Rational-spline approximation with automatic tension adjustment

An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline

Tomographic reconstruction of the three-dimensional structure of the HH30 jet

The physical parameters of Herbig-Haro jets are usually determined from emission line ratios, obtained from spectroscopy or narrow band imaging, assuming that the emitting region is homogeneous along the line of sight. Under the more general hypothesis of axisymmetry, we apply tomographic reconstruction techniques to the analysis of Herbig-Haro jets. We use data of the HH30 jet taken by Hartigan & Morse (2007) with the Hubble space telescope using the slitless spectroscopy technique. Using a non-parametric Tikhonov regularization technique, we determine the volumetric emission line intensities of the [SII]6716,6731, [OI]6300 and [NII]6583 forbidden emission lines. From our tomographic analysis of the corresponding line ratios, we produce "three-dimensional" images of the physical parameters. The reconstructed density, temperature and ionization fraction present much steeper profiles than those inferred using the assumption of homogeneity. Our technique reveals that the reconstructed jet is much more collimated than the observed one close to the source (a width ~ 5 AU vs. ~ 20 AU at a distance of 10 AU from the star), while they have similar widths at larger distances. In addition, our results show a much more fragmented and irregular jet structure than the classical analysis, suggesting that the the ejection history of the jet from the star-disk system has a shorter timescale component (~ some months) superimposed on a longer, previously observed timescale (of a few years). Finally, we discuss the possible application of the same technique to other stellar jets and planetary nebulae.Comment: 13 pages, 9 figures, accepted by Ap

The Argyris isogeometric space on unstructured multi-patch planar domains

Multi-patch spline parametrizations are used in geometric design and isogeometric analysis to represent complex domains. We deal with a particular class of $C^0$ planar multi-patch spline parametrizations called analysis-suitable $G^1$ (AS-$G^{1}$) multi-patch parametrizations (Collin, Sangalli, Takacs; CAGD, 2016). This class of parametrizations has to satisfy specific geometric continuity constraints, and is of importance since it allows to construct, on the multi-patch domain, $C^1$ isogeometric spaces with optimal approximation properties. It was demonstrated in (Kapl, Sangalli, Takacs; CAD, 2018) that AS-$G^1$ multi-patch parametrizations are suitable for modeling complex planar multi-patch domains. In this work, we construct a basis, and an associated dual basis, for a specific $C^1$ isogeometric spline space $\mathcal{W}$ over a given AS-$G^1$ multi-patch parametrization. We call the space $\mathcal{W}$ the Argyris isogeometric space, since it is $C^1$ across interfaces and $C^2$ at all vertices and generalizes the idea of Argyris finite elements to tensor-product splines. The considered space $\mathcal{W}$ is a subspace of the entire $C^1$ isogeometric space $\mathcal{V}^{1}$, which maintains the reproduction properties of traces and normal derivatives along the interfaces. Moreover, it reproduces all derivatives up to second order at the vertices. In contrast to $\mathcal{V}^{1}$, the dimension of $\mathcal{W}$ does not depend on the domain parametrization, and $\mathcal{W}$ admits a basis and dual basis which possess a simple explicit representation and local support. We conclude the paper with some numerical experiments, which exhibit the optimal approximation order of the Argyris isogeometric space $\mathcal{W}$ and demonstrate the applicability of our approach for isogeometric analysis

XAFS spectroscopy. I. Extracting the fine structure from the absorption spectra

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing parameter and the method for raising of stability with respect to k_min variation; (ii) interpolation spline with the varied knots; (iii) the line obtained from bayesian smoothing. This methods considers various prior information and includes a natural way to determine the errors of XAFS extraction. Particular attention has been given to the estimation of uncertainties in XAFS data. Experimental noise is shown to be essentially smaller than the errors of the background approximation, and it is the latter that determines the variances of structural parameters in subsequent fitting.Comment: 16 pages, 7 figures, for freeware XAFS analysis program, see http://www.crosswinds.net/~klmn/viper.htm

Boosting Additive Models using Component-wise P-Splines

We consider an efficient approximation of Bühlmann & Yu’s L2Boosting algorithm with component-wise smoothing splines. Smoothing spline base-learners are replaced by P-spline base-learners which yield similar prediction errors but are more advantageous from a computational point of view. In particular, we give a detailed analysis on the effect of various P-spline hyper-parameters on the boosting fit. In addition, we derive a new theoretical result on the relationship between the boosting stopping iteration and the step length factor used for shrinking the boosting estimates

Development Of A Semi-Swath Craft For Malaysian Waters

Small Waterplane Area Twin Hull (SWATH) and Catamaran vessels are known to have more stable platform as compared to mono-hulls. A further advantage of SWATH as compared to Catamaran is its smaller waterplane area that provides better seakeeping qualities. However, the significant drawback of the SWATH vessel is when encountering head-sea at high forward speed. Due to its low stiffness, it has a tendency for large pitch motions. Consequently, this may lead to excessive trim or even deck wetness. This phenomenon will not only degrade the comfortability but also results in structural damage with greater safety risks. In this research a modified SWATH design is proposed. The proposed design concept represents a combination of Catamaran and SWATH vessel hull features that will lead to reduce in bow-diving but still maintains good seakeeping capabilities. This is then called the Semi- SWATH vessel. In addition, the full-design of this vessel has been equipped by fixed fore fins and controllable aft fins attached on each lower hull. In the development of controllable aft fins, the PID controller system was applied to obtain an optimal vessel’s ride performance at speeds of 15 (medium) and 20 (high) knots. In this research work, the seakeeping performance of Semi-SWATH vessel was evaluated using time-domain simulation approach. The effect of fin stabilizer on the bare hull performance is considered. The validity of numerical evaluation was then compared with model experiments carried out in the Towing Tank at Marine Technology Laboratory, UTM. It is shown that the Semi-SWATH vessel with controllable fin stabilizer can have significantly reduction by about 42.57% of heave motion and 48.80% of pitch motion