scholarly journals Fluctuation-induced chiral symmetry breaking in autocatalytic reaction-diffusion systems

2007 ◽  
Vol 80 (2) ◽  
pp. 28001 ◽  
Author(s):  
V. S. Gayathri ◽  
M. Rao
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Chiral Symmetry Breaking ◽  
Reaction Diffusion ◽  
Autocatalytic Reaction ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems

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.

Energy Threshold for Chiral Symmetry Breaking in Molecular Self-Replication

2019 ◽  
Author(s):  
Neil Hawbaker ◽  
Donna Blackmond
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Parity Violation ◽  
Chiral Symmetry Breaking ◽  
Energy Difference ◽  
Autocatalytic Reaction ◽  
Energy Threshold ◽  
Chiral Amplification ◽  
Self Replication

We have determined the energy required for symmetry breaking and chiral amplification in the Soai autocatalytic reaction. This work examines the likelihood that parity violation energy difference of enantiomers is implicated in the origin of chiral symmetry breaking and highlights the challenges inherent in a search for a prebiotically plausible version of Soai autocatalysis.

scholarly journals From one pattern into another: analysis of Turing patterns in heterogeneous domains via WKBJ

2020 ◽  
Vol 17 (162) ◽  
pp. 20190621 ◽  
Author(s):  
Andrew L. Krause ◽  
Václav Klika ◽  
Thomas E. Woolley ◽  
Eamonn A. Gaffney
Keyword(s):  
Symmetry Breaking ◽  
Heterogeneous Media ◽  
Heterogeneous Reaction ◽  
Reaction Diffusion ◽  
Spatial Patterning ◽  
Instability Mechanism ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Turing Instabilities ◽  
Pattern Forming

Pattern formation from homogeneity is well studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is non-trivial to separate observed spatial patterning due to inherent spatial heterogeneity from emergent patterning due to nonlinear instability. We employ WKBJ asymptotics to investigate Turing instabilities for a spatially heterogeneous reaction–diffusion system, and derive conditions for instability which are local versions of the classical Turing conditions. We find that the structure of unstable modes differs substantially from the typical trigonometric functions seen in the spatially homogeneous setting. Modes of different growth rates are localized to different spatial regions. This localization helps explain common amplitude modulations observed in simulations of Turing systems in heterogeneous settings. We numerically demonstrate this theory, giving an illustrative example of the emergent instabilities and the striking complexity arising from spatially heterogeneous reaction–diffusion systems. Our results give insight both into systems driven by exogenous heterogeneity, as well as successive pattern forming processes, noting that most scenarios in biology do not involve symmetry breaking from homogeneity, but instead consist of sequential evolutions of heterogeneous states. The instability mechanism reported here precisely captures such evolution, and extends Turing’s original thesis to a far wider and more realistic class of systems.

EXAMPLES OF FORCED SYMMETRY-BREAKING TO HETEROCLINIC CYCLES AND NETWORKS IN THREE-DIMENSIONAL EUCLIDEAN-INVARIANT SYSTEMS

2009 ◽  
Vol 19 (05) ◽  
pp. 1655-1678
Author(s):  
M. J. PARKER ◽  
M. G. M. GOMES ◽  
I. N. STEWART
Keyword(s):  
Symmetry Breaking ◽  
Nonlinear Optical ◽  
Three Dimensional ◽  
Reaction Diffusion ◽  
Three Dimensions ◽  
Optical Systems ◽  
Heteroclinic Cycles ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Face Centered

In [Parker et al., 2008a] group theory was employed to prove the existence of homoclinic cycles in forced symmetry-breaking of simple (SC), face-centered (FCC), and body-centered (BCC) cubic planforms. In this paper we extend this classification demonstrating that more elaborate heteroclinic cycles and networks can arise through the same process. Our methods naturally generate graphs that represent possible heteroclinic cycles and networks. The results do not depend on the representation of the symmetry group and are thus quite general. This study is motivated by pattern formation in three dimensions which occur in reaction–diffusion systems, certain nonlinear optical systems and the polyacrylamide methylene blue oxygen reaction. This work extends previous work by Parker et al. [2006, 2008a, 2008b] and Hou and Golubitsky [1997].

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