A first principles model and numeric solution methods for a system of self-organizing conductors

Electrical networks have long been studied in the context of non-equilibrium thermodynamics, particularly in the linear regime, due to both their theoretical convenience and their experimental accessibility. Of more recent interest is the behaviour of self-organizing electrical networks which necessarily exist in the non-linear regime where several proposed non-equilibrium thermodynamic principles are conjectured to apply. However, extension of conventional electrical network models to this regime is challenging due to the requirement that the topology of the network be dynamic. Additionally, the system dynamics must be modelled in a way that retains the essential physics while still being numerically solvable. In this work, we develop a first-principles model of a system of electrically conducting particles which self-organizes to form complex electrical networks. The resulting model contains many non-linear interactions between the constituents, and so we develop the methods necessary to numerically integrate the equations of motion efficiently. This leads to a new method of numerically calculating the forces between conducting objects in a dynamic configuration. We then use these methods to reproduce experimental results regarding the network topology, and find that our model is in agreement with experiment. Interestingly, we observe that the model predicts various measures of the network topology remain constant during the self-organization process. These developments may be applied in further exploration of principles regarding energy dissipation and entropy production in electrical networks beyond the linear regime, as a physical model of the process as well as the methods of numerical solution has been developed and validated with comparison to experiment.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Stephenson, Cory Ryan

Contributors dc:contributor

• Hubler, Alfred W.
• Bezryadin, Alexey
• Dahmen, Karin A.
• Perdekamp, Mattias G
• Weaver, Richard

• Self-Organization

Statement dc:rights

• Copyright 2018 Cory Stephenson

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101167

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101167