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Numerical Methods for Computing Interfacial Mean Curvature.

Numerical Methods for Computing Interfacial Mean
Curvature.
(943 K)

Bullard, J. W.; Garboczi, E. J.; Carter, W. C.; Fuller,
E. R., Jr.

Computational Materials Science, Vol. 4, 103-116, 1995.

### Keywords:

building technology; computer models; interfaces; mean
curvature; sintering; equations

### Abstract:

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A procedure is described for computing the mean
curvature along condensed phase interfaces in two or
three dimensions, without knowledge of the spatial
derivatives of the interface. For any point P on the
interface, the method consists of computing the portion
of volume enclosed by a small template sphere, centered
on P, that lies on one side of the interface. That
portion of the template volume is shown to be linear in
the mean curvature of the surface, relative to the phase
lying on the opposite side of the interface, to within
terms that can usually be made negligible. An analogous
procedure is described in two dimensions. Application
of the procedure to compute the mean curvature along a
digitized surface is demonstrated. A burning algorithm
can be included to improve computational accuracy for
interfaces having sharp curvature fluctuations. A minor
extension of the method allows computation of the
orientation of an interfacial element relative to a
fixed reference frame.
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