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Updated: Jul 25, 2026
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Reservoir Condition Pore-scale Imaging of Multiple Fluid Phases Using X-ray Microtomography
Published on: February 25, 2015
Scaling and percolation in the small-world network model.
1Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
Summary
This study analyzes the Watts and Strogatz small-world network model, identifying a critical length-scale that governs network behavior and diverges at a critical point. This scale impacts disease propagation models and network dimensions.
Area of Science:
- Network Science
- Statistical Physics
- Complex Systems
Background:
- The Watts and Strogatz model captures key features of social interaction networks.
- Understanding network properties like length-scale is crucial for modeling complex systems.
Purpose of the Study:
- To investigate the critical length-scale in the small-world network model.
- To analyze network behavior, including crossover phenomena and effective dimensions.
- To model disease propagation using site percolation on these networks.
Main Methods:
- Analytical derivation of critical exponents and finite size scaling.
- Application of series expansion and Padé approximants.
- Numerical simulations to validate theoretical findings.
Main Results:
- Identification of a nontrivial length-scale governing large- to small-world transitions.
- Calculation of the effective dimension of small-world graphs, exhibiting multifractal-like behavior.
- Derivation of an approximate expression for epidemic threshold in disease propagation models.
Conclusions:
- The small-world network model exhibits a critical point and a characteristic length-scale.
- Network dimension is scale-dependent, similar to multifractals.
- Percolation analysis provides insights into disease spread dynamics on these networks.
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