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We postulate that almost any motion of an interface between two crystals can produce a coupled tangential motion of the two crystals relative to each other which is proportional to the normal motion of the interface. Such translations can produce grain rotations ; the special case of the rotations of shrinking included circular cylindrical grains which(More)
We use an expanded variational approach based on dissipation to study the motion of the boundary of a non-circular cylindrical, and thus essentially 2-dimensional, crystalline grain of arbitrary cross-section enclosed in another grain of the same material under conditions where the normal grain boundary motion is coupled to relative tangential motion of the(More)
The Burlington Mathfest in August 1995 included an AMS Special Session on Soap Bubble Geometry, organized by Frank Morgan. At the end of the session, participants were asked to pose open problems related to bubble geometry. We have collected those problems here, adding a few introductory comments. Participants in the special session included the following:(More)
Mathematical models for various types of crystal surface motions have been made. They all reduce some energy which includes a given (usually crystalline) anisotropic surface free energy and perhaps a bulk free energy. The mechanisms which govern the motions are attachment/detachment kinetics, diiusion of atoms over surfaces, and perhaps diiusion within the(More)
The sphere is the shape which minimizes the surface tension of a drop of fluid. On the atomic scale a fluid – gas or liquid – consists of an isotropic, disorderly configuration of particles. The Wulff shape plays the same minimum-surface-tension role, but for the orderly, nonisotropic particle configurations of solids. For an intuitive picture consider(More)
President David Eisenbud presided over the EC and ECBT portions of the meeting (items beginning with 0, 1, or 2). Board Chair John Conway presided over the BT portion of the meeting (items beginning with 3). Items occur in numerical order, which is not necessarily the order in which they were discussed at the meeting. President Eisenbud convened the meeting(More)