HR: 1340h
AN: NG33A-0164    [Abstracts]
TI: Stress Relaxation via Avalanche Dynamics in Materials: Long-Range Interaction in the Manna Model
AU: * Van Aalsburg, J
EM: jvan@cse.ucdavis.edu
AF: University of California at Davis Center for Comp. Science and Engr., One Shields Ave., Davis, CA 95616 United States
AU: Holliday, J
EM: holliday@cse.ucdavis.edu
AF: University of California at Davis Center for Comp. Science and Engr., One Shields Ave., Davis, CA 95616 United States
AU: Shcherbakov, R
EM: roshch@cse.ucdavis.edu
AF: University of California at Davis Center for Comp. Science and Engr., One Shields Ave., Davis, CA 95616 United States
AU: Rundle, J B
EM: rundle@cse.ucdavis.edu
AF: University of California at Davis Center for Comp. Science and Engr., One Shields Ave., Davis, CA 95616 United States
AB: Relaxation processes in solids, such as the relaxation of forces at dislocations and pinning sites, have been shown to be occur through avalanche processes. A simple example of such an avalanche process was described a number of years ago by Bak and colleagues. The Self-Organized Criticality model used the toppling of grains on a sand pile as a paradigm to describe the scaling and other physical processes associated with avalanche phenomena. According to Bak and colleagues, SOC is displayed by systems which naturally evolve toward a critical state independent of initial conditions. SOC has been proposed by some to describe a diverse array of phenomena including avalanches, forest fires, and earthquakes. At the heart of SOC is the dependence of large, complex systems on a few, relatively simple rules of interaction. Once in the critical state, small perturbations (the addition of a single particle of sand or the burning of a single tree) can result in events involving nearly all of the sites in the system. In fact, this ability to produce avalanches of any size is one of the key features of SOC. Perhaps even more importantly, these events obey a power law distribution. It is this behavior, that makes the study of self-organizing systems such a useful tool. While subsequent detailed examination by a wide variety of investigators has shown that most systems are not as simple as the SOC paradigm predicts, there are a few features of the SOC idea that merit further investigation. In particular, many real systems display long-range interactions, which produce mean field physics. We therefore study a two-state version of the sand pile model, the Manna model, with varying interaction range in two dimensions. Toppling rules are as outlined for the original Manna Model, with the ability to topple, or interact, beyond nearest-neighbor sites. The critical scaling exponents are calculated and shown to be consistent with the expected mean-field values.
DE: 4480 Self-organized criticality
DE: 4485 Self-organization
SC: Nonlinear Geophysics [NG]
MN: Fall Meeting 2005