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• W2912542703 abstract "Consider a particle whose position evolves along the edges of a network. One definition for the displacement of a particle is the length of the shortest path on the network between the current and initial positions of the particle. Such a definition fails to incorporate information of the actual path the particle traversed. In this work we consider another definition for the displacement of a particle on networked topologies. Using this definition, which we term the winding distance, we demonstrate that for Brownian particles, confinement to a network can induce a transition in the mean squared displacement from diffusive to ballistic behaviour, $langle x^2(t) rangle propto t^2$ for long times. A multiple scales approach is used to derive a macroscopic evolution equation for the displacement of a particle and uncover a topological condition for whether this transition in the mean squared displacement will occur. Furthermore, for networks satisfying this topological condition, we identify a prediction of the timescale upon which the displacement transitions to long-time behaviour. Finally, we extend the investigation of displacement on networks to a class of anomalously diffusive transport processes, where we find that the mean squared displacement at long times is affected by both network topology and the character of the transport process." @default.
• W2912542703 created "2019-02-21" @default.
• W2912542703 creator A5035520416 @default.
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• W2912542703 date "2019-02-13" @default.
• W2912542703 modified "2023-09-27" @default.
• W2912542703 title "Transport processes on networked topologies" @default.
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• W2912542703 hasPublicationYear "2019" @default.
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