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Updated: Jun 19, 2026
05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Conduction in rectangular quasi-one-dimensional and two-dimensional random resistor networks away from the
Thomas Kiefer1, Guillermo Villanueva, Jürgen Brugger
1Microsystems Laboratory, Ecole Polytéchnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland. thomas.kiefer@epfl.ch
Summary
This study models electrical conduction in random resistor networks. A new linear approximation for 2D systems offers engineering insights, contrasting with nonlinear 1D behavior.
Area of Science:
- Physics
- Materials Science
- Electrical Engineering
Background:
- Investigating electrical conduction in random resistor networks is crucial for understanding material properties.
- Percolation theory provides a framework for studying conductivity transitions in disordered systems.
Purpose of the Study:
- To analyze electrical conduction in finite random resistor networks in quasi-one and two dimensions, away from the percolation threshold.
- To compare different network topologies and their dependence on geometrical aspect ratio.
- To develop and validate a linear approximation for 2D systems for engineering applications.
Main Methods:
- Utilizing a bond percolation model to simulate electrical conduction.
- Comparing parallel linear chains (1D) and square/triangular lattices (2D).
- Analyzing conduction as a function of geometrical aspect ratio and distance from the percolation threshold.
Main Results:
- A universal scaling function describes conduction away from the percolation threshold in 2D, similar to finite-size scaling of thresholds.
- Quasi-one-dimensional systems exhibit highly nonlinear conduction behavior.
- A linear approximation for 2D conduction is proposed and its validity range analyzed.
Conclusions:
- The study provides a new scaling approach for electrical conduction in 2D random resistor networks.
- Findings offer practical engineering insights for designing materials with specific conductive properties.
- Results have potential applications in nanostructured materials, composites, and sensing technologies.
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