arXiv subjects

Daniel B. Wilson

Publications and source records attributed to Daniel B. Wilson.

3 recordsLinked to original sources

arXiv2021

Crowded transport within networked representations of complex geometries

Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport phenomena. However, in general, the interplay between crowding and geometry in complex real-life environments is poorly understood. Existing analytical methodologies are not always readily extendable to heterogeneous environments: in these situations predictions of crowded transport behaviour within heterogeneous environments rely on computationally intensive mesh-based approaches. Here, we take a different approach by employing networked representations of complex environments to provide an efficient framework within which the interactions between networked geometry and crowding can be explored. We demonstrate how the framework can be used to: extract detailed information at the level of the whole population or an individual within it; identify the topological features of environments that enable accurate prediction of transport phenomena; and, provide insights into the design of optimal environments.

physics.soc-ph↗

arXiv2019

Displacement of transport processes on networked topologies

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.

cond-mat.stat-mech↗

arXiv2018

Topology-dependent density optima for efficient simultaneous network exploration

A random search process in a networked environment is governed by the time it takes to visit every node, termed the cover time. Often, a networked process does not proceed in isolation but competes with many instances of itself within the same environment. A key unanswered question is how to optimise this process: how many concurrent searchers can a topology support before the benefits of parallelism are outweighed by competition for space? Here, we introduce the searcher-averaged parallel cover time (APCT) to quantify these economies of scale. We show that the APCT of the networked symmetric exclusion process is optimised at a searcher density that is well predicted by the spectral gap. Furthermore, we find that non-equilibrium processes, realised through the addition of bias, can support significantly increased density optima. Our results suggest novel hybrid strategies of serial and parallel search for efficient information gathering in social interaction and biological transport networks.

math.OC↗