Short- and Long- Time Transport Structures in a Three Dimensional Time Dependent Flow

Lagrangian transport structures for three-dimensional and time-dependent fluid flows are of great interest in numerous applications, particularly for geophysical or oceanic flows. In such flows, chaotic transport and mixing can play important environmental and ecological roles, for examples in pollution spills or plankton migration. In such flows, where simulations or observations are typically available only over a short time, understanding the difference between short-time and long-time transport structures is critical. In this paper, we use a set of classical (i.e. Poincar\'e section, Lyapunov exponent) and alternative (i.e. finite time Lyapunov exponent, Lagrangian coherent structures) tools from dynamical systems theory that analyze chaotic transport both qualitatively and quantitatively. With this set of tools we are able to reveal, identify and highlight differences between short- and long-time transport structures inside a flow composed of a primary horizontal contra-rotating vortex chain, small lateral oscillations and a weak Ekman pumping. The difference is mainly the existence of regular or extremely slowly developing chaotic regions that are only present at short time.Comment: 9 pages, 9 figure

Numerical solution of scattering problems using a Riemann--Hilbert formulation

A fast and accurate numerical method for the solution of scalar and matrix Wiener--Hopf problems is presented. The Wiener--Hopf problems are formulated as Riemann--Hilbert problems on the real line, and a numerical approach developed for these problems is used. It is shown that the known far-field behaviour of the solutions can be exploited to construct numerical schemes providing spectrally accurate results. A number of scalar and matrix Wiener--Hopf problems that generalize the classical Sommerfeld problem of diffraction of plane waves by a semi-infinite plane are solved using the approach

Using cross-lingual information to cope with underspecification in formal ontologies

Description logics and other formal devices are frequently used as means for preventing or detecting mistakes in ontologies. Some of these devices are also capable of inferring the existence of inter-concept relationships that have not been explicitly entered into an ontology. A prerequisite, however, is that this information can be derived from those formal definitions of concepts and relationships which are included within the ontology. In this paper, we present a novel algorithm that is able to suggest relationships among existing concepts in a formal ontology that are not derivable from such formal definitions. The algorithm exploits cross-lingual information that is implicitly present in the collection of terms used in various languages to denote the concepts and relationships at issue. By using a specific experimental design, we are able to quantify the impact of cross-lingual information in coping with underspecification in formal ontologies

High Resolution Spectroscopy of SN1987A's Rings: He I 10830 and H-alpha from the Hotspots

We present the first high-dispersion spectroscopy of He I 10830 from the hotspots in the ring around SN1987A, obtained at Gemini South, spatially resolving the near and far sides of the ring. We compare these line profiles to similar echelle spectra of H$\alpha$ and [N II] 6583 obtained at the Magellan Observatory. We find that the He I profiles are much broader than H-alpha or [N II], but the He I profiles also have different shapes -- they have enhanced emission at high speeds, with extra blueshifted emission on the north side of the ring, and extra redshifted emission on the south side. To explain this, we invoke a simple geometric picture where the extra He I emission traces hotter gas from faster shocks that strike the apex of the hotspots directly, while the H-alpha preferentially traces cooler lower-ionization gas from slower transverse shocks that penetrate into the sides of the ring.Comment: 3 pages. To appear in proceedings: "Supernova 1987A: 20 Years After: Supernovae and Gamma-Ray Bursters" AIP, New York, eds. S. Immler, K.W. Weiler, and R. McCra

The cosmological information of shear peaks: beyond the abundance

We study the cosmological information of weak lensing (WL) peaks, focusing on two other statistics besides their abundance: the stacked tangential-shear profiles and the peak-peak correlation function. We use a large ensemble of simulated WL maps with survey specifications relevant to future missions like Euclid and LSST, to explore the three peak probes. We find that the correlation function of peaks with high signal-to-noise (S/N) measured from fields of size 144 sq. deg. has a maximum of ~0.3 at an angular scale ~10 arcmin. For peaks with smaller S/N, the amplitude of the correlation function decreases, and its maximum occurs on smaller angular scales. We compare the peak observables measured with and without shape noise and find that for S/N~3 only ~5% of the peaks are due to large-scale structures, the rest being generated by shape noise. The covariance matrix of the probes is examined: the correlation function is only weakly covariant on scales < 30 arcmin, and slightly more on larger scales; the shear profiles are very correlated for theta > 2 arcmin, with a correlation coefficient as high as 0.7. Using the Fisher-matrix formalism, we compute the cosmological constraints for {Om_m, sig_8, w, n_s} considering each probe separately, as well as in combination. We find that the correlation function of peaks and shear profiles yield marginalized errors which are larger by a factor of 2-4 for {Om_m, sig_8} than the errors yielded by the peak abundance alone, while the errors for {w, n_s} are similar. By combining the three probes, the marginalized constraints are tightened by a factor of ~2 compared to the peak abundance alone, the least contributor to the error reduction being the correlation function. This work therefore recommends that future WL surveys use shear peaks beyond their abundance in order to constrain the cosmological model.Comment: 15 pages, 10 figures, submitted to MNRA