between bodies, which is difficult to change by varying external conditions. Here we show that graphene interacting with a metal can have the best known force contrast to the temperature and the Fermi level variations. In the distance range 50–300 nm the force is measurable and can vary a few times for graphene with a bandgap much larger than the temperature. In this distance range the main part of the force is due to the thermal fluctuations. We discuss also graphene on a dielectric membrane as a technologically robust configuration