Small-world networks in geophysics

  title={Small-world networks in geophysics},
  author={Xin-She Yang},
  journal={Geophysical Research Letters},
  • 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

Figures from this paper

Small World Behavior of the Planetary Active Volcanoes Network: Preliminary Results
The correlation among all active volcanoes of the world over the last two thousand years is calculated in order to create a functional network and the obtained complex network is characterized by small world features. Expand
Graph theory in the geosciences
Graph theory has long been used in quantitative geography and landscape ecology and has been applied in Earth and atmospheric sciences for several decades. Recently, however, there have beenExpand
Networks of Historical Contingency in Earth Surface Systems
Earth surface systems (ESS) are characterized by various degrees of historical contingency, which complicates efforts to relate observed features and phenomena to environmental controls. This articleExpand
Graph theory-recent developments of its application in geomorphology
It is argued that, if geomorphic system properties and behaviour depend on system structure and if graph theory is able to quantitatively describe the configuration of system components, then graph theory should provide us with tools that help in quantifyingSystem properties and in inferring system behaviour. Expand
Synchronization and scale in geomorphic systems
Abstract Geomorphic systems consist of coupled subsystems with traits of small-world networks (SWN), characterized by tightly connected clusters of components, with fewer connections between theExpand
Climate Modeling with Neural Diffusion Equations
A novel climate model is designed based on the two concepts, the neural ordinary differential equation (NODE) and the diffusion equation, and can learn an appropriate latent governing equation that best describes a given climate dataset. Expand
Pore-scale heterogeneity, flow channeling and permeability: Network simulation and comparison to experimental data
Abstract The flow and transport properties of rocks depend on the statically geometry and topology of the pore space, which can be viewed as a complex network, as well as the characteristics ofExpand
Small and Other Worlds: Global Network Structures from Local Processes1
Using simulation, we contrast global network structures—in particular, small world properties—with the local patterning that generates the network. We show how to simulate Markov graph distributionsExpand
sing adjacency matrices to lay out larger small-world networks
Many networks exhibit small-world properties. The structure of a small-world network is characterized by short average path lengths and high clustering coefficients. Few graph layout methods captureExpand
Scaling Laws in Chennai Bus Network
This paper studies the structural properties of the complex bus network of Chennai by identifying each bus stop as a node, and a bus which stops at any two adjacent bus stops as an edge connecting the nodes, and argues based on its various statistical properties. Expand


Fractals in small-world networks with time-delay
  • X. Yang
  • Computer Science, Physics
  • 2002
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
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
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
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.
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