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Complex networks appear in almost every aspect of our daily life and are widely studied in the fields of physics, mathematics, finance, biology and computer science. This work utilizes percolation theory in statistical physics to explore the percolation properties of complex networks and develops a reinforcement scheme on improving network resilience. This dissertation covers two major parts of my Ph.D. research on complex networks: i) probe—in the context of both traditional percolation and k-core percolation—the resilience of complex networks with tunable degree distributions or directed dependency links under random, localized or targeted attacks; ii) develop and propose a reinforcement scheme to eradicate catastrophic collapses that occur very often in interdependent networks. We first use generating function and probabilistic methods to obtain analytical solutions to percolation properties of interest, such as the giant component size and the critical occupation probability. We study uncorrelated random networks with Poisson, bi-Poisson, power-law, and Kronecker-delta degree distributions and construct those networks which are based on the configuration model. The computer simulation results show remarkable agreement with theoretical predictions. We discover an increase of network robustness as the degree distribution broadens and a decrease of network robustness as directed dependency links come into play under random attacks. We also find that targeted attacks exert the biggest damage to the structure of both single and interdependent networks in k-core percolation. To strengthen the resilience of interdependent networks, we develop and propose a reinforcement strategy and obtain the critical amount of reinforced nodes analytically for interdependent Erdős-Rényi networks and numerically for scale-free and for random regular networks. Our mechanism leads to improvement of network stability of the West U.S. power grid. This dissertation provides us with a deeper understanding of the effects of structural features on network stability and fresher insights into designing resilient interdependent infrastructure networks.

In this dissertation, we present and discuss development, implementation, and experimental results of reduced-order model based feedback control of subsonic cavity flows. Model based feedback control of subsonic flows have been studied and implemented by the flow control group at the Collaborative Center of Control Science (CCCS) at the Ohio State University (OSU). The team, composed of researchers from the departments of Electrical Engineering and Mechanical Engineering at the Ohio State, the Air Force Research Laboratory, and NASA Glenn Research Center, possesses synergistic capabilities in all of the required multidisciplinary areas of experimental data acquisition, computational flow simulation, low dimensional modeling, controller design, and experimental validation. The goal of the CCCS effort is to develop tools and methodologies for the use of closed-loop aerodynamic flow control to manipulate the flow over maneuvering air vehicles. The problem chosen for the initial study by the CCCS flow team is control of the resonant noise generated by subsonic flow past an open cavity. This phenomenon is characterized by a strong coupling between the flow dynamics and the flow-induced acoustic field that can lead to self-sustained resonance. Two approaches towards model development have been studied in this dissertation. One aims at representing the physical properties of the system by dynamical models in transfer function forms, referred to as the physics-based linear model in this dissertation. The other approach we have followed is based on proper orthogonal decomposition (POD) and Galerkin projection methods involving the flow governing equations, which is referred to as the nonlinear model or Galerkin model in the dissertation. Each model mentioned above can be further divided into two types: model derived from numerical simulation data and model derived from real time experimental data. Different types of feedback controllers have been designed for corresponding flow models. Closed-loop system performance has been evaluated by both numerical simulation and experimental implementation as well. These results confirm that model based feedback control represents a promising approach to flow control even in its current infancy state.