TY  - JOUR
A1  - Palyulin, Vladimir V.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Levy flights do not always optimize random blind search for sparse targets
JF  - Proceedings of the National Academy of Sciences of the United States of America
N2  - It is generally believed that random search processes based on scale-free, Levy stable jump length distributions (Levy flights) optimize the search for sparse targets. Here we show that this popular search advantage is less universal than commonly assumed. We study the efficiency of a minimalist search model based on Levy flights in the absence and presence of an external drift (underwater current, atmospheric wind, a preference of the walker owing to prior experience, or a general bias in an abstract search space) based on two different optimization criteria with respect to minimal search time and search reliability (cumulative arrival probability). Although Levy flights turn out to be efficient search processes when the target is far from the starting point, or when relative to the starting point the target is upstream, we show that for close targets and for downstream target positioning regular Brownian motion turns out to be the advantageous search strategy. Contrary to claims that Levy flights with a critical exponent alpha = 1 are optimal for the search of sparse targets in different settings, based on our optimization parameters the optimal a may range in the entire interval (1, 2) and especially include Brownian motion as the overall most efficient search strategy.
KW  - search optimization
KW  - stochastic processes
KW  - Levy foraging hypothesis
Y1  - 2014
U6  - https://doi.org/10.1073/pnas.1320424111
SN  - 0027-8424
VL  - 111
IS  - 8
SP  - 2931
EP  - 2936
PB  - National Acad. of Sciences
CY  - Washington
ER  - 
TY  - JOUR
A1  - Cherstvy, Andrey G.
A1  - Chechkin, Aleksei V.
A1  - Metzler, Ralf
T1  - Ageing and confinement in non-ergodic heterogeneous diffusion processes
JF  - Journal of physics : A, Mathematical and theoretical
N2  - We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
KW  - stochastic processes
KW  - anomalous diffusion
KW  - ageing
KW  - weak ergodicity breaking
Y1  - 2014
U6  - https://doi.org/10.1088/1751-8113/47/48/485002
SN  - 1751-8113
SN  - 1751-8121
VL  - 47
IS  - 48
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  -