Multi-periodicity from a hysteron model of cyclically sheared amorphous solids - an empirical study
Open Access
Author:
Mc Bride, Julius
Area of Honors:
Physics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
Richard Wallace Robinett, Thesis Honors Advisor Nathan C Keim, Thesis Supervisor
Keywords:
soft condensed matter hysteresis computational physics disorded systems neural networks
Abstract:
In an attempt to better understand the phenomenon of multi-periodicity from the hysteron model for soft spots in 2D amorphous solids subject to cyclic shear, numerical simulations with systems of interacting hysterons were conducted. Ensembles of 5 or 10 million systems of a chosen size, connectivity, and interaction makeup were generated and a search for multi-periodic orbits was conducted with the hysteron.py}module. Distributions of orbits across amplitude space were constructed and statistics on the probability of multi-periodicity were gathered. The principal results indicate that, though hysteron systems are used to model a nonlinear dynamical system with a transition from periodic to chaotic behavior, the model does not predict period-doubling behavior. In fact, it seems that higher response periods are most likely to occur at successively lower amplitudes. Additionally, physically motivated systems the overall frequencies of multi-periodicity, as well as the importance of frustrated interactions in multi-periodic orbits, were consistent with a previous study. Furthermore, the portion of constituent hysterons essential to the multi-periodic orbit of the system (participation fraction) was found to be $0.5$ or less on average in the majority of cases, in agreement with previous studies.
