Approximated Computation of Belief Functions for Robust Design Optimization

This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative measures, Belief and Plausibility, of the credibility of the computed value of the design budgets. The paper proposes some techniques to compute an approximation of Belief and Plausibility at a cost that is a fraction of the one required for an accurate calculation of the two values. Some simple test cases will show how the proposed techniques scale with the dimension of the problem. Finally a simple example of spacecraft system design is presented.Comment: AIAA-2012-1932 14th AIAA Non-Deterministic Approaches Conference. 23-26 April 2012 Sheraton Waikiki, Honolulu, Hawai

Dynamic Scaling in the Susceptibility of the Spin-1\2 Kagome Lattice Antiferromagnet Herbertsmithite

The spin-1/2 kagome lattice antiferromagnet herbertsmithite, ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid ground state. We show that the magnetic response of this material displays an unusual scaling relation in both the bulk ac susceptibility and the low energy dynamic susceptibility as measured by inelastic neutron scattering. The quantity $\chi T^\alpha$ with $\alpha \simeq 0.66$ can be expressed as a universal function of $H/T$ or $\omega/T$. This scaling is discussed in relation to similar behavior seen in systems influenced by disorder or by the proximity to a quantum critical point.Comment: 5 pages, 3 figures v2: updated to match published version

A very luminous, highly extinguished, very fast nova - V1721 Aquilae

Fast novae are primarily located within the plane of the Galaxy, slow novae are found within its bulge. Because of high interstellar extinction along the line of sight many novae lying close to the plane are missed and only the brightest seen. One nova lying very close to the Galactic plane is V1721 Aquilae, discovered in outburst on 2008 September 22. Spectra obtained 2.69 days after outburst revealed very high expansion velocities (FWHM ~6450 km/s). In this paper we have used available pre- and post-outburst photometry and post-outburst spectroscopy to conclude that the object is a very fast, luminous, and highly extinguished A_V=11.6+/-0.2) nova system with an average ejection velocity of ~3400 km/s. Pre-outburst near-IR colours from 2MASS indicate that at quiescence the object is similar to many quiescent CNe and appears to have a main sequence/sub-giant secondary rather than a giant. Based on the speed of decline of the nova and its emission line profiles we hypothesise that the axis ratio of the nova ejecta is ~1.4 and that its inclination is such that the central binary accretion disc is face-on to the observer. The accretion disc's blue contribution to the system's near-IR quiescent colours may be significant. Simple models of the nova ejecta have been constructed using the morphological modelling code XS5, and the results support the above hypothesis. Spectral classification of this object has been difficult owing to low S/N levels and high extinction, which has eliminated all evidence of any He/N or FeII emission within the spectra. We suggest two possibilities for the nature of V1721 Aql: that it is a U Sco type RN with a sub-giant secondary or, less likely, that it is a highly energetic bright and fast classical nova with a main sequence secondary. Future monitoring of the object for possible RN episodes may be worthwhile, as would archival searches for previous outbursts.Comment: 9 pages 10 figures, accepted for publication in A&A. Abstract has been slightly shortened from published versio

The matricial relaxation of a linear matrix inequality

Given linear matrix inequalities (LMIs) L_1 and L_2, it is natural to ask: (Q1) when does one dominate the other, that is, does L_1(X) PsD imply L_2(X) PsD? (Q2) when do they have the same solution set? Such questions can be NP-hard. This paper describes a natural relaxation of an LMI, based on substituting matrices for the variables x_j. With this relaxation, the domination questions (Q1) and (Q2) have elegant answers, indeed reduce to constructible semidefinite programs. Assume there is an X such that L_1(X) and L_2(X) are both PD, and suppose the positivity domain of L_1 is bounded. For our "matrix variable" relaxation a positive answer to (Q1) is equivalent to the existence of matrices V_j such that L_2(x)=V_1^* L_1(x) V_1 + ... + V_k^* L_1(x) V_k. As for (Q2) we show that, up to redundancy, L_1 and L_2 are unitarily equivalent. Such algebraic certificates are typically called Positivstellensaetze and the above are examples of such for linear polynomials. The paper goes on to derive a cleaner and more powerful Putinar-type Positivstellensatz for polynomials positive on a bounded set of the form {X | L(X) PsD}. An observation at the core of the paper is that the relaxed LMI domination problem is equivalent to a classical problem. Namely, the problem of determining if a linear map from a subspace of matrices to a matrix algebra is "completely positive".Comment: v1: 34 pages, v2: 41 pages; supplementary material is available in the source file, or see http://srag.fmf.uni-lj.si

Solid-phase C60 in the peculiar binary XX Oph?

We present infrared spectra of the binary XX Oph obtained with the Infrared Spectrograph on the Spitzer Space Telescope. The data show some evidence for the presence of solid C60– the first detection of C60 in the solid phase – together with the well-known ‘unidentified infrared’ emission features. We suggest that, in the case of XX Oph, the C60 is located close to the hot component, and that in general it is preferentially excited by stars having effective temperatures in the range 15 000–30 000 K. C60 may be common in circumstellar environments, but unnoticed in the absence of a suitable exciting source

Seasonal Salinization Decreases Spatial Heterogeneity of Sulfate Reducing Activity

Evidence of sulfate input and reduction in coastal freshwater wetlands is often visible in the black iron monosulfide (FeS) complexes that form in iron rich reducing sediments. Using a modified Indicator of Reduction in Soils (IRIS) method, digital imaging, and geostatistics, we examine controls on the spatial properties of FeS in a coastal wetland fresh-to-brackish transition zone over a multi-month, drought-induced saltwater incursion event. PVC sheets (10 - 15 cm) were painted with an iron oxide paint and incubated vertically belowground and flush with the surface for 24 h along a salt-influenced to freshwater wetland transect in coastal North Carolina, USA. Along with collection of complementary water and soil chemistry data, the size and location of the FeS compounds on the plate were photographed and geostatistical techniques were employed to characterize FeS formation on the square cm scale. Herein, we describe how the saltwater incursion front is associated with increased sulfate loading and decreased aqueous Fe(II) content. This accompanies an increased number of individual FeS complexes that were more uniformly distributed as reflected in a lower Magnitude of Spatial Heterogeneity at all sites except furthest downstream. Future work should focus on streamlining the plate analysis procedure as well as developing a more robust statistical based approach to determine sulfide concentration

Seasonal Salinization Decreases Spatial Heterogeneity of Sulfate Reducing Activity

This work is licensed under a Creative Commons Attribution 4.0 International License.Evidence of sulfate input and reduction in coastal freshwater wetlands is often visible in the black iron monosulfide (FeS) complexes that form in iron rich reducing sediments. Using a modified Indicator of Reduction in Soils (IRIS) method, digital imaging, and geostatistics, we examine controls on the spatial properties of FeS in a coastal wetland fresh-to-brackish transition zone over a multi-month, drought-induced saltwater incursion event. PVC sheets (10 × 15 cm) were painted with an iron oxide paint and incubated vertically belowground and flush with the surface for 24 h along a salt-influenced to freshwater wetland transect in coastal North Carolina, USA. Along with collection of complementary water and soil chemistry data, the size and location of the FeS compounds on the plate were photographed and geostatistical techniques were employed to characterize FeS formation on the square cm scale. Herein, we describe how the saltwater incursion front is associated with increased sulfate loading and decreased aqueous Fe(II) content. This accompanies an increased number of individual FeS complexes that were more uniformly distributed as reflected in a lower Magnitude of Spatial Heterogeneity at all sites except furthest downstream. Future work should focus on streamlining the plate analysis procedure as well as developing a more robust statistical based approach to determine sulfide concentration