Small-world networks in geophysics

@article{Yang2001SmallworldNI,
  title={Small-world networks in geophysics},
  author={Xin-She Yang},
  journal={Geophysical Research Letters},
  year={2001},
  volume={28},
  pages={2549-2552}
}
  • Xin-She Yang
  • Published 1 July 2001
  • Physics
  • Geophysical Research Letters
Many geophysical processes can be modelled as interconnected networks. The small-world network model has recently attracted much attention in physics and applied sciences. In this paper, we modify and apply the small-world network theory to model geophysical processes such as diffusion and transport in disordered porous rocks. We develop an analytical approach as well as numerical simulations to characterize the properties of small-world networks in geophysics using system saturation time and… Expand

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References

SHOWING 1-10 OF 15 REFERENCES
Fractals in small-world networks with time-delay
  • X. Yang
  • Computer Science, Physics
  • 2002
TLDR
An analytical approach as well as numerical simulations are developed to characterise the effect of time-delay on the properties of small-world networks and it is shown that small- world networks with time- delay generally have the multifractals property. Expand
Collective dynamics of ‘small-world’ networks
TLDR
Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs. Expand
Permeability prediction based on fractal pore‐space geometry
Estimating permeability from grain-size distributions or from well logs is attractive but difficult. In this paper we present a new, generally applicable, and relatively inexpensive approach whichExpand
Scaling and percolation in the small-world network model.
  • M. Newman, D. Watts
  • Mathematics, Physics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
TLDR
There is one nontrivial length-scale in the small-world network model of Watts and Strogatz, analogous to the correlation length in other systems, which is well-defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero, giving a normal critical point in this limit. Expand
Characterization and control of small-world networks.
  • S. Pandit, R. E. Amritkar
  • Mathematics, Physics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
TLDR
The concept of a "faraway" connection in a network is concretized by defining a far edge, which is algorithmic and independent of any external parameters such as topology of the underlying space of the network. Expand
Mean-field solution of the small-world network model.
TLDR
A mean-field solution for the average path length and for the distribution of path lengths in the small-world network model is presented, which is exact in the limit of large system size and either a large or small number of shortcuts. Expand
Small Worlds: The Dynamics of Networks between Order and Randomness
small worlds the dynamics of networks between order and. download small worlds the dynamics of networks between. small worlds and the dynamics of networks. small world networks oxford handbooks.Expand
Introduction to percolation theory
Preface to the Second Edition Preface to the First Edition Introduction: Forest Fires, Fractal Oil Fields, and Diffusion What is percolation? Forest fires Oil fields and fractals Diffusion inExpand
Small-World Networks: Evidence for a Crossover Picture
Watts and Strogatz [Nature (London) 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, theExpand
Spreading and shortest paths in systems with sparse long-range connections.
  • C. Moukarzel
  • Mathematics, Medicine
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1999
Spreading according to simple rules (e.g., of fire or diseases) and shortest-path distances are studied on d-dimensional systems with a small density p per site of long-range connectionsExpand
...
1
2
...