# Mathematics Colloquia and Seminars

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### Phase Transitions in Restricted Geometries and at Grain Boundaries: Wetting, Filling and All That.

**Mathematical Physics & Probability**

Speaker: | Douglas Abraham, Theoretical Physics,
University of Oxford. |

Location: | 693 Kerr |

Start time: | Tue, Mar 9 2004, 3:10PM |

This seminar will begin with a review of what is known about the structure of interfaces between coexistent equilibrium pure phases in the planar Ising Ferromagnet. The phenomenological, thermodynamically motivated picture of phase separation is seriously inadequate with a number of interesting consequences. Some of these are exemplified by introducing a substrate, giving two typical problems: firstly, when the substrate edge is straight line, we have half-plane problems, for which the concepts of wetting, sessile drops and contact angles are pertinent. Secondly, with a corner-shaped lattice, there is a new phenomenon -filling. Finally, novel phenomena occur when interfaces cross grain boundaries at controlled angles. The second part of the talk will discuss briefly the main technical features of the calculations without going into much detail. This will be followed by some speculations about future research directions.