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Margherita Vendruscolo1, Luca Salerno1, Carlo Camporeale1

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Summary
This summary is machine-generated.

This study models scalar transport in networks, finding that network connectivity significantly impacts dispersion. Edge travel times are more critical than bifurcation rules for signal evolution.

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Area of Science:

  • Complex Systems
  • Network Science
  • Mathematical Modeling

Background:

  • Many natural and engineered processes involve directed transport through complex networks.
  • Understanding signal or substance evolution during transport is crucial for various scientific disciplines.
  • Network connectivity and element properties influence transport dynamics.

Purpose of the Study:

  • To develop a mathematical model for scalar transport in directed networks.
  • To analyze the impact of network topology, edge travel times, and bifurcation rules on signal dispersion.
  • To investigate signal evolution including potential decay processes.

Main Methods:

  • Formulation of a mathematical model for directed transport networks.
  • Hypothesis of exponential edge travel times.
  • Derivation of an analytical solution incorporating decay processes.
  • Application and validation using braided rivers, random, and small-world networks.

Main Results:

  • Network-induced dispersion plays a crucial role in scalar transport.
  • Edge travel times dominate over bifurcation splitting rules in influencing transport.
  • Quasi-Gaussian signal shapes emerge as the signal traverses the network.
  • The model accurately describes transport in diverse network types.

Conclusions:

  • Network topology and edge properties significantly govern transport dynamics and dispersion.
  • The derived analytical solution provides a robust framework for analyzing scalar transport.
  • The findings have broad applicability in understanding transport phenomena across different systems.