Efficient and Perfect domination on circular-arc graphs

Given a graph $G = (V,E)$, a \emph{perfect dominating set} is a subset of vertices $V' \subseteq V(G)$ such that each vertex $v \in V(G)\setminus V'$ is dominated by exactly one vertex $v' \in V'$. An \emph{efficient dominating set} is a perfect dominating set $V'$ where $V'$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them

Selective Laser Sintering of Zirconia with Micro-Scale Features

Recent work in Selective Laser Sintering of ceramics at the University of Texas at Austin demonstrates the capability to produce zirconia parts with fine features. Zirconia powder was pre-processed into spherical particles, laser sintered with a sacrificial polymer binder, infiltrated and post-sintered to higher density. Optical micrographs show that hole sizes of 180 /-tm are possible in fully ceramic components.Mechanical Engineerin

Parametric study in weld mismatch of longitudinally welded SSME HPFTP inlet

Welded joints are an essential part of pressure vessels such as the Space Shuttle Main Engine (SSME) Turbopumps. Defects produced in the welding process can be detrimental to weld performance. Recently, review of the SSME high pressure fuel turbopump (HPFTP) titanium inlet x rays revealed several weld discrepancies such as penetrameter density issues, film processing discrepancies, weld width discrepancies, porosity, lack of fusion, and weld offsets. Currently, the sensitivity of welded structures to defects is of concern. From a fatigue standpoint, weld offset may have a serious effect since local yielding, in general, aggravates cyclic stress effects. Therefore, the weld offset issue is considered. Using the finite element method and mathematical formulations, parametric studies were conducted to determine the influence of weld offsets and a variation of weld widths in longitudinally welded cylindrical structures with equal wall thickness on both sides of the joint. From the study, the finite element results and theoretical solutions are presented

Squeezed-state generation in optical bistability

Experiments to generate squeezed states of light are described for a collection of two-level atoms within a high-finesse cavity. The investigation is conducted in a regime for which the weak-field coupling of atoms to the cavity mode produces a splitting in the normal mode structure of the atom-field system that is large compared with the atomic linewidth. Reductions in photocurrent noise of 30% (-1.55 dB) below the noise level set by the vacuum state of the field are observed in a balanced homodyne detector. A degree of squeezing of approximately 50% is inferred for the field state in the absence of propagation and detection losses. The observed spectrum of squeezing extends over a very broad range of frequencies (~±75 MHz), with the frequency of best squeezing corresponding to an offset from the optical carrier given by the normal mode splitting

Low-Energy Structures in Strong Field Ionization Revealed by Quantum Orbits

Experiments on atoms in intense laser pulses and the corresponding exact ab initio solutions of the time-dependent Schr\"odinger equation (TDSE) yield photoelectron spectra with low-energy features that are not reproduced by the otherwise successful work horse of strong field laser physics: the "strong field approximation" (SFA). In the semi-classical limit, the SFA possesses an appealing interpretation in terms of interfering quantum trajectories. It is shown that a conceptually simple extension towards the inclusion of Coulomb effects yields very good agreement with exact TDSE results. Moreover, the Coulomb quantum orbits allow for a physically intuitive interpretation and detailed analysis of all low-energy features in the semi-classical regime, in particular the recently discovered "low-energy structure" [C.I. Blaga et al., Nature Physics 5, 335 (2009) and W. Quan et al., Phys. Rev. Lett. 103, 093001 (2009)].Comment: 4 pages, 3 figures, REVTe

Micron-sized forsterite grains in the pre-planetary nebula of IRAS 17150-3224 - Searching for clues on the mysterious evolution of massive AGB stars

We study the grain properties and location of the forsterite crystals in the circumstellar environment of the pre-planetary nebula (PPN) IRAS 17150-3224 in order to learn more about the as yet poorly understood evolutionary phase prior to the PPN. We use the best-fit model for IRAS 17150-3224 of Meixner et al. (2002) and add forsterite to this model. We investigate different spatial distributions and grain sizes of the forsterite crystals in the circumstellar environment. We compare the spectral bands of forsterite in the mid-infrared and at 69 micrometre in radiative transport models to those in ISO-SWS and Herschel/PACS observations. We can reproduce the non-detection of the mid-infrared bands and the detection of the 69 micrometre feature with models where the forsterite is distributed in the whole outflow, in the superwind region, or in the AGB-wind region emitted previous to the superwind, but we cannot discriminate between these three models. To reproduce the observed spectral bands with these three models, the forsterite crystals need to be dominated by a grain size population of 2 micrometre up to 6 micrometre. We hypothesise that the large forsterite crystals were formed after the superwind phase of IRAS 17150-3224, where the star developed an as yet unknown hyperwind with an extremely high mass-loss rate (10^-3 Msol/yr). The high densities of such a hyperwind could be responsible for the efficient grain growth of both amorphous and crystalline dust in the outflow. Several mechanisms are discussed that might explain the lower-limit of 2 micrometre found for the forsterite grains, but none are satisfactory. Among the mechanisms explored is a possible selection effect due to radiation pressure based on photon scattering on micron-sized grains.Comment: Accepted by A&

The composition and size distribution of the dust in the coma of comet Hale-Bopp

We discuss the composition and size distribution of the dust in the coma of comet Hale-Bopp. We do this by fitting simultaneously the infrared emission spectrum measured by the infrared space observatory (ISO) and the measured degree of linear polarization of scattered light at various phase angles and 12 different wavelengths. The effects of particle shape on the modeled optical properties of the dust grains are taken into account. We constrain our fit by forcing the abundances of the major rock forming chemical elements to be solar. The infrared spectrum at long wavelengths reveals that large grains are needed in order to fit the spectral slope. The size and shape distribution we employ allows us to estimate the sizes of the crystalline silicates. The ratios of the strength of various forsterite features show that the crystalline silicate grains in Hale-Bopp must be submicron sized. We exclude the presence of large crystalline silicate grains in the coma. Because of this lack of large crystalline grains combined with the fact that we do need large amorphous grains to fit the emission spectrum at long wavelengths, we need only approximately 4% of crystalline silicates by mass. After correcting for possible hidden crystalline material included in large amorphous grains, our best estimate of the total mass fraction of crystalline material is approximately 7.5%, significantly lower than deduced in previous studies in which the typical derived crystallinity is 20-30%. The implications of this on the possible origin and evolution of the comet are discussed. The crystallinity we observe in Hale-Bopp is consistent with the production of crystalline silicates in the inner solar system by thermal annealing and subsequent radial mixing to the comet forming region.Comment: Accepted for publication in Icaru

The problematically short superwind of OH/IR stars - Probing the outflow with the 69 {\mu}m spectral band of forsterite

Spectra of OH/IR stars show prominent spectral bands of crystalline olivine (Mg$_{(2-2x)}$Fe$_{(2x)}$SiO$_{4}$). To learn more about the timescale of the outflows of OH/IR stars, we study the spectral band of crystalline olivine at 69 {\mu}m. The 69 {\mu}m band is of interest because its width and peak wavelength position are sensitive to the grain temperature and to the exact composition of the crystalline olivine. With Herschel/PACS, we observed the 69 {\mu}m band in the outflow of 14 OH/IR stars. By comparing the crystalline olivine features of our sample with those of model spectra, we determined the size of the outflow and its crystalline olivine abundance. The temperature indicated by the observed 69 {\mu}m bands can only be reproduced by models with a geometrically compact superwind ($R_{\rm{SW}}\lesssim$ 2500 AU = 1400 R$_{*}$).This means that the superwind started less than 1200 years ago (assuming an outflow velocity of 10 km/s). The small amount of mass lost in one superwind and the high progenitor mass of the OH/IR stars introduce a mass loss and thus evolutionary problem for these objects, which has not yet been understood.Comment: Accepted by A&