eprintid: 7168
rev_number: 9
eprint_status: archive
userid: 1
dir: disk0/00/00/71/68
datestamp: 2007-02-06 13:45:25
lastmod: 2015-04-22 05:51:47
status_changed: 2012-08-14 15:20:52
type: preprint
metadata_visibility: show
creators_name: Mommer, Mario S.
creators_name: Lebiedz, Dirk
title: Modeling Subdiffusion Using Reaction Diffusion Systems
ispublished: pub
subjects: ddc-510
divisions: i-708000
cterms_swd: Anomale Diffusion
cterms_swd: Diffusion
cterms_swd: Modellierung
abstract:   In many types of media, and in particular within living cells or   within their membranes, diffusing species do not follow Fick's laws,   but instead show transient subdiffusive behavior. Formulating   spatiotemporal models that take this behavior into account is a   delicate matter, as one is faced with the choice of resorting either   to fractional calculus or to microscopic descriptions. In this   article, we provide an alternative designed to be easier to tackle   analytically and numerically than the existing approaches.   Specifically, starting from the Continuous Time Random Walk model,   we construct linear reaction diffusion systems that can be used as   components within such a model, and which capture the defining   properties of subdiffusion. We show how to impose physically   relevant parameters, and prove stability and mass conservation.   While applications to cellular biology are our main motivation, our   approach is abstract, and should thus be applicable to any situation   where anomalous subdiffusion is observed. 
abstract_translated_lang: eng
class_scheme: msc
class_labels: 35K57, 76R50
date: 2007
date_type: published
id_scheme: DOI
id_number: 10.11588/heidok.00007168
portal_cluster_id: p-iwrpp
portal_order: 07168
ppn_swb: 1646175530
own_urn: urn:nbn:de:bsz:16-opus-71684
language: eng
bibsort: MOMMERMARIMODELINGSU2007
full_text_status: public
series: IWR-Preprints
citation:   Mommer, Mario S. ; Lebiedz, Dirk  (2007) Modeling Subdiffusion Using Reaction Diffusion Systems.  [Preprint]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/7168/1/adiff.pdf