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leverage theoretical foundations to innovate and optimize designs in subject areas such as thermodynamics, fluid mechanics, and materials science? Specifically, how do theoretical frameworks guide the development of efficient energy systems, enhance the performance of fluid dynamics in various applications, and optimize material selection for durability and functionality? Furthermore, how do these theories integrate with computational methods and experimental validation to ensure accurate predictions and reliable outcomes in real$-$world scenarios? Lastly, what emerging theoretical paradigms are shaping the future of mechanical engineering, particularly in fields like robotics, nanotechnology, and sustainable manufacturing?