scholarly journals Trend to Equilibrium for Reaction-Diffusion Systems Arising from Complex Balanced Chemical Reaction Networks

2017 ◽  
Vol 49 (4) ◽  
pp. 2666-2709 ◽  
Author(s):  
Laurent Desvillettes ◽  
Klemens Fellner ◽  
Bao Quoc Tang
Keyword(s):  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

CHEMICAL PATTERNS IN SIMPLE FLOW SYSTEMS

2003 ◽  
Vol 06 (01) ◽  
pp. 155-162 ◽  
Author(s):  
ANNETTE TAYLOR
Keyword(s):  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Stationary Concentration ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Differential Flow ◽  
Chemical Waves ◽  
Pattern Forming ◽  
Simple Flow ◽  
Concentration Patterns

The addition of flow to chemical reaction-diffusion systems provides robust pattern-forming mechanisms which are expected to occur in a wide variety of natural and artificial systems. Experiments demonstrating some of these mechanisms are presented here, including the differential-flow-induced chemical instability (DIFICI), which gives rise to traveling chemical waves, and flow-distributed oscillations (FDO), which produce stationary concentration patterns.

Computational Study of Traveling Wave Solutions of Isothermal Chemical Systems

2016 ◽  
Vol 19 (5) ◽  
pp. 1461-1472 ◽  
Author(s):  
Yuanwei Qi ◽  
Yi Zhu
Keyword(s):  
Chemical Reaction ◽  
Traveling Waves ◽  
Flow Reactor ◽  
Computational Study ◽  
Chemical Species ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Autocatalytic Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

AbstractThis article studies propagating traveling waves in a class of reaction-diffusion systems which model isothermal autocatalytic chemical reactions as well as microbial growth and competition in a flow reactor. In the context of isothermal autocatalytic systems, two different cases will be studied. The first is autocatalytic chemical reaction of order m without decay. The second is chemical reaction of order m with a decay of order n, where m and n are positive integers and m>n≥1. A typical system in autocatalysis is A+2B→3B and B→C involving two chemical species, a reactant A and an auto-catalyst B and C an inert chemical species.The numerical computation gives more accurate estimates on minimum speed of traveling waves for autocatalytic reaction without decay, providing useful insight in the study of stability of traveling waves.For autocatalytic reaction of order m = 2 with linear decay n = 1, which has a particular important role in chemical waves, it is shown numerically that there exist multiple traveling waves with 1, 2 and 3 peaks with certain choices of parameters.

scholarly journals ASYMPTOTIC BEHAVIOR IN CHEMICAL REACTION-DIFFUSION SYSTEMS WITH BOUNDARY EQUILIBRIA

2018 ◽  
Vol 8 (3) ◽  
pp. 836-858
Author(s):  
Michel Pierre ◽  
◽  
Takashi Suzuki ◽  
Haruki Umakoshi ◽  
◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

scholarly journals Programmable patterns in a DNA-based reaction–diffusion system

Soft Matter ◽  
2020 ◽  
Vol 16 (14) ◽  
pp. 3555-3563 ◽  
Author(s):  
Sifang Chen ◽  
Georg Seelig
Keyword(s):  
Chemical Reaction ◽  
In Silico ◽  
Reaction Diffusion ◽  
Chemical Reaction Networks ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reaction Networks ◽  
System P

We report programmable reaction–diffusion patterns in DNA-based hydrogels, simulated and designed in silico using chemical reaction networks.

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