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Error Estimates for Discrete Network Approximation
Optimization| Speaker: | Dr. Alexei Novikov, Caltech |
| Location: | 693 Kerr |
| Start time: | Thu, Oct 18 2001, 3:10PM |
Description
We apply a discrete network approximation to the problem of the
effective conductivity of the high contrast,
highly packed composites when the conductivities of the hosting medium and
the inclusions are vastly different and the
volume fraction of the inclusions is very high. The inclusions are
irregularly (randomly) distributed in the hosting medium,
so that a significant fraction of them does not participate in the
conducting spanning cluster. For this class of geometrical
arrays we derive a discrete network approximation and obtain an error
estimate for this approximation in which all the
constants are explicitly computed. The main advantage of the discrete
network approximation is that it is easy to implement numerically and
at the same time it captures geometric patterns of
the location of inclusions in the matrix. We use
variational techniques to provide rigorous mathematical justification for
the approximation and its error estimate.
Attendance will be taken for students registered
for credit.