The most prevalent method for simulating distributed media in more than one dimension, such as membranes and plates, is by means of a modal expansion. That is, the resonances of the object are explicitly simulated using second-order resonators, typically arranged in parallel. More recently, explicit physical models in higher dimensions have been developed using meshes of coupled digital waveguides [66,47,68]. A particularly convincing example is gong synthesis developed by Scott Van Duyne using nonlinearities and lowpass losses around the rim of a lossless waveguide mesh .
Since ``plate reverbs'' are considered better than ``spring reverbs'' (which are essentially one dimensional), and since three-dimensional acoustic reverberation (such as in a concert hall) is considered superior to plate reverberation, it is logical to ask whether waveguide meshes in dimensions higher than three will provide yet better reverberation. This remains largely a subject of future research.