Propagation and kinetic roughening of wave fronts in disordered lattices
Loading...
Access rights
© 1997 American Physical Society (APS). This is the accepted version of the following article: Åström, Jan & Kellomäki, Markku & Alava, Mikko J. & Timonen, Jussi. 1997. Propagation and kinetic roughening of wave fronts in disordered lattices. Physical Review E. Volume 56, Issue 5. 6042-6049. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.56.6042, which has been published in final form at http://journals.aps.org/pre/abstract/10.1103/PhysRevE.56.6042.
URL
Journal Title
Journal ISSN
Volume Title
School of Science |
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.
Date
1997
Major/Subject
Mcode
Degree programme
Language
en
Pages
6042-6049
Series
Physical Review E, Volume 56, Issue 5
Abstract
The dynamics of a wave front propagating in diluted square lattices of elastic beams is analyzed. We concentrate on the propagation of the first maximum of a semi-infinite wave train. Two different limits are found for the velocity depending on the bending stiffness of the beams. If it vanishes, a one-dimensional chain model is derived for the velocity and the amplitude is found to decrease exponentially. The first maximum is localized and the average width of the wave front is always finite. For very stiff beams an effective-medium model gives the correct velocity and the amplitude of the first maximum decays according to a power law. No localization of the first maximum is observed in the simulations. In this limit scaling arguments based on Huygen’s principle suggest a growth exponent of 1/2, and a roughness exponent of 2/3. The growth exponent fits the simulation data well, but a considerably lower roughness exponent (0.5) is obtained. There is a crossover region for the bending stiffness, wherein the wave-front behavior cannot be explained by these limiting cases.Description
Keywords
dynamics of a wave front propagating, diluted square lattices, elastic beams
Other note
Citation
Åström, Jan & Kellomäki, Markku & Alava, Mikko J. & Timonen, Jussi. 1997. Propagation and kinetic roughening of wave fronts in disordered lattices. Physical Review E. Volume 56, Issue 5. 6042-6049. ISSN 1539-3755 (printed). DOI: 10.1103/physreve.56.6042.