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The dual-mode scramjet is a propulsive concept for contemporary hypersonic vehicles promising flight cruise speeds upwards of Mach 5. Despite decades of development and a recent resurgence in interest, such engines are not routinely deployed for commercial or military purposes. Instead, they have been confined to the realm of ground-test research and limited one-off flight test missions. One of the key stumbling blocks on the critical path to deployment of a dual-mode scramjet is the optimal design and stable operation of the isolator, a typically constant area duct that separates the scramjet inlet from the combustor. During ramjet mode at Mach numbers from 3 to 5 and during the transition to scramjet mode at higher Mach numbers, the isolator contains the pseudo-shock. Necessary to meet the back-pressure in the combustor, the pseudo-shock is typically divided into a shock dominated shock train region followed by a turbulence driven mixing region. Fluctuations in combustor pressure due to vehicle maneuvering, throttling, or combustion instabilities drive the shock train to shift streamwise within the isolator. In response to sharp pressure fluctuations, the shock train is unable to stabilize within the isolator, and the scramjet unstarts by ejecting the shock train out the inlet. This work addresses three key gaps in understanding of the isolator pseudo-shock. The phenomenon is studied in three experimental facilities to investigate the quasi-steady and unsteady fluid dynamics of the shock train in fueled and un-fueled test conditions. The strong link between boundary layer morphology and shock train structure is studied in detail and used as a tool to evaluate the state-of-the-art definitions and models of the pseudo-shock. Identifying the limitations of these models, a new process driven flux-conserved pseudo-shock model is proposed. This provides a computationally efficient model grounded in the fluid dynamic mechanisms of the pseudo-shock with better predictive capability than the current state-of-the-art across all facilities tested. The unsteady behavior of the shock train is further investigated to identify and understand two distinct forced dynamic modes: mechanically induced, low-rate forcing and high-rate combustion driven unsteadiness that sheds upstream propagating shocks. The proposed process driven model is found to be effective in the the limiting case of high-rate combustion driven unsteadiness by evaluating the model in a shock stationary reference frame. Further analysis identifies the approximately rigid chain motion of the shock train structure to mechanically induced forcing. The time delay between the onset of forced dynamics is found to saturate to a constant value and maximum shock train speed along the isolator with respect to the perturbation rate of change. The result of this work provides dual-mode scramjet designers with improved tools and physical understanding to develop more efficient, robust, and capable propulsion systems for hypersonic vehicles.