Simple Models for Complex Nonequilibrium Problems in Nanoscale Friction and Network Dynamics
Abstract: This doctoral thesis investigates three different topics: How friction evolves in atomically thin layered materials (2D materials); How social dynamics can be used to model grand scale common-pool resource games; Benchmarking of various image reconstruction algorithms in atomic force microscopy experiments. While these topics are diverse, they share being complex out-of-equilibrium systems. Furthermore, our approach to these topics will be the same: using simple models to obtain qualitative information about a system's dynamics. In the case of atomically thin layered materials, we will be expanding on the influential Prandtl-Tomlinson model and obtain an improved model constituting a substantial improvement in the theoretical description of friction in these systems. In the context of social dynamics, we will introduce a novel model representing a new approach to consensus rates on social networks in relation to society spanning coordination problems. For the image reconstruction project, our ambition is to investigate a new method for recreating free-energy surfaces based on AFM experiment, however, for this project only preliminary results are included.
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