Effect of a columnar defect on the shape of slow-combustion fronts

Abstract

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough excess driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a non-zero excess driving in agreement with the simulated behavior of the ASEP model.

Correlation Functions and Queuing Phenomena in Growth Processes with Drift

“…This asymmetric behavior of C(r) and G(r) is a unique behavior for the drifted EW equation with a perfect defect. In contrast the height-height correlation function around a defect for KPZ-type surface growth [14] always shows the lateral symmetry C(r) = C(−r). In KPZ-type surface growth model with the defect [14], the height-height correlation function C(r, p) changes from C(r, p) ∼ A|r| + B|r|…”

“…It is well established that many driven flow processes belong to the same universality class as Kardar-ParisiZhang (KPZ) type growth of one dimensional interfaces [7,13]. For example, a traffic jam [14] caused by slow and fast bond of the so-called asymmetric simple exclusion process (ASEP) [15] is related to the faceting on KPZ growth. ASEP breaks translational invariance in many ways.…”

“…ASEP breaks translational invariance in many ways. One of them is to retain periodic boundary conditions, but to introduce a defect into the system by modifying the transition rates locally [14,16]. By properly chosen injection/removal rates or defect strength, nonequilibrium phase transitions occur between profiles of different shapes and average densities.…”

“…Therefore it is very interesting to compare our new queuing phenomena to earlier studied KPZ type queuing phenomena. In this paper, we want to investigate new queuing phenomena from the defect and the drift using our stochastic discrete model and apply it to the parking garage model [14].…”

A KPZ Cocktail-Shaken, not Stirred...

“…A separate, critical paper by Prähofer and Spohn [57] introduced the notion of the Airy process, bringing spatial correlations into the RMT context, and tightening ties between KPZ physics and TW mathematical communities. During this period, flameless Finnish firefronts continued to burn [58,59,60], mode-coupling [61] and nonperturbative [62,63] approaches developed further, and a suggestive Dutch chemical vapor deposition experiment appeared [64], providing evidence of an asymmetric 2+1 KPZ height fluctuation PDF. For a recent example of the nice interplay of KPZ/DPRM statistical physics and TW/BR mathematics, as well as a brief account of the foundational Ulam-LIS numerics of Baer and Brock, see [65]; note, too- [66,67].…”