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Topological properties of a self-assembled electrical network via ab initio calculation
C Stephenson1, D Lyon1, A Hübler1
1Department of Physics, University of Illinois at Urbana Champaign, Urbana, Illinois, USA.
Scientific Reports
|February 4, 2017
Summary
Electrical conductors self-assemble into tree-like networks. A new model confirms experimental findings on network structure, showing consistent fractions of endpoints and branch points, even during network formation.
Area of Science:
- Physics of complex systems
- Electrical engineering
- Materials science
Background:
- Electrical conductors spontaneously form complex, tree-like networks under applied voltage or current.
- Previous experiments revealed consistent degree distributions in steady-state networks across various sizes.
Purpose of the Study:
- To develop a novel model for conductor self-assembly based on underlying physical interactions.
- To validate the model's predictions against experimental data for steady-state and dynamic network formation.
Main Methods:
- Development of a new physical model simulating conductor self-assembly.
- Analysis of network properties, including endpoint/branch point fractions and node Strahler number distributions.
Main Results:
- The model accurately predicts constant fractions for endpoints (0.252) and branch points (0.237) in steady-state networks.
- Predicted scaling properties hold true during the network's approach to steady state.
- The model reproduces experimentally observed node distributions based on Strahler numbers.
Conclusions:
- The new model provides a robust physical basis for understanding the self-assembly of tree-like electrical networks.
- The model's success in predicting scaling properties and node distributions validates its accuracy for both steady-state and dynamic network formation.
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