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Publication - Dr Luca Giuggioli

    Comparison of two models of tethered motion


    Giuggioli, L, Gupta, S & Chase, M, 2019, ‘Comparison of two models of tethered motion’. Journal of Physics A: Mathematical and Theoretical, vol 52.


    We consider a random walker whose motion is tethered around a focal
 point. We use two models that exhibit the same spatial dependence in the
 steady state but widely different dynamics. In one case, the walker is
 subject to a deterministic bias towards the focal point, while in the
 other case, it resets its position to the focal point at random times.
 The deterministic tendency of the biased walker makes the forays away
 from the focal point more unlikely when compared to the random nature of
 the returns of the resetting walker. This difference has consequences on
 the spatio-temporal dynamics at intermediate times. To show the
 differences in the two models, we analyze their probability distribution
 and their dynamics in presence and absence of partially or fully
 absorbing traps. We derive analytically various quantities: (i) mean
 first-passage times to one target, where we recover results obtained
 earlier by a different technique, (ii) splitting probabilities to either of two targets as well as survival probabilities when one or either target is partially absorbing. The interplay between confinement, diffusion and absorbing traps produces interesting non-monotonic effects in various quantities, all potentially accessible in experiments. The formalism developed here may have a diverse range of applications, from study of animals roaming within home ranges and of electronic excitations moving in organic crystals to developing efficient search algorithms for locating targets in a crowded environment.

    Full details in the University publications repository