Abstract
Recent progress in variational methods helps to provide general principles for microstructural evolution. Especially when several processes are interacting, such general principles are useful to formulate dynamical equations and to specify rules for evolution processes. Variational methods provide new insight and apply even under conditions of nonlinearity, nondifferentiability, and extreme anisotropy. Central to them is the concept of gradient flow with respect to an inner product. This article shows, through examples, that both well-known kinetic equations and new triple junctions motions fit in this context.
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W. Craig Carter earned his Ph.D. in materials science at the University of California at Berkeley in 1989. He is currently a research scientist at the National Institute of Standards and Technology.
J.E. Taylor earned her Ph.D. in mathematics at Princeton University in 1973. She is currently a professor at Rutgers University.
J.W. Cahn earned his Ph.D. in chemistry at the University of California at Berkeley in 1952. He is currently a metallurgist at the National Institute of Standards and Technology. Dr. Cahn is also a fellow of TMS.
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Carter, W.C., Taylor, J.E. & Cahn, J.W. Variational methods for microstructural-evolution theories. JOM 49, 30–36 (1997). https://doi.org/10.1007/s11837-997-0027-2
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DOI: https://doi.org/10.1007/s11837-997-0027-2