Localized Dynamics in 2D Disordered Granular Systems Open Access

Robe, Dominic (Spring 2019)

Permanent URL: https://etd.library.emory.edu/concern/etds/gm80hw39q?locale=en


Disordered solids are ubiquitous in modern materials. The structural and dynamical properties of these materials are still poorly understood. Basic properties such as viscosity, elasticity, or magnetization can depend in a complex way on not just the elementary components of a material, but the details of its environment throughout its lifetime. In this thesis I describe and unify a set of phenomena in disordered systems which at first inspection appear anomalous and disconnected.

Physical aging is a relaxation process in which material properties appear to change over time despite fixed environmental conditions. This drift follows a sudden change in the environment to which the system could not equilibrate. Here I report analysis of experimental and simulation data which fit a trend in physical aging across a broad class of disordered systems. I implement particle tracking techniques and optimize simulations to observe dynamic trends over three orders of magnitude in time.

In dense disordered systems, movement of particles is generally intermittent and heterogeneous. I capture dynamical data with a fine enough temporal resolution to illustrate the obvious appearance of these sudden, localized rearrangements in a dense colloid. Paradoxically I also illustrate the lack of a distinction between a quiescent particle and one which is participating in a rearrangement. I resolve this conflict by measuring activity not by movement, but by contact with a neighboring particle.

The disordered structure in granular systems also leads to localized vibrational modes, which imbue systems with interesting acoustic and mechanical properties. I characterize the vibrational modes in systems of attractive particles with a variety of disorder types. Some acoustic properties are attributed to quantum mechanical effects. I demonstrate that similar effects can be present in a classical system. 

All the phenomena I report here speak to the complexity of behavior that arises from a rough energy landscape. Localization, intermittency, history-dependence, and decelerating relaxation can all be found in a system with simple interactions if the multitude of interactions become frustrated. This critical feature connects the dynamics of disordered granular systems intimately with a vast field of complex systems.

Table of Contents

Abstract Cover Page


Cover Page

Table of Contents

List of Figures

Citations to Previously Published Work



1 Introduction 1

1.1 Glass

1.1.1 Disorder

1.1.2 Frustration and satisfaction

1.1.3 Spin glass

1.2 Aging

1.2.1 Slowing down

1.2.2 Over the hill

1.3 Cooperation

1.4 Soft Spots

1.4.1 Local order

1.4.2 Vibrational modes

1.5 Thesis layout

2 Aging in a 2D colloidal suspension

2.1 Introduction

2.2 Theoretical background

2.3 Results from experimental data

2.3.1 Statistics of record-sized events

2.3.2 Mean-square displacement

2.3.3 Persistence

2.3.4 Mobility correlations

2.3.5 Data at lower area fraction

2.4 Comparison with simulations of the cluster model

2.5 Conclusions

3 Two-time dynamics in a simulated colloidal glass

3.1 Introduction

3.2 Simulation details

3.3 Mean squared displacement

3.4 Distinguishing rearrangement events

3.5 Displacement distribution

3.6 Discussion

3.7 Outlook

4 Log-Poisson nature of physical aging

4.1 Introduction

4.2 Deceleration in a renewal process

4.3 Irreversible event rates

4.4 Record dynamics

4.5 Conclusions

5 Localized vibrational modes in nonlinear networks

5.1 Introduction

5.1.1 Normal mode calculation

5.2 Simulation details5.2.1 Tuning nonlinearity

5.2.2 Tuning disorder

5.3 Vibrational modes

5.3.1 Localization

5.3.2 Amplitude dependence

5.4 Excitation Pulses

5.4.1 Resonant absorption

5.5 Conclusions

6 Computational methods

6.1 Particle dynamics

6.1.1 Interactions

6.1.2 GPU Acceleration

6.1.3 Time Step

6.1.4 Other methods

6.2 Cluster Model

7 Summary


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