TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Metzler, Ralf
T1  - Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We show that for a subdiffusive continuous time random walk with scale-free waiting time distribution the first-passage dynamics on a finite interval can be optimized by introduction of a piecewise linear potential barrier. Analytical results for the survival probability and first-passage density based on the fractional Fokker-Planck equation are shown to agree well with Monte Carlo simulations results. As an application we discuss an improved design for efficient translocation of gradient copolymers compared to homopolymer translocation in a quasi-equilibrium approximation.
KW  - first passage
KW  - anomalous diffusion
KW  - potential landscape
KW  - polymer translocation
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/3/032002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 3
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Chechkin, Aleksei V.
A1  - Klages, Rainer
A1  - Metzler, Ralf
T1  - Search reliability and search efficiency of combined Levy-Brownian motion: long relocations mingled with thorough local exploration
JF  - Journal of physics : A, Mathematical and theoretical
N2  - A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the search reliability of ever locating the target and the search efficiency of doing so economically of such dynamics thus poses an important problem. Here we model this dynamics by a one-dimensional fractional Fokker-Planck equation combining unbiased Brownian motion and Levy flights. By solving this equation both analytically and numerically we show that the superposition of recurrent Brownian motion and Levy flights with stable exponent alpha < 1, by itself implying zero probability of hitting a point on a line, leads to transient motion with finite probability of hitting any point on the line. We present results for the exact dependence of the values of both the search reliability and the search efficiency on the distance between the starting and target positions as well as the choice of the scaling exponent a of the Levy flight component.
KW  - random search process
KW  - first passage
KW  - first arrival
KW  - Levy flights
KW  - Brownian motion
Y1  - 2016
U6  - https://doi.org/10.1088/1751-8113/49/39/394002
SN  - 1751-8113
SN  - 1751-8121
VL  - 49
SP  - 2189
EP  - 2193
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -