# Mathematics Colloquia and Seminars

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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 |

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.