Acoustic diffusion described using the largest Lyapunov exponents

In this study, we theoretically established a method to map ray movements in 3D enclosures and used a ray-tracing algorithm to describe the paths along which a ray propagates in space. Moreover, we used the time-series points extracted from these paths to calculate the largest Lyapunov exponents (LLEs). Two models, ray reflections in rectangular enclosure spaces assigned with 1–16 cylindrical and 1–8 spherical diffusers, were established. By investigating how the LLEs of ray systems vary with the diffuser parameters, we found that the LLEs can be used as a function of the number of diffusers in the spaces. The results showed that LLEs can be potentially implemented in diffusers to improve room acoustics.