Applied mathematics research enables scientists to solve problems previously unsolvable, especially in biological systems. For example, fluid mechanics has begun to interact with biology to focus on environmental questions. New areas of research such as control theory and dynamical systems are being used to study problems in biology. This includes systems biology, mathematical medicine, and computational neuroscience. As well, current research includes the construction of mathematical models of biological mechanisms and then reverse-engineering these processes.
Another hot area of research is in quantum information science, which is used in technologies such as semiconductors, superconductors, medical NMRs, solar panels and lasers. For example, carbon nano-structures are being examined for uses in a wide array of technologies, and investigating their properties involves a range of mathematical and computational methods.
Further practical applications of quantum theory, such as quantum computers, or the custom designing of pharmaceutical molecules, are being developed. Researchers are using these principles to develop more secure communications, as well as faster and more powerful computers.
Research in fluid mechanics uses applied mathematics including mathematical modeling, analysis, and computational mathematics. Researchers are using fluid mechanics to study theoretical problems such as proving the existence, uniqueness and regularity for the Navier-Stokes equations. Practical applications include atmospheric, ocean, and climate dynamics, stellar wind dynamics, and the dynamics of shock waves.
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