Spreading of Failures in Small-World Networks: A Connectivity-Dependent Load Sharing Fibre Bundle Model
| Autor: | Zbigniew Domański |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Small-world network
Materials Science (miscellaneous) Biophysics General Physics and Astronomy State (functional analysis) Topology small-world network lcsh:QC1-999 fiber bundle model Set (abstract data type) statistics failure evolution Range (statistics) Fiber bundle simulations Enhanced Data Rates for GSM Evolution Physical and Theoretical Chemistry switchable load sharing Unit (ring theory) lcsh:Physics Mathematical Physics Mathematics Weibull distribution |
| Zdroj: | Frontiers in Physics, Vol 8 (2020) |
| ISSN: | 2296-424X |
| DOI: | 10.3389/fphy.2020.552550 |
| Popis: | A rich variety of multicomponent systems operating under parallel loading may be mapped on and then examined by employing a family of the Fiber Bundle Models. As an example, we consider a system composed of N immobile units located in nodes of a network G and subjected to a growing external load F imposed uniformly on the units. Each unit, characterized by a load threshold δ, is classified as reliable or irreversibly failed, depending on whether δ is bigger, or respectively smaller, than the load felt by the unit. A pair of interdependent units is uniquely indicated by an edge of G. Initially all the units are reliable. When a unit fails, its load is distributed locally among interdependent neighbors if they are reliable, or is otherwise shared globally by all the reliable units. Because of the growing F and the loads that are transferred according to such a see-saw switch between the local and global sharing rules (sLGS), a set of nodes, that holds the reliable units, evolves as G→∅. During the evolution, a subset Gc⊂G emerges that represents the limiting state of the system’s functionality when the smallest group of nc reliable units sustains the highest load Fc. We concentrate on how the Fiber Bundle Model and switching Local-Global-Sharing conspire to drive the system toward Gc. Specifically, we assume that {δ}G are quenched-random quantities distributed uniformly over (0,1) or governed by the Weibull distribution and networks G are the Watts-Strogatz “small-world” graphs with the rewiring probability p that characterizes possible rearrangements of edges in G. We have identified a range of values of p, where the mean highest load fc(N)=〈Fc〉/N, supported by reliable units, scales linearly with the average global-clustering coefficient of the host network. Similar scaling holds for 〈nc〉 and 〈Fc/nc〉. We have also found that in the large N limit fc(N)→fc∞>0, for all values of p and both considered distributions of {δ}G. The symbol 〈…〉 represents averaging over {δ}G and a suitable ensemble of networks {G}. |
| Databáze: | OpenAIRE |
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