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Popowski, Jared

University of British Columbia

Many large dynamical systems evolve according to interactions that have a well-defined length scale, such as short-range intermolecular forces in a liquid or the typical domain size in a magnet. However, external conditions can sometimes drive systems to a critical point, where the length scale diverges and measured quantities fluctuate in a scale-free manner, independent of the microscopic details of the system. There are countless examples of critical systems in nature, such as bird flocking, neural networks, financial markets, earthquakes, magnets, and avalanching amorphous solids. The collective behaviors of a system's constituents as it approaches a critical point are increasingly being studied using information theory-based observables, such as the mutual information and transfer entropy, which quantify the reductions in one's uncertainty following system observations. Previous studies have found that certain critical systems exhibit a peak in the mutual information and transfer entropy at the critical point, while the system-wide information flow as quantified by the global transfer entropy peaks strictly in the disordered phase, before the critical point is reached. This is a fascinating albeit still poorly understood result, which implies that one could use the global transfer entropy as a precursor for an upcoming critical point in certain situations. In this thesis, code to estimate the mutual information, transfer entropy and global transfer entropy is developed and tested against a series of analytically solvable models. Focus is then placed on the analysis of avalanche datasets from a mesoscopic model of a shear-driven amorphous solid, which exhibits nonequilibrium criticality at the yielding transition. It is found that the weighted integral of the mutual information provides a valid definition for a correlation length in the amorphous model, and the nature of the correlation length's decay in the high temperature and strain rate regimes are characterized with the aid of a novel avalanche binning procedure. Finally, the transfer entropy and global transfer entropy are applied for the first time to amorphous solids, for the purpose of searching for a precursor to the nonequilibrium brittle-ductile transition, with inconclusive results due to a lack of sufficient statistics.

Text

2023-10-05

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86084

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/