eprintid: 35273
rev_number: 14
eprint_status: archive
userid: 8370
dir: disk0/00/03/52/73
datestamp: 2024-08-14 07:36:59
lastmod: 2024-08-20 14:16:36
status_changed: 2024-08-14 07:36:59
type: doctoralThesis
metadata_visibility: show
creators_name: Brazke, Denis
title: Asymptotic Expansion of a Non-local Isoperimetric Energy and Application to Mechanochemical Models related to Pattern Formation in Biological Membranes
subjects: ddc-510
divisions: i-110400
adv_faculty: af-11
abstract: In this thesis, we derive a macroscopic limit for a sharp interface version of a modelproposed by Komura, Shimokawa and Andelman (2006) to investigate pattern formationdue to competition of chemical and mechanical forces. The problem is reformulated as anon-local isoperimetric problem, for which we identify sub- and supercritical parameterregimes in terms of the relative strength of the competing local and non-local interactions.Using the Autocorrelation Function, we find an asymptotic expansion of the energyin terms of the length scale parameter up to first order and derive the Γ–limit in thesubcritical regime, and the Γ–limit of the rescaled energy in the critical regime. Concerningthe analysis of the Autocorrelation Function, we show that regularity near the origin isinherited from the regularity of the corresponding set and present formulas for higherderivatives at the origin.
date: 2024
id_scheme: DOI
id_number: 10.11588/heidok.00035273
ppn_swb: 1899204725
own_urn: urn:nbn:de:bsz:16-heidok-352733
date_accepted: 2024-08-09
advisor: HASH(0x55a9a63be280)
language: eng
bibsort: BRAZKEDENIASYMPTOTIC
full_text_status: public
place_of_pub: Heidelberg
citation:   Brazke, Denis  (2024) Asymptotic Expansion of a Non-local Isoperimetric Energy and Application to Mechanochemical Models related to Pattern Formation in Biological Membranes.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/35273/1/thesis_brazke.pdf