Methods of Boundary Homogenisation in the Problems of Laplacian Transport

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• Alex Skvortsov (University of New South Wales)
• Friday 05 July 2024, 10:15-10:45
• Seminar Room 1, Newton Institute.

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WHTW02 - WHT Follow on: the applications, generalisation and implementation of the Wiener-Hopf Method

We present several approximations in the theory of Laplacian transport near complex or heterogeneously boundaries. This phenomenon, governed by the Laplace operator, is ubiquitous in fields as diverse as chemical physics, hydrodynamics, electrochemistry, heat transfer, wave propagation, theory of elasticity and random processes. We overview the mathematical basis and various applications of the effective medium approximation and the related boundary homogenization when a complex heterogeneous boundary is replaced by an effective much simpler boundary.  Two parameters of the simplified boundary (its position and effective impedance) are calculated by means of conformal mapping or matched asymptotic expansions. Some specific examples are discussed in detail.

This talk is part of the Isaac Newton Institute Seminar Series series.

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