TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Metzler, Ralf
T1  - How a finite potential barrier decreases the mean first-passage time
JF  - Journal of statistical mechanics: theory and experiment
N2  - We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.
KW  - diffusion
Y1  - 2012
U6  - https://doi.org/10.1088/1742-5468/2012/03/L03001
SN  - 1742-5468
IS  - 1
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Magdziarz, Marcin
A1  - Metzler, Ralf
A1  - Szczotka, Wladyslaw
A1  - Zebrowski, Piotr
T1  - Correlated continuous-time random walks-scaling limits and Langevin picture
JF  - Journal of statistical mechanics: theory and experiment
N2  - In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations.
KW  - stochastic processes (theory)
KW  - diffusion
Y1  - 2012
U6  - https://doi.org/10.1088/1742-5468/2012/04/P04010
SN  - 1742-5468
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -