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Spatial Temporal Analysis of Fieldwise Flow in Microvasculature
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Networks from flows--from dynamics to topology.

Nora Molkenthin1, Kira Rehfeld2, Norbert Marwan3

  • 11] Potsdam Institute for Climate Impact Research, P.O.Box 601203, 14412 Potsdam, Germany [2] Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.

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Complex network analysis reveals climate system dynamics. New methods link flow dynamics to network measures, showing transition zones, not information propagation, create key network structures.

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Area of Science:

  • * Complex systems science
  • * Geophysics and climate science
  • * Network theory

Background:

  • * Complex network approaches are increasingly used to study continuous spatial dynamical systems, such as climate.
  • * The relationship between the dynamics of atmospheric/oceanic flows and network measures derived from them remains poorly understood.
  • * Existing methods often lack a clear link to the underlying physical processes.

Purpose of the Study:

  • * To bridge the gap between dynamical systems theory and complex network analysis in climate science.
  • * To define a continuous analytical analogue of correlation networks for advection-diffusion dynamics.
  • * To provide a foundational understanding of climate networks based on fluid dynamics.

Main Methods:

  • * Development of a continuous analytical analogue of Pearson correlation networks for advection-diffusion processes.
  • * Analysis of complex networks derived from prototypical fluid flow models.
  • * Application to time series data from the equatorial Pacific region.

Main Results:

  • * The proposed analytical model successfully reproduces key features of complex climate networks.
  • * A direct relationship between the background flow's velocity field and network measures was established.
  • * High betweenness centrality in networks corresponds to flow transition zones, not information propagation pathways.

Conclusions:

  • * The study provides a general theoretical foundation for understanding climate networks.
  • * Network structures are directly interpretable in terms of underlying fluid dynamics.
  • * The findings re-evaluate the interpretation of network measures like betweenness in dynamical systems.