The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc.
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Avalanche Dynamics in Driven Systems: From Plastic Deformation to Fluid Invasion

Lasse Laurson

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Information and Natural Sciences for public examination and debate in Auditorium N at Helsinki University of Technology (Espoo, Finland) on the 30th of September, 2008, at 13 o'clock.

Overview in PDF format (ISBN 978-951-22-9537-1)   [1633 KB]
Dissertation is also available in print (ISBN 978-951-22-9536-4)

Abstract

A large class of interacting systems in Nature respond to externally applied driving in an intermittent and heterogeneous manner. Typically, the statistics of sizes of the observed bursts of activity, or avalanches, can be described by scale free power law distributions. Also the temporal correlations associated to such an activity time series are of interest, and can be studied by computing the power spectrum of the time series. This power spectrum typically scales as a power law of the frequency, 1⁄fα, thus constituting an example of 1⁄f noise, a phenomenon ubiquitous in Nature.

In this thesis a number of simplified model systems exhibiting such phenomenology are studied, both analytically and by computer simulations. In particular, a relation between the avalanche and noise descriptions of the intermittent activity, originally proposed in the context of Barkhausen noise, is shown to apply more generally to systems with avalanche dynamics. This has important implications especially in the context of sandpile models of self-organized criticality, as it allows to demonstrate how such models can exhibit non-trivial scaling of the power spectra, contrary to earlier claims. The general nature of this relation is further emphasized by showing that it applies also in the apparently very different context of a propagating fluid front when a fluid invades porous media as a sequence of avalanches, as well as for avalanches of plastic deformation activity in a simple two dimensional discrete dislocation dynamics model.

For the dislocation model, also other issues such as correlations between different avalanches and history dependent response to externally applied stresses are studied. An effort is made to understand the role of grain boundaries to the propagation of dislocation avalanches in plastically deforming polycrystals, by studying the screening effect arising from the deformation of a simplified grain boundary in the stress field of a single edge dislocation. Finally, a simple random walk-based model mimicking a dislocation interacting with a cloud of diffusing solute atoms in metallic alloys is studied. Such a system is shown to exhibit fluctuations characterized by power-law distributions with a cut-off.

This thesis consists of an overview and of the following 6 publications:

  1. Lasse Laurson, Mikko J. Alava, and Stefano Zapperi. 2005. Power spectra of self-organized critical sandpiles. Journal of Statistical Mechanics: Theory and Experiment, L11001, 8 pages. © 2005 Institute of Physics Publishing. By permission.
  2. Martin Rost, Lasse Laurson, Martin Dubé, and Mikko Alava. 2007. Fluctuations in fluid invasion into disordered media. Physical Review Letters, volume 98, 054502, 4 pages. © 2007 American Physical Society. By permission.
  3. L. Laurson and M. J. Alava. 2006. 1⁄f noise and avalanche scaling in plastic deformation. Physical Review E, volume 74, 066106, 5 pages. © 2006 American Physical Society. By permission.
  4. M.-Carmen Miguel, L. Laurson, and M. J. Alava. 2008. Material yielding and irreversible deformation mediated by dislocation motion. The European Physical Journal B, volume 64, pages 443-450.
  5. Paolo Moretti, Lasse Laurson, and Mikko J. Alava. 2008. Dislocation interactions mediated by grain boundaries. Journal of Statistical Mechanics: Theory and Experiment, P05010, 13 pages. © 2008 Institute of Physics Publishing. By permission.
  6. Lasse Laurson and Mikko J. Alava. 2008. A driven particle in a cloud of mobile impurities. Journal of Statistical Mechanics: Theory and Experiment, P07003, 10 pages. © 2008 Institute of Physics Publishing. By permission.

Keywords: avalanches, noise, self-organized criticality, plastic deformation, imbibition

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© 2008 Helsinki University of Technology

Last update 2011-05-26