scholarly journals Pattern formation mechanisms of self-organizing reaction-diffusion systems

2020 ◽  
Vol 460 (1) ◽  
pp. 2-11 ◽  
Author(s):  
Amit N. Landge ◽  
Benjamin M. Jordan ◽  
Xavier Diego ◽  
Patrick Müller
2021 ◽  
Vol 7 (16) ◽  
pp. eabe3801
Author(s):  
Amanda J. Ackroyd ◽  
Gábor Holló ◽  
Haridas Mundoor ◽  
Honghu Zhang ◽  
Oleg Gang ◽  
...  

Chemical organization in reaction-diffusion systems offers a strategy for the generation of materials with ordered morphologies and structural hierarchy. Periodic structures are formed by either molecules or nanoparticles. On the premise of new directing factors and materials, an emerging frontier is the design of systems in which the precipitation partners are nanoparticles and molecules. We show that solvent evaporation from a suspension of cellulose nanocrystals (CNCs) and l-(+)-tartaric acid [l-(+)-TA] causes phase separation and precipitation, which, being coupled with a reaction/diffusion, results in rhythmic alternation of CNC-rich and l-(+)-TA–rich rings. The CNC-rich regions have a cholesteric structure, while the l-(+)-TA–rich bands are formed by radially aligned elongated bundles. The moving edge of the pattern propagates with a finite constant velocity, which enables control of periodicity by varying film preparation conditions. This work expands knowledge about self-organizing reaction-diffusion systems and offers a strategy for the design of self-organizing materials.


Author(s):  
Houye Liu ◽  
Weiming Wang

Amplitude equation may be used to study pattern formatio. In this chapter, we establish a new mechanical algorithm AE_Hopf for calculating the amplitude equation near Hopf bifurcation based on the method of normal form approach in Maple. The normal form approach needs a large number of variables and intricate calculations. As a result, deriving the amplitude equation from diffusion-reaction is a difficult task. Making use of our mechanical algorithm, we derived the amplitude equations from several biology and physics models. The results indicate that the algorithm is easy to apply and effective. This algorithm may be useful for learning the dynamics of pattern formation of reaction-diffusion systems in future studies.


Sign in / Sign up

Export Citation Format

Share Document