TY  - GEN
A1  - Palyulin, Vladimir V
A1  - Blackburn, George
A1  - Lomholt, Michael A
A1  - Watkins, Nicholas W
A1  - Metzler, Ralf
A1  - Klages, Rainer
A1  - Chechkin, Aleksei V.
T1  - First passage and first hitting times of Lévy flights and Lévy walks
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - For both Lévy flight and Lévy walk search processes we analyse the full distribution of first-passage and first-hitting (or first-arrival) times. These are, respectively, the times when the particle moves across a point at some given distance from its initial position for the first time, or when it lands at a given point for the first time. For Lévy motions with their propensity for long relocation events and thus the possibility to jump across a given point in space without actually hitting it ('leapovers'), these two definitions lead to significantly different results. We study the first-passage and first-hitting time distributions as functions of the Lévy stable index, highlighting the different behaviour for the cases when the first absolute moment of the jump length distribution is finite or infinite. In particular we examine the limits of short and long times. Our results will find their application in the mathematical modelling of random search processes as well as computer algorithms.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 785 
KW  - Lévy flights
KW  - Lévy walks
KW  - first-passage time
KW  - first-hitting time
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-439832
SN  - 1866-8372
IS  - 785
ER  - 
TY  - GEN
A1  - Palyulin, Vladimir V.
A1  - Ala-Nissila, Tapio
A1  - Metzler, Ralf
T1  - Polymer translocation: the first two decades and the recent diversification
N2  - Probably no other field of statistical physics at the borderline of soft matter and biological physics has caused such a flurry of papers as polymer translocation since the 1994 landmark paper by Bezrukov, Vodyanoy, and Parsegian and the study of Kasianowicz in 1996. Experiments, simulations, and theoretical approaches are still contributing novel insights to date, while no universal consensus on the statistical understanding of polymer translocation has been reached. We here collect the published results, in particular, the famous–infamous debate on the scaling exponents governing the translocation process. We put these results into perspective and discuss where the field is going. In particular, we argue that the phenomenon of polymer translocation is non-universal and highly sensitive to the exact specifications of the models and experiments used towards its analysis.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 179 
KW  - solid-state nanopores
KW  - single-stranded-dna
KW  - posttranslational protein translocation
KW  - anomalous diffusion
KW  - monte-carlo
KW  - structured polynucleotides
KW  - dynamics simulation
KW  - equation approach
KW  - osmotic-pressure
KW  - membrane channel
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-76287
SP  - 9016
EP  - 9037
ER  -