Sound source reconstruction using inverse boundary element calculations

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.     

Non-Equispaced Fast Fourier Transforms with Applications to Tomography

In this article we describe a non-equispaced fast Fourier transform. It is similar to the algorithms of Dutt and Rokhlin and Beylkin but is based on an exact Fourier series representation. This results in a greatly simplified analysis and increased flexibility. The latter can be used to achieve more efficiency. Accuracy and efficiency of the resulting algorithm are illustrated by numerical examples. In the second part of the article the non-equispaced FFT is applied to the reconstruction problem in Computerized Tomography. This results in a different view of the gridding method of OSullivan and in a new ultra fast reconstruction algorithm. The new reconstruction algorithm outperforms the filtered backprojection by a speedup factor of up to 100 on standard hardware while still producing excellent reconstruction quality.     

Structure of the set of annihilators

We investigate the right annihilator lattice of a^*-ring and ask whether it is orthomodular with respect to a naturally given involution. In particular, we introduce a new class of^*-rings with orthomodular right annihilator lattice.     

Ionenschallinstabilitäten in Edelgas-Gleichstromentladungen bei niedrigen Drücken. II. Vergleich der experimentellen Ergebnisse mit einer eindimensionalen kinetischen Dispersionstheorie

The experimental measurements of the propagation properties of self-exicted ion acoustic waves in a de-low pressure column are compared with a one dimensional dispersion theory. The corresponding dispersion relation is developed starting from the linearised Vlasov equation with a Davydov-type collision term. It is shown, that the mean features of the propagation behaviour of the ion acoustic waves can be explained by the theory. The experimental results concerning the dependence of the upper limit frequency of the waves upon the discharge current should be analysed on the base of new results from plasma diagnostics, taking also into account nonlinear and geometrical effects.     

Numerical Study of the Instability in a Maxwellian Beam-Plasma System II. Many Wave Regime

The relaxation of the beam-plasma system with several preliminarily excited unstable waves in its spectrum is investigated on the basis of computer simulations. The nature of the waves and particles interaction during the instability development is analysed. It is shown that the destroying of the amplitude oscillations of the single wave after saturation in the presence of additional waves is caused by the well known effect of resonance overlapping. A chaotization of the motion of the beam particles occurs even in the case when the amplitudes of the neighbouring waves are small.     

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