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Author:Kyttä, Klaus
Title:Computational Studies of Pattern Formation in Multiple Layer Turing Systems
Laskennallisia tutkimuksia kuvionmuodostuksesta monikerroksisissa Turing-systeemeissä
Publication type:Master's thesis
Publication year:2007
Pages:ix + 74 s. + liitt. 4      Language:   eng
Department/School:Sähkö- ja tietoliikennetekniikan osasto
Main subject:Laskennallinen tekniikka   (S-114)
Supervisor:Kaski, Kimmo
Instructor:Barrio, Rafael
Electronic version URL: http://urn.fi/urn:nbn:fi:tkk-007645
OEVS:
Electronic archive copy is available via Aalto Thesis Database.
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Location:P1 Ark S80     | Archive
Keywords:Turing system
reaction-diffusion
pattern formation
Turingin systeemi
reaktio-diffuusioyhtälö
kuvionmuodostus
Abstract (eng):This thesis concerns mainly on reaction-diffusion systems, of the kind proposed by a British mathematician Alan Turing in 1950's.
During the past two decades a lot of papers have been published dealing with Turing patterns.
Partly that is because todays' computers make possible to solve those equations accurately in reasonable time but on the other hand the recent findings have also speeded up the research work.

In this thesis we present Turing systems in general and show results of coupled systems.
From the pattern formation point of view people have studied Turing systems for a long time but only recently there has been growing interest in the interaction of many systems.
Usually the coupling has been linear, but we extend the study to non-linear coupling and find out what that brings into the scene.
To our knowledge this has not been studied earlier in spite of the intriguing applications it may offer.

Our motivation for studying these systems is both biological and technical.
For possible applications one can mention calcium waves of cardiac cells and electric impulses in neurons.
So far very few real Turing base models have been introduced due to their complexity but a few simple situations can be modeled already.
Abstract (fin):Tämä diplomityö käsittelee brittiläisen matemaatikon Alan Turingin ehdottamia Turingin systeemeiksi kutsuttuja reaktio-diffuusio systeemejä.
Kahden viime vuosikymmenen aikana on julkaistu paljon Turingin kuvioita käsitteleviä tutkimuksia.
Osittain tämä johtuu siitä, että nykyiset tietokoneet mahdollistavat näiden numeerisen käsittelyn, mutta toisaalta myös viimeaikaiset löydöt ovat osaltaan vauhdittaneet tutkimusta.

Tässä diplomityössä käsitellään Turing systeemejä ja esitetään tuloksia kerroksellisista systeemeistä.
Kuvionmuodostuksen kannalta Turingin systeemejä on tutkittu jo pitkään, mutta vasta viime aikoina on ryhdytty tutkimaan useamman systeemin välistä vuorovaikutusta.
Useinmiten kytkentä on suoritettu lineaarisesti, mutta tässä työssä tutkitaan epälineaarisen kytkennän tuomia mahdollisuuksia, mitä ei ole aiemmin numeerisesti tutkittu huolimatta sen tarjoamista mielenkiintoisista sovelluskohteista.

Motivaatiomme näiden systeemien tutkimiselle on sekä biologinen että tekninen.
Sovelluskohteista voidaan mainita sydänsolujen kalsiumaallot ja impulssien eteneminen hermosoluissa.
Toistaiseksi todellisten mallien luominen on osoittautunut liian haasteelliseksi, mutta joitain yksinkertaisia tilanteita on jo pystytty simuloimaan.
ED:2007-01-05
INSSI record number: 33093
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