JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    •   OpenBU
    • Theses & Dissertations
    • Boston University Theses & Dissertations
    • View Item
    •   OpenBU
    • Theses & Dissertations
    • Boston University Theses & Dissertations
    • View Item

    Transport ad percolation in complex networks

    Thumbnail
    Download/View
    Li_Guanliang_2...pdf (1.737Mb)
    Date Issued
    2013
    Author
    Li, Guanliang
    Share to FacebookShare to TwitterShare by Email
    Export Citation
    Download to BibTex
    Download to EndNote/RefMan (RIS)
    Metadata
    Show full item record
    Embargoed until:
    2031-01-01
    Permanent Link
    https://hdl.handle.net/2144/12807
    Abstract
    To design complex networks with optimal transport properties such as flow efficiency, we consider three approaches to understanding transport and percolation in complex networks. We analyze the effects of randomizing the strengths of connections, randomly adding longrange connections to regular lattices, and percolation of spatially constrained networks. Various real-world networks often have links that are differentiated in terms of their strength, intensity, or capacity. We study the distribution P(σ) of the equivalent conductance for Erdös-Rényi (ER) and scale-free (SF) weighted resistor networks with N nodes, for which links are assigned with conductance σi = e^-axi, where xi is a random variable with 0 < xi < 1. We find, both analytically and numerically, that P(σ) for ER networks exhibits two regimes: (i) For σ < e^-apc, P(σ) is independent of N and scales as a power law P(σ) ~ σ^(k)/a-1. Here pc = 1/(k) is the critical percolation threshold of the network and (k) is the average degree of the network. (ii) For σ > e^-apc, P(σ) has strong N dependence and scales as P(σ) ~ f(σ,apc/N^1/3). Transport properties are greatly affected by the topology of networks. We investigate the transport problem in lattices with long-range connections and subject to a cost constraint, seeking design principles for optimal transport networks. Our network is built from a regular d-dimensional lattice to be improved by adding long-range connections with probability Pij ~ rij^-α, where Tij is the lattice distance between site i and j. We introduce a cost constraint on the total length of the additional links and find optimal transport in the system for α = d + 1, established here for d = 1, 2 and 3 for regular lattices and df for fractals. Remarkably, this cost constraint approach remains optimal, regardless of the strategy used for transport, whether based on local or global knowledge of the network structure. To further understand the role that long-range connections play in optimizing the transport of complex systems, we study the percolation of spatially constrained networks. We now consider originally empty lattices embedded in d dimensions by adding long-range connections with the same power law probability p(r) ~ r^-α. We find that, for a ≤ d, the percolation transition belongs to the universality class of percolation in ER networks, while for α > 2d it belongs to the universality class of percolation in regular lattices (for one-dimensional linear chain, there is no percolation transition). However for d < α < 2d, the percolation properties show new intermediate behavior different from ER networks, with critical exponents that depend on α.
    Description
    Thesis (Ph.D.)--Boston University PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.
    Collections
    • Boston University Theses & Dissertations [4374]

    Contact Us | Send Feedback | Help
     

     

    Browse

    All of OpenBUCommunities & CollectionsIssue DateAuthorsTitlesSubjectsThis CollectionIssue DateAuthorsTitlesSubjects

    Deposit Materials

    LoginNon-BU Registration

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Contact Us | Send Feedback | Help