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Title: Anomalous physical transport in complex networks

Abstract

The emergence of scaling in transport through interconnected systems is a consequence of the topological structure of the network and the physical mechanisms underlying the transport dynamics. We study here transport by advection and diffusion in scale-free and Erdös-Rényi networks. Velocity distributions derived from a flow potential exhibit power-law scaling with exponent $${\nu}{\approx}{\gamma}+1$$, where $${\gamma}$$ is the exponent of network connectivity. Using stochastic particle simulations, we find anomalous (nonlinear) scaling of the mean-square displacement with time. We show the connection with existing descriptions of anomalous transport in disordered systems, and explain the mean transport behavior from the coupled nature of particle jump lengths and transition times.

Authors:
 [1];  [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1505821
Grant/Contract Number:  
SC0003907
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 82; Journal Issue: 5; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Nicolaides, Christos, Cueto-Felgueroso, Luis, and Juanes, Ruben. Anomalous physical transport in complex networks. United States: N. p., 2010. Web. doi:10.1103/physreve.82.055101.
Nicolaides, Christos, Cueto-Felgueroso, Luis, & Juanes, Ruben. Anomalous physical transport in complex networks. United States. doi:10.1103/physreve.82.055101.
Nicolaides, Christos, Cueto-Felgueroso, Luis, and Juanes, Ruben. Wed . "Anomalous physical transport in complex networks". United States. doi:10.1103/physreve.82.055101. https://www.osti.gov/servlets/purl/1505821.
@article{osti_1505821,
title = {Anomalous physical transport in complex networks},
author = {Nicolaides, Christos and Cueto-Felgueroso, Luis and Juanes, Ruben},
abstractNote = {The emergence of scaling in transport through interconnected systems is a consequence of the topological structure of the network and the physical mechanisms underlying the transport dynamics. We study here transport by advection and diffusion in scale-free and Erdös-Rényi networks. Velocity distributions derived from a flow potential exhibit power-law scaling with exponent ${\nu}{\approx}{\gamma}+1$, where ${\gamma}$ is the exponent of network connectivity. Using stochastic particle simulations, we find anomalous (nonlinear) scaling of the mean-square displacement with time. We show the connection with existing descriptions of anomalous transport in disordered systems, and explain the mean transport behavior from the coupled nature of particle jump lengths and transition times.},
doi = {10.1103/physreve.82.055101},
journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
number = 5,
volume = 82,
place = {United States},
year = {2010},
month = {11}
}

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Cited by: 18 works
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Works referenced in this record:

Understanding individual human mobility patterns
journal, June 2008

  • González, Marta C.; Hidalgo, César A.; Barabási, Albert-László
  • Nature, Vol. 453, Issue 7196
  • DOI: 10.1038/nature06958

Towards Design Principles for Optimal Transport Networks
journal, January 2010


What is special about diffusion on scale-free nets?
journal, January 2005


Community structure and ethnic preferences in school friendship networks
journal, June 2007

  • González, M. C.; Herrmann, H. J.; Kertész, J.
  • Physica A: Statistical Mechanics and its Applications, Vol. 379, Issue 1
  • DOI: 10.1016/j.physa.2007.01.002

Anomalous Transport in Random Fracture Networks
journal, November 1997


Anomalous transit-time dispersion in amorphous solids
journal, September 1975


Statistical mechanics of complex networks
journal, January 2002


Epidemic Spreading in Scale-Free Networks
journal, April 2001


Rules for Biologically Inspired Adaptive Network Design
journal, January 2010


Universal Behavior of Load Distribution in Scale-Free Networks
journal, December 2001


Transport behavior of coupled continuous-time random walks
journal, October 2008


Classes of small-world networks
journal, September 2000

  • Amaral, L. A. N.; Scala, A.; Barthelemy, M.
  • Proceedings of the National Academy of Sciences, Vol. 97, Issue 21
  • DOI: 10.1073/pnas.200327197

Global organization of metabolic fluxes in the bacterium Escherichia coli
journal, February 2004


Transport between multiple users in complex networks
journal, May 2007


The random walk's guide to anomalous diffusion: a fractional dynamics approach
journal, December 2000


Emergence of Scaling in Random Networks
journal, October 1999


Robustness of trans-European gas networks
journal, July 2009


Derivation of the Continuous-Time Random-Walk Equation
journal, January 1980


Asymptotic solutions of continuous-time random walks
journal, May 1974

  • Shlesinger, Michael F.
  • Journal of Statistical Physics, Vol. 10, Issue 5
  • DOI: 10.1007/BF01008803

Anomalous Transport in Scale-Free Networks
journal, June 2005


Random walks on complex trees
journal, July 2008

  • Baronchelli, Andrea; Catanzaro, Michele; Pastor-Satorras, Romualdo
  • Physical Review E, Vol. 78, Issue 1
  • DOI: 10.1103/PhysRevE.78.011114

Random Walks on Complex Networks
journal, March 2004


The large-scale organization of metabolic networks
journal, October 2000

  • Jeong, H.; Tombor, B.; Albert, R.
  • Nature, Vol. 407, Issue 6804
  • DOI: 10.1038/35036627

Modeling non-Fickian transport in geological formations as a continuous time random walk
journal, January 2006

  • Berkowitz, Brian; Cortis, Andrea; Dentz, Marco
  • Reviews of Geophysics, Vol. 44, Issue 2
  • DOI: 10.1029/2005RG000178

Scaling theory of transport in complex biological networks
journal, April 2007

  • Gallos, L. K.; Song, C.; Havlin, S.
  • Proceedings of the National Academy of Sciences, Vol. 104, Issue 19
  • DOI: 10.1073/pnas.0700250104

Fgf8 morphogen gradient forms by a source-sink mechanism with freely diffusing molecules
journal, September 2009

  • Yu, Shuizi Rachel; Burkhardt, Markus; Nowak, Matthias
  • Nature, Vol. 461, Issue 7263
  • DOI: 10.1038/nature08391

A critical point for random graphs with a given degree sequence
journal, March 1995


Transport in networks with multiple sources and sinks
journal, October 2008


Random Walks on Lattices. II
journal, February 1965

  • Montroll, Elliott W.; Weiss, George H.
  • Journal of Mathematical Physics, Vol. 6, Issue 2
  • DOI: 10.1063/1.1704269

Modelling the scaling properties of human mobility
journal, September 2010

  • Song, Chaoming; Koren, Tal; Wang, Pu
  • Nature Physics, Vol. 6, Issue 10
  • DOI: 10.1038/nphys1760

Scale-Free Networks on Lattices
journal, November 2002


Random walk and trapping processes on scale-free networks
journal, October 2004


Transport and percolation theory in weighted networks
journal, April 2007


    Works referencing / citing this record:

    Extreme Events on Complex Networks
    journal, May 2011