The Diffuse Field Reciprocity Relationship as a Framework for a General Power Flow Model

Following the wave approach to Statistical Energy Analysis (SEA), one can idealize the power flow through a subsystem by introducing the concept of direct and reverberant fields. The direct field is that arising at boundaries where power flows into or out of the subsystem when anechoic termination is assumed elsewhere. The reverberant field is that arising after multiple reflections of the direct field at the subsystem "random" boundaries. If the damping in the reverberant field is small enough, then it can be assumed diffuse. Then, the direct field injects power into the diffuse reverberant field, which stores and dissipates the energy. Under these circumstances, the diffuse field reciprocity relationship postulates that the knowledge of a deterministic model for the direct field suffice to quantify both the power being injected into and power lost by the reverberant field at the deterministic connections, providing a path to construct SEA-like power flow models in a generalized manner. Hence, the obtained framework not only provides an answer to the mid-frequency problem, as already discussed by other authors, by seamlessly allowing coupling between deterministic and statistical subsystems, but also generalizes classical SEA to arbitrarily complex structures that cannot be described by simple analytical models