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Ondrej Hovorka
Advisor: Gary Friedman, Ph.D.
Abstract:
Many complex systems such as magnets, type-II superconductors, shape memory alloys as well as socioeconomic and biological systems are known to display hysteresis during varying external parameters. This inherently irreversible process is a consequence of multi-scale system dynamics and the existence of many metastable states. Although hysteresis is typically illustrated by closed minor loops, other types of hysteretic trajectories are often observed where closed loops form gradually after several external field periods or not at all. The question arises: What in the structure of a system determines these qualitatively different behaviors of hysteretic trajectories?
In this thesis we will describe our investigations of network structure induced changes of hysteretic behavior. As a paradigm for complex systems we first develop a simple microscopic model with disorder, which can be viewed as a collection of bistable elements interacting via complex interaction network. Our main focus is on studying the minor loop formation process during cyclically varying external parameter. We observe that stable minor loops form at different rates, depending on the sign of the interactions, disorder level, and on the connectivity and topology of the interaction networks. For dense interaction networks, we discover hysteretic trajectories that do not converge to minor loop after an arbitrarily large number of external parameter periods, and show that their appearance is due to the presence of specific topological elements in the network.
Our study demonstrates several links between the particular type of macroscopic hysteresis and the underlying structure of interactions, and opens new directions for developing techniques for identifying structure of complex hysteretic networks.
Thursday, August 9th, 2007 at 11 a.m.
Bossone 303
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