  Electromagnetic (EM) wave scattering in electrically large, irregularly
shaped, environments is a common phenomenon. The deterministic, or first
principles, study of this process is usually computationally expensive and the
results exhibit extreme sensitivity to scattering details. For this reason, the
deterministic approach is often dropped in favor of a statistical one. The
Random Coupling Model (RCM) is one such approach that has found great success
in providing a statistical characterization for wave chaotic systems in the
frequency domain. Here we aim to transform the RCM into the time domain and
generalize it to new situations. The proposed time-domain RCM (TD-RCM) method
can treat a wave chaotic system with multiple ports and modes. Two features are
now possible with the time-domain approach for chaotic resonators: the
incorporation of earlytime short-orbit transmission path effects between the
ports, and the inclusion of arbitrary nonlinear or time-varying port load
impedances. We have conducted short-pulse time-domain experiments in wave
chaotic enclosures, and used the TD-RCM to simulate the corresponding
experimental setup. We have also examined a diode-loaded port and compared
experimental results with a numerical TD-RCM treatment and found agreement.
