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Flow over open cavities is mainly governed by a feedback mechanism due to the interaction of shear layer instabilities and acoustic forcing propagating upstream in the cavity. This phenomenon is known to lead to resonant tones that can reach 180 dB in the far-field and may cause structural fatigue issues and annoying noise emission. This paper concerns the use of optimal control theory for reducing the noise level emitted by the cavity. Boundary control is introduced at the cavity upstream corner as a normal velocity component. Model-based optimal control of cavity noise involves multiple simulations of the compressible Navier–Stokes equations and its adjoint, which makes it a computationally expensive optimization approach. To reduce the computational costs, we propose to use a reduced-order model (ROM) based on Proper Orthogonal Decomposition (POD) as a surrogate model of the forward simulation. For that, a control input separation method is first used to introduce explicitly the control effect in the model. Then, an accurate and robust POD ROM is derived by using an optimization-based identification procedure and generalized POD modes, respectively. Since the POD modes describe only velocities and speed of sound, we minimize a noise-related cost functional characteristic of the total enthalpy unsteadiness. After optimizing the control function with the reduced-order model, we verify the optimality of the solution using the original, high-fidelity model. A maximum noise reduction of 4.7 dB is reached in the cavity and up to 16 dB at the far-field. [ABSTRACT FROM AUTHOR]

The Ebola virus disease is caused by the Ebola virus which belongs to the filoviridae virus family. The 2014 outbreaks were estimated to have caused over 11,000 fatalities. In this paper, we formulate and analyze a system of ordinary differential equations which incorporates disease relapse and reinfection. The Ebola model with disease relapse and reinfection is locally-asymptotically stable when the basic reproduction number is less than unity. The model exhibits in the presence of disease reinfection, the phenomenon of backward bifurcation, where the stable disease-free equilibrium co-exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The feasibility of backward bifurcation occurring increases with increasing values of both relapse and reinfection. The total number of new cases of Ebola-infected individuals increases with increasing values of the relapse and reinfection parameters. Further simulations show that Ebola transmission models that do not incorporate relapse and reinfection may under-estimate disease burden in the community. Similar under-estimation is observed in models that include only one infected and recovered classes. Using results obtained from sensitivity analysis indicates that Ebola (given disease relapse and reinfection) can be effectively curtailed in the community by using control measures with a high-effectiveness level. This strategy is more effective than either the moderate- or low-effectiveness levels. [ABSTRACT FROM AUTHOR]