Random walks on jammed networks: Spectral properties.

Area of Science:

• Physics
• Materials Science
• Network Science

Background:

• Diffusive transport is crucial in various physical systems.
• Understanding transport on disordered networks is challenging.
• Sphere packings near the jamming transition exhibit complex contact networks.

Purpose of the Study:

• To investigate diffusive transport on networks from compressed sphere packings.
• To analyze the properties of these networks near the jamming transition.
• To distinguish topological from geometric disorder sources.

Main Methods:

• Random walk analysis on particle contact networks.
• Modeling transport as a Markov process using narrow escape time.
• Analysis of the transition rate matrix's spectral density.

Main Results:

• Network structures from jammed particles share similarities with Euclidean lattices but possess unique characteristics.
• The distribution of eigenvalues of the transition rate matrix follows a power law with a spectral dimension of 3.
• Eigenvector statistics reveal subtle differences from homogeneous lattices, enabling distinction between disorder types.

Conclusions:

• Jammed sphere packing networks exhibit complex properties that bridge ordered and disordered systems.
• The spectral analysis provides a method to characterize network disorder.
• This work offers insights into transport phenomena in disordered granular materials.