Forecasting flutter echo: The role of largest local Lyapunov exponents

In this article, we theoretically established a method of mapping ray movement in three-dimensional (3D) enclosures and used a ray-tracing algorithm to describe the paths along which a ray propagates in a space with a slope or Sinai geometry. Time series points extracted from the paths were used to calculate the largest local Lyapunov exponents (LLLEs). We investigated the LLLE distributions for ray systems in the two spaces. The distributions contained considerable information on ray system dynamics; this information can be used to study the evolution of ergodic properties. A comparison of the LLLEs of the ray systems in the two spaces showed that the Sinai geometry produced a diffusive characteristic, whereas the slope geometry produced flutter echo. By applying the method to building acoustics, the acoustic fields in different rooms were described. A diffuse acoustic performance was indicated by the uniformity of the sound pressure level (SPL) by simulations and experiment. The results show that LLLEs have potential for use in acoustic performance description.