Lyon Statistical Mode Shape Functions

From 1983 to 1995, Richard H. Lyon published several papers on Statistical Phase Analysis, showing that the average phase of the transfer functions in complex systems grows with frequency in proportion to the modal density of the system. In one dimensional systems this phase growth is the same as that of freely propagating waves. However, in two and three dimensional systems this phase growth is much larger than the corresponding freely propagating wave. Recent work has shown that these phase growth functions can be used as mode shape functions in discrete system models to obtain results consistent with Statistical Energy Analysis. This paper reviews these results and proposes naming the statistical mode shape functions in honor of Lyon.