Sound absorption by Menger sponge fractal.

For the purpose of investigation on acoustic properties of fractals, the sound absorption coefficients are experimentally measured by using the Menger sponge which is one of typical three-dimensional fractals. From the two-microphone measurement, the frequency range of effectively absorbing sound waves is shown to broaden with degree of fractality, which comes from the fractal property of the homothetic character. It is shown that experimental features are qualitatively explained by an electrical equivalent circuit model for the Menger sponge.

Application of Hamiltonian of ray motion to room acoustics.

Based on a standard Hamiltonian of acoustic ray, it is shown that a ray motion in a finite region can be treated as a particle motion inside a potential well. The boundary reflections of ray can be described by introducing a so-called confining potential to confine a ray motion in a closed domain. It is shown that the square well potential model for the ray motion can reproduce the reverberation time in a two-dimensional room with irregular walls which is consistent with the Norris-Eyring law.

Riemannian geometric approach to chaos in SU(2) Yang-Mills theory.

Based on the Riemannian geometric approach to Hamiltonian systems with many degrees of freedom, we study a chaotic nature of the SU(2) Yang-Mills field. Particularly, we study the Lyapunov exponent of the Wu-Yang magnetic-monopole solution of the SU(2) Yang-Mills field equation by use of an analytic formula which is determined by the average Ricci curvature and its fluctuation on the Riemannian manifold. It is shown that the system is chaotic from the positive values of the Lyapunov exponent.

Indicator of chaos based on the Riemannian geometric approach.

Using the Riemannian geometric approach to Hamiltonian systems, we show that the empirical indicator of chaos proposed by Kosloff and Rice [J. Chem. Phys.

Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system.

Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system.