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Theory of Living Matter Group

First tutorial of the TLM group



Date and venue

Date: Wednesday, 24th September from 5-7pm

Venue: Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, room MR 15

For room MR 15 go downstairs right behind the main entrance. There will be signs which will guide the way.


Schedule

In this tutorial Philip Greulich and Steffen Rulands will give an Introduction to pattern formation. The lecture is intended to be understandable for a broad audience with an interest in and basic knowledge of mathematics. No preliminary knowledge in non linear dynamics or pattern formation will be required. However, participants are supposed to have basic training in mathematical methods, especially differential equations and some linear algebra.

The general struggle for existence of animate beings is not a struggle for raw materials – these, for organisms, are air, water and soil, all abundantly available – nor for energy which exists in plenty in any body in the form of heat, but a struggle for [negative] entropy, which becomes available through the transition of energy from the hot sun to the cold earth.

Ludwig Boltzmann

Life is an ongoing struggle for order. While the second law of thermodynamics predicts that in any closed system the degree of disorder increases with time, biological systems exhibit a great amount of organization. Indeed, functional differentiation of the organism’s internal structure is a necessity for the development of life. Such functional differentiation is established through the formation of complex patterns. As an example, eukaryotic cells are complex organisms which are, in part, organized by smaller subunits, the organelles. On the level of tissues, the establishment of spatial order is one of the most important tasks in embryonic development. Starting from a homogeneous cluster, cells differentiate to a variety of different forms of tissue. But how can cells which share identical genetic information develop into the correct cell types in order to build functioning organisms?

To understand the formation of spatial patterns mathematical models combining nonlinear reactions and diffusion have been extensively studied. In his visionary work, Alan Turing investigated the stability of the simplest possible reaction-diffusion system which is capable of forming a pattern from a uniform state. In this lecture we will give an introduction to some elementary methods and simple models in the theory of pattern formation. The first part will deal with elementary definitions and the concept of linear stability, which will then be applied to derive Turing's mechanism. The second part will cover some more advanced pattern forming processes, such as wave propagation.

After the lecture we will have some wine and cookies and opportunity for discussions.

The lecture notes for the second part of the tutorial can be obtained here.

Literature


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