Ph.D Student | Daniel Hexner |
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Subject | Spatial Organization in Periodically Driven Systems |

Department | Department of Physics |

Supervisor | Full Professor Levine Dov |

Full Thesis text |

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In this thesis I study spatial organization in interacting systems both in and out of equilibrium. The main part of my research deals with driven systems far from equilibrium, but I will begin by describing the equilibrium system, a lattice model based on the Kari Culik Wang tiles, since this work preceded the others chronologically.

The Kari-Culik system is the smallest set of Wang tiles (square tiles with edge colorings which constrain their juxtaposition) which tiles the plane only aperiodically. It differs from other tilings studied in that its matching rules are derived algebraically, which leads to its distinctive properties. We find that the as the system is cooled, a series of phase transitions occur where the system orders into periodic configurations with larger and larger periods. We show that the ground state entropy is extensive and argue that as a result competing length scales lead to behavior analogous to the Frenkel-Kontorova model. Entropy, favoring periodic configurations, plays the role of potential strength in the F-K model, while energy favors quasi-periodicity.

The remainder of this thesis deals with two models for periodically driven systems which are far from equilibrium. The first model was introduced to understand a reversible-irreversible phase transition observed in periodically sheared colloidal suspension which was shown to belong to the universality class of conserved directed percolation. We uncovered a hidden order present in the system at the critical point, displaying anomalously small density fluctuations. Such a phenomenon is termed hyperuniformity and is a clear signature of non-equilibrium dynamics. Using this observation, we also define a structural length scale which characterizes the divergence of the correlation length near the critical point. We conclude by suggesting a scaling relation for the new exponent characterizing hyperuniformity

The second model we introduced and studied aims at understanding the occurrence of limit cycles recently observed in simulations of periodically driven granular material with friction. We find that after an initial transient, the system organizes into a mosaic of ordered regions which are either striped or checker-board. These ordered regions are static, or invariant, under strobing, similar to the reversible arrangements in the driven colloidal setup. Interestingly, motion occurs along closed paths on the boundaries between these two invariant configurations and the paths are both self-avoiding non-intersecting. We explore the possibility that the self-avoiding paths have the statistics of other self avoiding curves by measuring the gyration radius as a function of length.