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Durham University

Research & business

Research lectures, seminars and events

The events listed in this area are research seminars, workshops and lectures hosted by Durham University departments and research institutes. If you are not a member of the University, but  wish to enquire about attending one of the events please contact the organiser or host department.


Applied Mathematics Seminars: Stochastic homogenisation of high-contrast media

Presented by Mikhail Cherdantsev, Cardiff University
26 January 2018 14:00 in CM301

It has been known for almost two decades (starting with a 2000 paper by Zhikov) that elliptic partial differential operators with periodic high-contrast coefficients, describing certain composite materials, have band gap spectrum described by Zhikov's beta-function in the homogenisation limit. The homogenised operator is of the two-scale nature, it has a macroscopic and microscopic (corresponding to the period of the composite) parts. While the stochastic homogenisation is a well established area of mathematics, the high-contrast stochastic homogenisation has hardly been addressed, and it seems that there is not a single paper studying the spectral problems in high-contrast stochastic homogenisation. We initiate the research in this direction and show that similarly to the periodic case in the stochastic high contrast setting(under some lenient conditions) the spectrum has a band gap structure characterised by a function similar to Zhikov's beta-function, we study the limit two-scale operator with the stochastic microscopic component and prove the convergence of the spectra.

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