19,869 research outputs found

    A Dynamically Adaptive Sparse Grid Method for Quasi-Optimal Interpolation of Multidimensional Analytic Functions

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    In this work we develop a dynamically adaptive sparse grids (SG) method for quasi-optimal interpolation of multidimensional analytic functions defined over a product of one dimensional bounded domains. The goal of such approach is to construct an interpolant in space that corresponds to the "best MM-terms" based on sharp a priori estimate of polynomial coefficients. In the past, SG methods have been successful in achieving this, with a traditional construction that relies on the solution to a Knapsack problem: only the most profitable hierarchical surpluses are added to the SG. However, this approach requires additional sharp estimates related to the size of the analytic region and the norm of the interpolation operator, i.e., the Lebesgue constant. Instead, we present an iterative SG procedure that adaptively refines an estimate of the region and accounts for the effects of the Lebesgue constant. Our approach does not require any a priori knowledge of the analyticity or operator norm, is easily generalized to both affine and non-affine analytic functions, and can be applied to sparse grids build from one dimensional rules with arbitrary growth of the number of nodes. In several numerical examples, we utilize our dynamically adaptive SG to interpolate quantities of interest related to the solutions of parametrized elliptic and hyperbolic PDEs, and compare the performance of our quasi-optimal interpolant to several alternative SG schemes

    Mode-medium instability and its correction with a Gaussian reflectivity mirror

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    A high power CO2 laser beam is known to deteriorate after a few microseconds due to a mode-medium instability (MMI) which results from an intensity dependent heating rate related to the vibrational-to-translational decay of the upper and lower CO2 lasing levels. An iterative numerical technique is developed to model the time evolution of the beam as it is affected by the MMI. The technique is used to study the MMI in an unstable CO2 resonator with a hard-edge output mirror for different parameters like the Fresnel number and the gas density. The results show that the mode of the hard edge unstable resonator deteriorates because of the diffraction ripples in the mode. A Gaussian-reflectivity mirror was used to correct the MMI. This mirror produces a smoother intensity profile which significantly reduces the effects of the MMI. Quantitative results on peak density variation and beam quality are presented

    Ab-initio determined electronic and magnetic properties of half-metallic NiCrSi and NiMnSi Heusler alloys; the role of interfaces and defects

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    Using state-of-the-art first-principles calculations we study the properties of the ferromagnetic Heusler compounds NiYSi where Y stands for V, Cr or Mn. NiCrSi and NiMnSi contrary to NiVSi are half-metallic at their equilibrium lattice constant exhibiting integer values of the total spin magnetic moment and thus we concentrate on these two alloys. The minority-spin gap has the same characteristics as for the well-known NiMnSb alloy being around ∼\sim1 eV. Upon tetragonalization the gap is present in the density of states even for expansion or contraction of the out-of-plane lattice parameter by 5%. The Cr-Cr and Mn-Mn interactions make ferromagnetism extremely stable and the Curie temperature exceeds 1000 K for NiMnSi. Surface and interfaces with GaP, ZnS and Si semiconductors are not half-metallic but in the case of NiCrSi the Ni-based contacts present spin-polarization at the Fermi level over 90%. Finally, we show that there are two cases of defects and atomic-swaps. The first-ones which involve the Cr(Mn) and Si atoms induce states at the edges of the gap which persists for a moderate-concentration of defects. Defects involving Ni atoms induce states localized within the gap completely destroying the half-metallicity. Based on single-impurity calculations we associate these states to the symmetry of the crystal

    3d-electron induced magnetic phase transition in half-metallic semi-Heusler alloys

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    We study the effect of the non-magnetic 3\textit{d} atoms on the magnetic properties of the half-metallic (HM) semi-Heusler alloys Co1−x_{1-x}Cux_{x}MnSb and Ni1−x_{1-x}Cux_{x}MnSb (0≤x≤10 \leq x \leq 1) using first-principles calculations. We determine the magnetic phase diagram of both systems at zero temperature and obtain a phase transition from a ferromagnetic to an antiferromagnetic state. For low Cu concentrations the ferromagnetic RKKY-like exchange mechanism is dominating, while the antiferromagnetic superexchange coupling becomes important for larger Cu content leading to the observed magnetic phase transition. A strong dependence of the magnetism in both systems on the position of the Fermi level within the HM gap is obtained. Obtained results are in good agreement with the available experimental data

    Interpretation of Solar Magnetic Field Strength Observations

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    This study based on longitudinal Zeeman effect magnetograms and spectral line scans investigates the dependence of solar surface magnetic fields on the spectral line used and the way the line is sampled in order to estimate the magnetic flux emerging above the solar atmosphere and penetrating to the corona from magnetograms of the Mt. Wilson 150-foot tower synoptic program (MWO). We have compared the synoptic program \lambda5250\AA line of Fe I to the line of Fe I at \lambda5233\AA since this latter line has a broad shape with a profile that is nearly linear over a large portion of its wings. The present study uses five pairs of sampling points on the λ5233\lambda5233\AA line. We recommend adoption of the field determined with a line bisector method with a sampling point as close as possible to the line core as the best estimate of the emergent photospheric flux. The combination of the line profile measurements and the cross-correlation of fields measured simultaneously with \lambda5250\AA and \lambda5233\AA yields a formula for the scale factor 1/\delta that multiplies the MWO synoptic magnetic fields. The new calibration shows that magnetic fields measured by the MDI system on the SOHO spacecraft are equal to 0.619+/-0.018 times the true value at a center-to-limb position 30 deg. Berger and Lites (2003) found this factor to be 0.64+/-0.013 based on a comparison the the Advanced Stokes Polarimeter.Comment: Accepted by Solar Physic

    "The fridge door is open" : temporal verification of a robotic assistant's behaviours

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    Robotic assistants are being designed to help, or work with, humans in a variety of situations from assistance within domestic situations, through medical care, to industrial settings. Whilst robots have been used in industry for some time they are often limited in terms of their range of movement or range of tasks. A new generation of robotic assistants have more freedom to move, and are able to autonomously make decisions and decide between alternatives. For people to adopt such robots they will have to be shown to be both safe and trustworthy. In this paper we focus on formal verification of a set of rules that have been developed to control the Care-O-bot, a robotic assistant located in a typical domestic environment. In particular, we apply model-checking, an automated and exhaustive algorithmic technique, to check whether formal temporal properties are satisfied on all the possible behaviours of the system. We prove a number of properties relating to robot behaviours, their priority and interruptibility, helping to support both safety and trustworthiness of robot behaviours

    Surfactant mixtures at the oil–water interface

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    NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Colloid and Interface Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in JOURNAL OF COLLOID AND INTERFACE SCIENCE, VOL 398, (2013) DOI 10.1016/j.jcis.2013.01.06

    Keeping the word : On orality and literacy (with a sideways glance at Navajo)

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    This article investigates the relationship between "orality" and "literacy." I take as my starting point the discussion by Walter Ong (1982) of the shift in "consciousness" that resulted from the movement from an "oral culture" to a "literate culture." I discuss a number of specific examples of the relationship between orality and literacy. My purpose in these examples is to suggest that literacy and orality are kinds of specific linguistic ideologies (see Silverstein 1979) and that we need a much more complex understanding of literacy as an ideological position than Ong has offered. In this article, I wish to explore orality and literacy as complex and interacting notions. My purpose is not so much as to critique Ong (though there will be some of that), but rather to elaborate what we might mean by "orality" and "literacy" as on the ground, linguacultural phenomena (see Friedrich 1989).Not

    Generation of spin-motion entanglement in a trapped ion using long-wavelength radiation

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    Applying a magnetic-field gradient to a trapped ion allows long-wavelength radiation to produce a mechanical force on the ion's motion when internal transitions are driven. We demonstrate such a coupling using a single trapped Yb+171 ion and use it to produce entanglement between the spin and motional state, an essential step toward using such a field gradient to implement multiqubit operations
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