Biomedical subjects

K Schaadt

Publications and source records attributed to K Schaadt.

6 recordsLinked to original sources

PubMed2005

Universality of rescaled curvature distributions.

We applied a recently proposed rescaling of curvatures of eigenvalues of parameter-dependent random matrices to experimental data from acoustic systems and to a theoretical result. It is found that the data from four different experiments, ranging from isotropic plates to anisotropic three-dimensional objects, and the theoretical result always agree with the universal curvature distribution, if only the curvatures are rescaled such that the average of their absolute values is unity.

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PubMed2003

Experiments on elastomechanical wave functions in chaotic plates and their statistical features.

We measure the amplitude of the elastomechanical displacement at a fine grid of points on a free plate having the shape of a Sinai stadium. The obtained displacement field formally corresponds to a wave function in a quantum system. While the distribution of the squared amplitudes agrees with the prediction of random matrix theory (RMT), there is a strong deviation of the spatial correlator from the standard prediction for quantum chaotic systems. We show that this is due to the presence of two modes, leading to a beating phenomenon. We construct a proper extension of the spatial correlator within the framework of RMT.

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PubMed2003

Chaotic sound waves in a regular billiard.

We present experimental results for the ultrasound transmission spectra and standing wave patterns of a rectangular block of fused quartz. A comparison is made between our data and an approximation of the theoretical staircase function for three-dimensional isotropic elasticity. The main emphasis of our study is on the role of mode conversion in regular ray-splitting billiards. We present the fluctuation statistics and find that these are described by the Gaussian orthogonal ensemble of random matrix theory, despite the fact that the system is not classically chaotic, as demonstrated with numerical simulation. Using temperature perturbation, we find that the vast majority of the resonances are mixtures of transverse and longitudinal wave motion, yet a small number of special resonances remain pure. We further illuminate this by presenting standing wave patterns measured on one face of the block.

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PubMed2001

Random matrix theory and acoustic resonances in plates with an approximate symmetry.

We discuss a random matrix model of systems with an approximate symmetry and present the spectral fluctuation statistics and eigenvector characteristics for the model. An acoustic resonator like, e.g., an aluminum plate may have an approximate symmetry. We have measured the frequency spectrum and the widths for acoustic resonances in thin aluminum plates, cut in the shape of the so-called three-leaf clover. Due to the mirror symmetry through the middle plane of the plate, each resonance of the plate belongs to one of two mode classes and we show how to separate the modes into these two classes using their measured widths. We compare the spectral statistics of each mode class with results for the Gaussian orthogonal ensemble. By cutting a slit of increasing depth on one face of the plate, we gradually break the mirror symmetry and study the transition that takes place as the two classes are mixed. Presenting the spectral fluctuation statistics and the distribution of widths for the resonances, we find that this transition is well described by the random matrix model.

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PubMed2001

Spectral properties of a mixed system using an acoustical resonator.

We experimentally study the spectral properties of a mixed system using the flexural modes of a clover shaped plate. The system is called mixed because the corresponding ray dynamics has both chaotic and integrable regions in its phase space. The eigenvalue statistics show intermediate properties between the universal statistics corresponding to chaotic geometries which show Gaussian orthogonal ensemble statistics and integrable geometries that show Poisson statistics. We further investigate the Fourier transform of the peaks to study the influence of the length scales of the plate on the properties of the acoustic resonances. We observe a weak signal of the periodic orbits in the experimental data. Although some of the peaks in the Fourier transform of the eigenvalue spectrum correspond to the shortest stable periodic orbits, other strong peaks are also observed. To understand the role of symmetries, we start with a clover shaped plate belonging to the C(4v) point symmetry group, and progressively reduce the symmetry by sanding one of the edges. A Shnirelman peak in P(s) is observed for the highly symmetric situation due to level clustering.

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PubMed1999

Experimental investigation of universal parametric correlators using a vibrating plate.

The parametric variation of the eigenfrequencies of a chaotic plate is measured and compared to random matrix theory using recently calculated universal correlation functions. The sensitivity of the flexural modes of the plate to pressure is used to isolate this symmetry class of modes and simplify the data analysis. The size of the plate is used as the external parameter and the eigenvalues are observed to undergo one or two oscillations in the experimental window. The correlations of the eigenvalues are in good agreement with statistical measures such as the parametric number variance, the velocity autocorrelation, and the intralevel velocity autocorrelation derived for the Gaussian orthogonal ensemble of random matrix theory. Our results show that the theory can be also applied to wave systems other than quantum systems.

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