scholarly journals A Synthetic Replicator Drives a Propagating Reaction–Diffusion Front

2016 ◽  
Vol 138 (21) ◽  
pp. 6723-6726 ◽  
Author(s):  
Ilaria Bottero ◽  
Jürgen Huck ◽  
Tamara Kosikova ◽  
Douglas Philp
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front

scholarly journals Dynamic multiscaling of the reaction-diffusion front formA+nB→0

1995 ◽  
Vol 52 (4) ◽  
pp. 3500-3505 ◽  
Author(s):  
Stephen Cornell ◽  
Zbigniew Koza ◽  
Michel Droz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front

scholarly journals Pointwise stability of reaction diffusion fronts

2019 ◽  
Vol 150 (5) ◽  
pp. 2216-2254
Author(s):  
Yingwei Li
Keyword(s):  
Spectral Decomposition ◽  
Exponential Convergence ◽  
Reaction Diffusion ◽  
Spatial Diffusion ◽  
Diffusion Front ◽  
Function Decomposition ◽  
Viscous Shock Waves ◽  
New Feature ◽  
Rates Of Decay ◽  
Short Time

AbstractUsing pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential convergence in weighted Lp and Sobolev norms, while capturing the new feature of spatial diffusion at Gaussian rate. Novel features of the argument are a pointwise Green function decomposition reconciling spectral decomposition and short-time Nash-Aronson estimates and an instantaneous tracking scheme similar to that used in the study of stability of viscous shock waves.

scholarly journals Coarsening of precipitation patterns in a moving reaction-diffusion front

2009 ◽  
Vol 80 (5) ◽  
Author(s):  
A. Volford ◽  
I. Lagzi ◽  
F. Molnár ◽  
Z. Rácz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front ◽  
Precipitation Patterns

The development of travelling waves in a simple isothermal chemical system II. Cubic autocatalysis with quadratic and linear decay

1990 ◽  
Vol 430 (1879) ◽  
pp. 315-345 ◽  
Keyword(s):  
Numerical Solutions ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Travelling Wave ◽  
Chemical System ◽  
Necessary Condition ◽  
Travelling Wave Solution ◽  
Diffusion Front ◽  
Initial Value ◽  
Linear Decay

The possibility of travelling reaction-diffusion waves developing in the isothermal chemical system governed by the cubic autocatalytic reaction A + 2B → 3B (rate k 3 ab 2 ) coupled with either the linear decay step B → C (rate k 2 b ) or the quadratic decay step B + B → C (rate k 4 b 2 ) is examined. Two simple solutions are obtained,namely the well-stirred analogue of the spatially inhomogeneous problem and the solution for small input of the autocatalyst B. Both of these suggest that, for the quadratic decay case, a wave will develop only if the non-dimensional parameter k ═ k 4 / k 3 a 0 < 1 (where a 0 is the initial concentration of the reactant A), with there being no restriction on the initial input of the autocatalyst B. However, for the linear decay case the initiation of a travelling wave depends on the parameter v ═ k 2 / k 3 a 2 0 and that, in addition, there is an input threshold on B before the formation of a wave will occur. The equations governing the fully developed travelling waves are then considered and it is shown that for the quadratic decay case the situation is similar to previous work in quadratic autocatalysis with linear decay, with a necessary condition for the existence of a travelling-wave solution being that K < 1. However, the case of linear decay is quite different, with a necessary condition for the existence of a travelling wave solution now found to be v < 1/4 Numerical solutions of the equations governing this case reveal further that a solution exists only for v < v c , with v c ≈ 0.0465, and that there are two branches of solution for 0 < v < v c . The behaviour of these lower branch solutions as v → 0 is discussed. The initial-value problem is then considered. For the quadratic decay case it is shown that the uniform state a ═ a 0 , b ═ 0 is globally asymptotically stable (i. e. a → a 0 , b → 0 uniformly for large times) for all k > 1. For the linear decay case it is shown that the development of a travelling wave requires β 0 > v (where β 0 is a measure of the initial input of B) for v < v c . These theoretical results are then complemented by numerical solutions of the initial-value problem for both cases, which confirm the various predictions of the theory. The behaviour of the solution of the equations governing the travelling waves is then discussed in the limits K → 0, v → 0 and K → 1. In the first case the solution approaches the solution for K ═ 0 (or v =0) on the length scale of the reaction-diffusion front, with there being a long tail region of length scale O ( K -1 ) (or O ( v -1 )) in which the autocatalyst B decays to zero. In the latter case we find that the concentration of reactant A is 1 + O [(1 - k )] and autocatalyst B is O[(1 - k 2 ] with the thickness of the reaction-diffusion front becoming large, of thickness O [(1- k ) -3/2 ].

scholarly journals Localization-delocalization transition of a reaction-diffusion front near a semipermeable wall

1997 ◽  
Vol 56 (5) ◽  
pp. 5343-5350 ◽  
Author(s):  
Bastien Chopard ◽  
Michel Droz ◽  
Jéro⁁me Magnin ◽  
Zoltán Rácz
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front

Dynamical localization-delocalization transition of the reaction-diffusion front at a semipermeable cellulose membrane

2007 ◽  
Vol 75 (2) ◽  
Author(s):  
Sung Hyun Park ◽  
Hailin Peng ◽  
Raoul Kopelman ◽  
Haim Taitelbaum
Keyword(s):  
Reaction Diffusion ◽  
Dynamical Localization ◽  
Cellulose Membrane ◽  
Diffusion Front

Influence of base additives on the reaction-diffusion front of model chemically amplified photoresists

2007 ◽  
Vol 25 (1) ◽  
pp. 175 ◽  
Author(s):  
Bryan D. Vogt ◽  
Shuhui Kang ◽  
Vivek M. Prabhu ◽  
Ashwin Rao ◽  
Eric K. Lin ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front ◽  
Chemically Amplified

scholarly journals Fluctuation effects and multiscaling of the reaction-diffusion front for A+B to OE

1995 ◽  
Vol 28 (13) ◽  
pp. 3599-3621 ◽  
Author(s):  
M Howard ◽  
J Cardy
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Front ◽  
Fluctuation Effects

Asymptotic properties of the A + B → 0 reaction diffusion front

1998 ◽  
Vol 77 (5) ◽  
pp. 1437-1440
Author(s):  
Zbigniew Koza
Keyword(s):  
Asymptotic Properties ◽  
Reaction Diffusion ◽  
Diffusion Front
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