Modelling, Simulating and Analysing Structure Formation in Tissue and in Cellular Automata

Date

Feb 28, 2013

Time

3:00 PM - 4:00 PM

Speaker

Andreas Dress

Affiliation

Bielefeld

Series

TUD ZIH Kolloquium

Language

de

Main Topic

Informatik

Other Topics

Biologie, Informatik, Mathematik

Host

Ralph Müller-Pfefferkorn, Zentrum für Informationsdienste und Hochleistungsrechnen

Description

Structure formation has fascinated mankind ever since antiquity. And, after the introduction of infinitesimal calculus, partial differential equations appeared for a long time to constitute the only proper mathematical methodology to generate and analyse spatio-temporal models of structure formation. So, it came as a slight surprise that even rather coarse-grained and simplistic CA-type models could capture essential features of structure formation processes. In the lecture, I will first recall how we first learned about this almost 30 years ago when, jointly with Martin Gerhardt, Nils Jaeger, Peter Plath, and Heike Schuster, we tried to analyse heterocatalytic processes on metal surfaces and, this way, discovered that such processes might potentially form interesting spatial-temporal patterns -- a finding that was confirmed only later by Ronald Imbihl in a number of beautiful experiments (now in Hannover, then working at Gerhard Ertl's lab in Berlin). I will then go on to present various CA-type models that were later developed jointly with Peter Serocka at Bielefeld in the 1990s and clearly exhibited striking phase transitions in "pattern space", going e.g. from patterns of ever turning spirals to patterns of "growing, intermingling, and solidifying empires" upon one slight change of parameters for one time step, only, -- thus furnishing intriguing metaphors for the onset and establishment of e.g. cancer in healthy tissue caused (perhaps) by a slight disturbance of cell metabolism. Finally, I will turn to a mathematical analysis of certain CA dynamics and discuss some mathematical tools like discrete Fourier transforms that, as was recently shown by LIN Wei from Fudan U, can be used to treat at least some aspects of these models in proper mathematical terms.

Links

• http://tu-dresden.de/veranstaltungen/termin?id=TUD510ba88351441

Last modified: Feb 28, 2013, 8:55:53 AM