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Abstract / Description of output
We consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r. We consider several generalizations of the model of Evans and Majumdar (2011 Phys. Rev. Lett. 106 160601): (i) a spacedependent resetting rate r(x); (ii) resetting to a random position z drawn from a resetting distribution P(z); and (iii) a spatial distribution for the absorbing target PT (x). As an example of (i) we show that the introduction of a nonresetting window around the initial position can reduce the mean time to absorption provided that the initial position is sufficiently far from the target. We address the problem of optimal resetting, that is, minimizing the mean time to absorption for a given target distribution. For an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows.
Original language  English 

Article number  435001 
Number of pages  15 
Journal  Journal of Physics A: Mathematical and Theoretical 
Volume  44 
Issue number  43 
DOIs  
Publication status  Published  11 Oct 2011 
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 1 Finished

Edinbugrh Soft Matter and Statistical Physics Programme Grant Renewal
Cates, M., Poon, W., Ackland, G., Clegg, P., Evans, M., MacPhee, C. & Marenduzzo, D.
1/10/07 → 31/03/12
Project: Research