This book discusses many of the connections between cutting edge applications and advanced numerical and algorithmic techniques. Topics include models for long-range molecular forces; biological and chemical contamination, including hierarchical problem-solving ideas from computer science; discrete mathematics, including connections to the buckyball structure of carbon 60; dimension-reduction techniques in incompressible fluid mechanics; aspects of charge transport, bridging compressible fluids (gas dynamics) and semiconductors; the approximation problem in control theory; questions related to weighted approximation by polynomials in the complex plane; and high friction limits of hydrodynamic models.
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