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Phys. Rev. E 62, R13–R16 (2000)

Subdiffusive fluctuations of “pulled” fronts with multiplicative noise

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Andrea Rocco1, Ute Ebert2, and Wim van Saarloos3
1Departament ECM, Facultat de Física, Universitat de Barcelona, Avenida Diagonal 647, E-08028 Barcelona, Spain
2Centrum voor Wiskunde en Informatica, Postbus 94079, 1090 GB Amsterdam, The Netherlands
3Instituut-Lorentz, Universiteit Leiden, Postbus 9506, 2300 RA Leiden, The Netherlands

Received 6 April 2000; published in the issue dated July 2000

We study the propagation of a “pulled” front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large t creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering Δ(t)∼t1/4, not t1/2. The subdiffusive behavior is confirmed by numerical simulations: For t<~600, these yield an effective exponent slightly larger than 1/4.

© 2000 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevE.62.R13
DOI:
10.1103/PhysRevE.62.R13
PACS:
05.40.-a, 47.54.+r
 
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