Phase Field Models
A phase field model is a mathematical model for solving interfacial problems. It has mainly been applied to solidification dynamics, but it has also been applied to other situations such as viscous fingering, fracture dynamics, vesicle dynamics, etc.
The method substitutes boundary conditions at the interface by a partial differential equation for the evolution of an auxiliary field (the phase field) that takes the role of an order parameter. This phase field takes two distinct values (for instance +1 and −1) in each of the phases, with a smooth change between both values in the zone around the interface, which is then diffuse with a finite width. A discrete location of the interface may be defined as the collection of all points where the phase field takes a certain value (e.g., 0).
A phase field model is usually constructed in such a way that in the limit of an infinitesimal interface width (the so-called sharp interface limit) the correct interfacial dynamics are recovered. This approach permits to solve the problem by integrating a set of partial differential equations for the whole system, thus avoiding the explicit treatment of the boundary conditions at the interface.
Phase field models were first introduced by Fix and Langer, and have experienced a growing interest in solidification and other areas.
Read more about Phase Field Models: Equations of The Phase Field Model, Multi Phase Field Models, Software, Further Reading
Famous quotes containing the words phase, field and/or models:
“This is certainly not the place for a discourse about what festivals are for. Discussions on this theme were plentiful during that phase of preparation and on the whole were fruitless. My experience is that discussion is fruitless. What sets forth and demonstrates is the sight of events in action, is living through these events and understanding them.”
—Doris Lessing (b. 1919)
“Better risk loss of truth than chance of error—that is your faith-vetoer’s exact position. He is actively playing his stake as much as the believer is; he is backing the field against the religious hypothesis, just as the believer is backing the religious hypothesis against the field.”
—William James (1842–1910)
“The greatest and truest models for all orators ... is Demosthenes. One who has not studied deeply and constantly all the great speeches of the great Athenian, is not prepared to speak in public. Only as the constant companion of Demosthenes, Burke, Fox, Canning and Webster, can we hope to become orators.”
—Woodrow Wilson (1856–1924)