Analysis of self-equilibrated networks through cellular modelling.
O Aloui1, D Orden2, N Bel Hadj Ali3,4
1Department of Civil, Architectural and Environmental Engineering, University of Miami, Coral Gables, FL 33146, USA.
Proceedings. Mathematical, Physical, and Engineering Sciences
|October 19, 2020
Summary
This study introduces a new method for analyzing self-equilibrated networks using graph theory. By modeling networks as collections of cells, their equilibrium states can be determined by examining individual cell interactions.
Area of Science:
- Network science
- Graph theory
- Systems engineering
Background:
- Network equilibrium models are crucial for analyzing complex systems in science and engineering.
- Existing models are used to study system behavior under perturbations and damage.
Purpose of the Study:
- To revisit network equilibrium models using graph theory.
- To propose a novel approach for analyzing self-equilibrated networks.
Main Methods:
- Modeling self-equilibrated networks as collections of predefined elementary network units (cells).
- Analyzing individual cell equilibria and their interactions to determine the overall system equilibrium.
- Combining topological and geometrical considerations.
Main Results:
- Demonstrated that any self-equilibrated network can be composed of these elementary cells.
- The proposed approach simplifies the analysis of complex self-equilibrated systems.
- Examples showcase the flexibility of the model in deciphering system states.
Conclusions:
- The cell-based approach offers a new perspective on network equilibrium analysis.
- This method is effective for understanding complex systems, particularly those in self-equilibrium.
- The combination of topological and geometrical insights enhances system state deciphering.
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