What is … diffusion?

This page hosts information on Maciek Korzec's talk "What is … diffusion?" at the "What is …?" seminar. The talk will take place on Friday, October 21, 1pm at the BMS Loft at Urania. This talk will help you better understand the talk by Charlie Elliot, which will start at 2pm.

We will again be ordering delivery pizza. If you would like to order pizza with us, please arrive to the "What is …?" seminar by 12:45pm.

Abstract

One of the most fundamental differential operators appearing in partial differential equations (PDEs) is the Laplace operator. Its understanding is essential to be able to treat models describing real-world problems. One of the most basic PDEs relates the rate of change of some quantity to the Laplace operator applied to the same function: the diffusion equation u_t = k \nabla^2 u, also known as heat equation. In this talk several examples for diffusion will be explained. A connection between random walks and continuous diffusion will be established, a Gaussian filter will be linked to diffusion in image processing and the anisotropic diffusion equation u_t = \nabla \cdot k(x) \nabla u will be used to improve an image by advocating diffusion in small slope regions only. In this way the edges in an image remain intact while noise or similar image failures are diffused out. Finally the heat equation will be derived in a bulk material, and also on a regular surface, resulting in a surface diffusion equation, u_t = \nabla_{\!s} \cdot k(x) \nabla_{\!s} u.

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