Wed 17th April 12:30 – 13:30. This seminar will be in person (G14, Newton Building). A teams link is also available to join online.
Abstract
Chaos theory represents a recently developed robust mathematical method that may allow for the quantification of diffuseness by the Lyapunov exponent, and the ergodicity characteristic can be implemented in a chaotic system to investigate the diffuseness of the sound field in a room. A positive Lyapunov exponent (LE) indicates that the system is chaotic. Based on billiards theory, two adjoint rays separate exponentially at the rate that the Lyapunov exponent evolves over time in a diffuse field. A positive LE indicates that separation of the acoustic rays is sensitive to the initial conditions of the chaotic system, which results in a higher uniformity of the sound field in the enclosed space. The sensitivity of the ray separation to the initial conditions of the chaotic system makes it possible to investigate the diffusive behavior of rays in various enclosed spaces. This talk presents theory behind the methods for depicting ray performance using largest Lyapunov exponent (LLE). The characteristics of rays in an enclosure can be described by the LLE as follows: when the LLE approaches 0, the ray moves regularly (bouncing back and forth), and when the LLE is positive (which shows that the ray system is chaotic), the ray performance is diffusive. The LLE method can be used to evaluate the ray performance in rooms with complex geometries; especially when the rooms are treated by the diffusers.
Biography
Hengling Song studied Acoustics (MSc from 2008 to 2011). He obtained his PhD in 2018 for his work on “Study of Spatial sound field using Ray Chaos Methods”. In January 2019, Hengling Song was appointed Lecturer at the Shijiazhuang Tiedao University.