A Computationally Efficient Modeling Code for Sh-Waves in Austenitic Welds Using an Explicit Space-Time Green-Function

For ultrasonic inspection of austenitic welds and cladded components horizontally polarized shear (SH) waves — as generated by electromagnetic acoustic transducers (EMATs) — have certain benefits compared with quasi-vertically polarized shear and quasi-pressure waves. SH-waves suffer the least distortion of all three wave modes when propagated through anisotropic weld material and no energy is lost through mode conversion at the steel/free surface or base metal/weld interfaces. To explain experimentally observed phenomena and to predict the cases where SH-waves might be best employed, modeling of the respective wave propagation effects is useful. In this contribution, a computationally efficient modeling code is presented for SH-waves propagating in transversely isotropic media, thus particularly applicable to ideally fiber-textured austenitic weld material. An explicit space-time domain far-field representation of Green’s dyadic function has been derived with respect to the wave type under concern, the fiber direction being included as a free parameter. The obtained relationships have been applied to the Generalized Point-Source-Synthesis method (GPSS [1,2]) to model radiation, propagation and scattering effects. The code thus improved — SH-GPSS— is characterized by a considerable reduction of computer run-time and is therefore particularly convenient in view of a respective extension to inhomogeneous weldments. Numerical results are presented for both continuous wave and time-dependent rf-impulse modeling for austenitic weld metal specimens, covering field profiles as well as wave front snapshots for a phased array EMAT-probe

Relatively computably enumerable reals

A real X is defined to be relatively c.e. if there is a real Y such that X is c.e.(Y) and Y does not compute X. A real X is relatively simple and above if there is a real Y <_T X such that X is c.e.(Y) and there is no infinite subset Z of the complement of X such that Z is c.e.(Y). We prove that every nonempty Pi^0_1 class contains a member which is not relatively c.e. and that every 1-generic real is relatively simple and above.Comment: 5 pages. Significant changes from earlier versio

Genericity and measure for exponential time

AbstractRecently, Lutz [14, 15] introduced a polynomial time bounded version of Lebesgue measure. He and others (see e.g. [11, 13–18, 20]) used this concept to investigate the quantitative structure of Exponential Time (E = DTIME(2lin)). Previously, Ambos-Spies et al. [2, 3] introduced polynomial time bounded genericity concepts and used them for the investigation of structural properties of NP (under appropriate assumptions) and E. Here we relate these concepts to each other. We show that, for any c ⩾ 1, the class of nc-generic sets has p-measure 1. This allows us to simplify and extend certain p-measure 1-results. To illustrate the power of generic sets we take the Small Span Theorem of Juedes and Lutz [11] as an example and prove a generalization for bounded query reductions

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur