scholarly journals Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System

2019 ◽  
Vol 18 (3) ◽  
pp. 1334-1390 ◽  
Author(s):  
Frédéric Paquin-Lefebvre ◽  
Wayne Nagata ◽  
Michael J. Ward
Keyword(s):  
Pattern Formation ◽  
Surface Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Two Dimensional ◽  
Oscillatory Dynamics ◽  
Bulk Surface

scholarly journals A bulk-surface reaction-diffusion system for cell polarization

2020 ◽  
Vol 22 (1) ◽  
pp. 85-117
Author(s):  
Barbara Niethammer ◽  
Matthias Röger ◽  
Juan Velázquez
Keyword(s):  
Surface Reaction ◽  
Reaction Diffusion ◽  
Cell Polarization ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Bulk Surface

scholarly journals Stability analysis and simulations of coupled bulk-surface reaction–diffusion systems

2015 ◽  
Vol 471 (2175) ◽  
pp. 20140546 ◽  
Author(s):  
Anotida Madzvamuse ◽  
Andy H. W. Chung ◽  
Chandrasekhar Venkataraman
Keyword(s):  
Surface Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Reaction Diffusion Equations ◽  
Diffusion System ◽  
Diffusion Equations ◽  
Surface Dynamics ◽  
Bulk Reaction ◽  
Bulk Surface ◽  
Type Boundary

In this article, we formulate new models for coupled systems of bulk-surface reaction–diffusion equations on stationary volumes. The bulk reaction–diffusion equations are coupled to the surface reaction–diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction–diffusion system can induce patterning on the surface independent of whether the surface reaction–diffusion system produces or not, patterning. On the other hand, the surface reaction–diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction–diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.

Programmable reactions and diffusion using DNA for pattern formation in hydrogel medium

2019 ◽  
Vol 4 (3) ◽  
pp. 639-643 ◽  
Author(s):  
Keita Abe ◽  
Ibuki Kawamata ◽  
Shin-ichiro M. Nomura ◽  
Satoshi Murata
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
And Diffusion

We demonstrate a method of pattern formation based on an artificial reaction diffusion system in hydrogel medium.

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