Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slows down under cooling. The specific pattern of slowing down depends on the material considered. We poorly understand this dependence, in particular, which aspects of the microscopic structures control the dynamics and other macroscopic properties is unclear. Attacking this question is one of the two main aspects of this dissertation. We have introduced a new class of models of supercooled liquids, which captures the central aspects of the correspondence between structure and elasticity on the one hand, structure and thermodynamic and dynamic properties on the other. These models can also be resolved analytically, leading to theoretical insights into the question. Our results also shed new light on the temperature-dependence of the topology of covalent networks, in particular, on the rigidity transition that occurs when the valence is increased. Observations suggested the presence of a "rigidity window" where rigidity is barely satisfied and the system is near criticality. Our work rules out the predominant explanation for this phenomenon.
Other questions appear in glassy systems at zero temperature, when the thermal activation time is infinitely long. In that situation, a glassy system can flow if an external driving force is imposed above some threshold. Near the threshold, the dynamics are critical. To describe the dynamics, one must understand how the system self-organizes into specific configurations.
The first example we will consider is the erosion of a river bed. Grains or pebbles are pushed by a fluid and roll on a disordered landscape made by the static particles. Experiments support the existence of a threshold forcing, below which no erosion flux is observed. Near the threshold, the transient state takes very long and the flux converges very slowly toward its stationary value. In the field, this long transient state is called "armoring" and corresponds to the filling up of holes on the frozen landscape by moving particles. The dynamics near threshold are relevant for geophysical applications – river beds tend to spontaneously sit at the threshold where erosion stops, but are poorly understood. In this dissertation, we present a novel microscopic model to describe the erosion near threshold. This model makes new quantitative predictions for the erosion flux vs the applied forcing and predicts that the spatial reparation of the flux is highly non-trivial: it is power-law distributed in space with long-range correlation in the flux direction, but no correlations in the perpendicular directions. We introduce a mean-field model to capture analytically some of these properties.
To study further the self-organization of driven glassy systems, we investigate, as our last example, the athermal dynamics of mean-field spin glasses. Like many of other glasses, such as electron glasses, random close packings, etc., the spin glass self-organizes into configurations that are stable, but barely so. Such marginal stability appears in the presence of a pseudogap in soft excitations – a density of states vanishing as a power-law distribution at zero energy. How such pseudogaps appear dynamically as the systems are prepared and driven was not understood theoretically. We elucidate this question, by introducing a stochastic process mimicking the dynamics, and show that the emergence of a pseudogap is deeply related to very strong anti-correlations emerging among soft excitations.
|Commitee:||Chaikin, Paul M., Grosberg, Alexander Y., Pine, David, Stein, Daniel L.|
|School:||New York University|
|School Location:||United States -- New York|
|Source:||DAI-B 77/05(E), Dissertation Abstracts International|
|Keywords:||Dynamics, Erosion, Glassy systems, Network glasses, Rigidity transition, Spin glasses|
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