Network-driven dispersion in transport phenomena

A variety of key processes can be mathematically described in terms of directed transport networks, where a scalar (e.g., a signal or a substance) travels through a network until it reaches the exit. Different actions can intervene during transport, causing signal evolution. Here we focus on dispersion due to network connectivity. A mathematical model is built, under the hypothesis of exponential edge travel times. Three network elements are considered: network topology, edge-specific mean travel times, and signal partition at bifurcations. An analytical solution is given, which accounts for possible decay processes. Applications to model transport of conservative scalars in braided rivers and in random and small-world networks show the crucial role played by network-induced dispersion, the dominant role of edge travel times over bifurcation splitting rules, and occurrence of quasi-Gaussian shapes as the signal travels through the network.