Propagation and kinetic roughening of wave fronts in disordered lattices

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© 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.

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Journal Title

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Volume Title

School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

1997

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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.

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Keywords

dynamics of a wave front propagating, diluted square lattices, elastic beams

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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.