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Origins of scale invariance in growth processes
Open accessAbstract
This review describes recent progress in the understanding of the emergence of scale invariance in far-from-equilibrium growth. The first section is devoted to ‘solvable’ needle models which illustrate the relationship between long-range competition mediated, for example, through shadowing or a Laplacian field, and scale invariance. The following three sections, which comprise the bulk of the article, develop the theory of kinetic surface roughening in a comprehensive manner. The two large classes of kinetic roughening processes, characterized by non-conserved (Kardar-Parisi-Zhang) and conserved (ideal molecular beam epitaxy (MBE)) surface relaxation, respectively, are treated separately. For the former case, which has been extensively reviewed elsewhere, the focus is on recent developments. For the case of ideal MBE we give a systematic derivation of the various universality classes in terms of microscopic processes, and compare the predictions of continuum theory to computer simulations and experiments.
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Citations
Cites
Fractal Concepts in Surface Growth
Barabási, A. L., & Stanley, H. E. (1995) · doi:10.1017/cbo9780511599798 · Cited by 3,925
Cited by
Universality classes in nonequilibrium lattice systems
Ódor, G. (2004) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.663 · Cited by 835
One-Dimensional Kardar-Parisi-Zhang Equation: An Exact Solution and its Universality
Sasamoto, T., & Spohn, H. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.230602 · Cited by 451
Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate
Fontaine, Q., Squizzato, D., Baboux, F., Amelio, I., Lemaître, A., Morassi, M., Sagnes, I., Le Gratiet, L., Harouri, A., Wouters, M., et al. (2022) · Nature · doi:10.1038/s41586-022-05001-8 · Cited by 119
A network model of channel competition in fracture dissolution
Szymczak, P., & Ladd, A. J. C. (2006) · Geophysical Research Letters · doi:10.1029/2005gl025334 · Cited by 75
Metadata
- Authors
- Krug, J.
- Venue
- Advances in Physics
- Publisher
- Informa UK Limited
- Published
- 1997-04
- Volume
- 46
- Issue
- 2
- Pages
- 139-282
- ISSN
- 0001-8732 (ISSN-L)
- 1460-6976
- OpenAlex
- W2066116321
- Cited by
- 1,016
- References
- 1
- FWCI
- 33.50
- Type
- journal article
- Language
- en
- Open access
- green
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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