Resilience in Hierarchical Fluid Flow Networks
arXiv:1808.01077 · doi:10.1103/PhysRevE.99.012321
Abstract
The structure of flow networks determines their function under normal conditions as well as their response to perturbative damage. Brain vasculature often experiences transient or permanent occlusions in the finest vessels, but it is not clear how these micro-clots affect the large scale blood flow or to what extent they decrease functionality. Motivated by this, we investigate how flow is rerouted after the occlusion of a single edge in networks with a hierarchy in edge conductivities. We find that in 2D networks, vessels formed by highly conductive edges serve as barriers to contain the displacement of flow due to a localized perturbation. In this way, the vein provides shielding from damage to surrounding edges. We show that once the conductivity of the vein surpasses an initial minimal value, further increasing the conductivity can no longer extend the shielding provided by the vein. Rather, the length scale of the shielding is set by the network topology. Upon understanding the effects of a single vein, we investigate the global resilience of networks with complex hierarchical order. We find that a system of veins arranged in a grid is able to modestly increase the overall network resilience, outperforming a parallel vein pattern.
arXiv comment16 pages, 14 figures
References in corpus (18)
- Error and attack tolerance of complex networks
- Resilience of the Internet to random breakdowns
- Attack vulnerability of complex networks
- Structural Vulnerability of the North American Power Grid
- Damage and fluctuations induce loops in optimal transport networks
- Fluctuations and redundancy in optimal transport networks
- Cascading Power Outages Propagate Locally in an Influence Graph that is not the Actual Grid Topology
- Global Optimization, Local Adaptation, and the Role of Growth in Distribution Networks
- Critical links and nonlocal rerouting in complex supply networks
- Architecture of optimal transport networks
- The Key Player Problem in Complex Oscillator Networks and Electric Power Grids: Resistance Centralities Identify Local Vulnerabilities
- Perturbation of infinite networks of resistors
- Network susceptibilities: theory and applications
- Nonlocal failures in complex supply networks by single link additions
- Dual theory of transmission line outages
- Non-Local Impact of Link Failures in Linear Flow Networks
- Long-Range Response to Transmission Line Disturbances in DC Electricity Grids
- Current Redistribution in Resistor Networks: Fat-Tail Statistics in Regular and Small-World Networks
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- Dual communities in spatial networks
- Network structure and dynamics of effective models of non-equilibrium quantum transport
- Line defects in infinite networks of resistors