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.

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.

Effect of symmetry breaking on level curvature distributions.

We derive an exact general formalism that expresses the eigenvector and the eigenvalue dynamics as a set of coupled equations of motion in terms of the matrix elements dynamics. Combined with an appropriate model Hamiltonian, these equations are used to investigate the effect of the presence of a discrete symmetry in the level curvature distribution. An explanation of the unexpected behavior of the data regarding frequencies of acoustic vibrations of quartz block is provided.

Bubble and spherical air shell formation dynamics.

We studied the formation dynamics of air bubbles emitted from a nozzle submerged in aqueous glycerol solutions of different viscosities. We describe the evolution of the bubbling regimes by using the air flow rate as a control parameter and the time between successive bubbles as a dynamical variable. Some results concerning bubbling coalescence were emulated with a combination of simple maps. We also observed the formation of air shells surrounding liquid drops inside the liquid, known as antibubbles. The antibubbling conditions were related to an intermittent regime.