Velocity of front propagation in 1-dimensional autocatalytic reactions

Abstract

2A in one dimension. Looking at the dynamics of propagation, we find that in the low-concentration limit the average velocity of propagation approaches v = theta/2, where theta is the concentration, and, in the high concentration limit, we nd the velocity approaches v = 1 - e-theta/2.]]>

Effects of fluctuations on propagating fronts

“…However, in the actual lattice model for N → 0, this is not the case: dimensional arguments, confirmed by simulation shows that v N ∝ DN, while the front diffusion coefficient D f is ∝ D, with proportionality constants of O(1) [71]. In a discrete-time equivalent of this model, where time is measured in discrete units of D (thereby rendering D = 1) and the system is parallelly updated, the front speed has been shown to behave as [118,119] v…”

“…As N is reduced "too much", the fluctuations in the number of particles per lattice site in the stable state become stronger and stronger. Perhaps in view of II above, in the sense that due to the lack of first-principle based predictive theory for finite-N corrections, works on such values of N are somewhat rare [71,118,119]. The extreme limit of this, namely the case when there is at most one particle is allowed per lattice site, however, is very well studied (we will refer to this scenario as "N ≤ 1").…”

Asymptotic front behavior in anA+B→2Areaction under subdiffusion

“…(8) by assuming the width of atomically sharp front to correspond to the interparticle distance, w ≃ l = c −1 . Repeating the same crossover arguments, as in the previous case, this kind of behavior under normal diffusion is mirrored onto the form v(t) ∝ t α−1 (9) for the velocity time dependence in the subdiffusive case.…”

“…Since the subdiffusive front is slowing down and becoming steeper in the course of time, any system will sooner or later enter a regime already discussed in [4] for subdiffusion and in [6,7] for normal diffusion. This regime is a fluctuation dominated one and is no longer Under such a condition the velocity of the front's motion can be estimated using the following argument (adapted from [9,10] for our sequential updating scheme). Let us consider the front position as fixed by the rightmost A-particle(s), and concentrate on the next jump of the front particle.…”

Disorder and Self-Organization on Surfaces

“…considered small concentration and large reaction rate. In [Warren 20001 we studied a version of A+B-+2A in this regime in one dimension, and we managed to solve the problem exactly. By studying our solution, we are able to see that the small velocity is a giantfluctuation effect which goes qualitatively as follows.…”