Cellular automaton models for time-correlated random walks: derivation and analysis

Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This...

Full description

Saved in:
Bibliographic Details
Published in:Scientific reports 2017-12, Vol.7 (1), p.16952-13, Article 16952
Main Authors: Nava-Sedeño, J. M., Hatzikirou, H., Klages, R., Deutsch, A.
Format: Article
Language:English
Subjects:
631/114/2397
639/705/1041
Brownian motion
Cell adhesion & migration
Cell migration
Cell Movement
Computer applications
Data processing
Decay
Diffusion
Humanities and Social Sciences
Models, Biological
multidisciplinary
Phase transitions
Probability
Random Allocation
Science
Science (multidisciplinary)
Time Factors
Velocity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is “data-driven”. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-017-17317-x