Breakdown of the standard perturbation theory and moving boundary approximation for "pulled" fronts

被引:32
作者
Ebert, U
van Saarloos, W
机构
[1] Ctr Wiskunde & Informat, NL-1090 GB Amsterdam, Netherlands
[2] Leiden Univ, Inst Lorentz, NL-2300 RA Leiden, Netherlands
来源
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS | 2000年 / 337卷 / 1-2期
关键词
D O I
10.1016/S0370-1573(00)00059-4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A moving boundary approximation or similar perturbative schemes for the response of a coherent structure like a front, vortex or pulse to external forces and noise can generally be derived if two conditions are obeyed: (i) there must be a separation of the time scales of the dynamics on the inner and outer scale, and (ii) solvability-type integrals must converge. We point out that both of these conditions are not satisfied for pulled fronts propagating into an unstable state: their relaxation on the inner scale is algebraic rather than exponential, and in conjunction with this, solvability integrals diverge. This behavior can be explained by the fact that the important dynamics of pulled fronts occurs in the leading edge of the front rather than in the nonlinear internal front region itself. As a consequence, the dynamical behavior of pulled fronts is often qualitatively different from the standard case in which fronts between two (meta)stable states are considered, as has recently been established for the relaxation, the stochastic behavior and the response to multiplicative noise. We here show that this is also true for the coupling of pulled fronts to other fields. (C) 2000 Elsevier Science B.V. All rights reserved.
引用
收藏
页码:139 / 156
页数:18
相关论文
共 78 条
[61]   PATTERN SELECTION AND SPATIOTEMPORAL TRANSITION TO CHAOS IN THE GINZBURG-LANDAU EQUATION [J].
NOZAKI, K ;
BEKKI, N .
PHYSICAL REVIEW LETTERS, 1983, 51 (24) :2171-2174
[62]   STRUCTURAL STABILITY AND RENORMALIZATION-GROUP FOR PROPAGATING FRONTS [J].
PAQUETTE, GC ;
CHEN, LY ;
GOLDENFELD, N ;
OONO, Y .
PHYSICAL REVIEW LETTERS, 1994, 72 (01) :76-79
[63]  
POMEAU Y, 1992, SOLIDS FAR EQUILIBRI
[64]   Pearling and pinching: Propagation of Rayleigh instabilities [J].
Powers, TR ;
Goldstein, RE .
PHYSICAL REVIEW LETTERS, 1997, 78 (13) :2555-2558
[65]  
ROCCO A, IN PRESS PHYS REV E
[66]   ON THE KINETICS OF PARTIALLY CONSERVED ORDER PARAMETERS - A POSSIBLE MECHANISM FOR PATTERN-FORMATION [J].
SALJE, EKH .
JOURNAL OF PHYSICS-CONDENSED MATTER, 1993, 5 (27) :4775-4784
[67]   2 TYPES OF MOVING FRONT IN QUASILINEAR DIFFUSION [J].
STOKES, AN .
MATHEMATICAL BIOSCIENCES, 1976, 31 (3-4) :307-315
[68]  
STORM C, IN PRESS PHYS REV E
[69]   ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS [J].
TORCINI, A ;
GRASSBERGER, P ;
POLITI, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (16) :4533-4541
[70]   Vortex dynamics in dissipative systems [J].
Tornkvist, O ;
Schroder, E .
PHYSICAL REVIEW LETTERS, 1997, 78 (10) :1908-1911