On the stochastic correlations in a randomly perturbed chemical front

External Fluctuations in Front Propagation

“…The case with the most direct comparison with the present work [9] found no change in the front velocity. On the other hand, previous analytical approaches for external fluctuations [13,14] have been based on small noise perturbative expansions which turn out to have a rather small range of validity for our purposes.Here we will introduce a new approach which relies on a physically intuitive picture of the problem but which is nonperturbative. As the accompanying numerical simulations will show, our theoretical approach gives an accurate quantitative description for a very broad range of noise intensities and allows for a general discussion of selection criteria in the presence of external fluctuations.…”

“…The case with the most direct comparison with the present work [9] found no change in the front velocity. On the other hand, previous analytical approaches for external fluctuations [13,14] have been based on small noise perturbative expansions which turn out to have a rather small range of validity for our purposes.…”

“…Here we will focus on the simplest case in which a globally stable state invades an unstable or metastable state. This problem has been extensively studied in the recent literature [2][3][4][5][6][7][8] particularly concerning the issue of velocity selection.On the other hand, in the last few years there has been a growing interest in the theoretical study of the role of fluctuations in front propagation [7,[9][10][11][12][13][14], and in particular there have been some experiments on the effects of stochastic turbulence in front propagation in the context of chemical fronts [15]. These studies have been basically concerned with the modification of the front velocity and the spreading of the front due to fluctuations.…”

“…On the other hand, in the last few years there has been a growing interest in the theoretical study of the role of fluctuations in front propagation [7,[9][10][11][12][13][14], and in particular there have been some experiments on the effects of stochastic turbulence in front propagation in the context of chemical fronts [15]. These studies have been basically concerned with the modification of the front velocity and the spreading of the front due to fluctuations.…”

“…Internal [9][10][11][12] and external [13,14] fluctuations have been introduced in particular models using both Langevin [9,11,13,14] and master equation formalisms [10,12], but no systematic studies have been carried out concerning the modification of the well established selection criteria of the deterministic case. For internal fluctuations mostly numerical studies of different situations have obtained distinct effects on the front propagation.…”