38146
2014
2014
eng
13
3
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Speeding up the first-passage for subdiffusion by introducing a finite potential barrier
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.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/3/032002
1751-8113 (print)
1751-8121 (online)
wos:2014
032002
WOS:000329042400002
Palyulin, VV (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA2042/1-1]; Academy of Finland within
the FiDiPro scheme
Vladimir V. Palyulin
Ralf Metzler
eng
uncontrolled
first passage
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
potential landscape
eng
uncontrolled
polymer translocation
Institut für Physik und Astronomie
Referiert
36072
2012
2012
eng
10
1
article
IOP Publ. Ltd.
Bristol
1
--
--
--
How a finite potential barrier decreases the mean first-passage time
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.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2012/03/L03001
1742-5468 (print)
wos:2011-2013
L03001
WOS:000302246400002
Palyulin, VV (reprint author), Tech Univ Munich, Dept Phys, D-85747 Garching, Germany., vladimir.palyulin@tum.de; rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Academy of Finland
Vladimir V. Palyulin
Ralf Metzler
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
46386
2017
2017
eng
20
37
16
90
article
Springer
New York
1
--
--
--
Comparison of pure and combined search strategies for single and multiple targets
We address the generic problem of random search for a point-like target on a line. Using the measures of search reliability and efficiency to quantify the random search quality, we compare Brownian search with Levy search based on long-tailed jump length distributions. We then compare these results with a search process combined of two different long-tailed jump length distributions. Moreover, we study the case of multiple targets located by a Levy searcher.
The European physical journal : B, Condensed matter and complex systems
10.1140/epjb/e2017-80372-4
1434-6028
1434-6036
wos:2017
170
WOS:000411061000008
Chechkin, AV (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany.; Chechkin, AV (reprint author), Akhiezer Inst Theoret Phys NSC KIPT, UA-61108 Kharkov, Ukraine., achechkin@kipt.kharkov.ua
RF President Grant for young scientists [MD-4550.2016.2]; Deutsche Forschungsgemeinschaft through Project "Random search processes, Levy flights, and random walks on complex networks" [ME 1535/6-1]
importub
2020-04-20T01:02:01+00:00
filename=package.tar
c840dc6e95c2b3c2372a84225ae4f80e
Vladimir V. Palyulin
Vladimir N. Mantsevich
Rainer Klages
Ralf Metzler
Aleksei V. Chechkin
Institut für Physik und Astronomie
Referiert
Import
38043
2014
2014
eng
2931
2936
6
8
111
article
National Acad. of Sciences
Washington
1
--
--
--
Levy flights do not always optimize random blind search for sparse targets
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.
Proceedings of the National Academy of Sciences of the United States of America
10.1073/pnas.1320424111
24516153
0027-8424 (print)
wos:2014
WOS:000332180900022
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland
(FiDiPro scheme)
Vladimir V. Palyulin
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
search optimization
eng
uncontrolled
stochastic processes
eng
uncontrolled
Levy foraging hypothesis
Institut für Physik und Astronomie
Referiert
37424
2014
2014
eng
32
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
Based on the space-fractional Fokker-Planck equation with a delta-sink term, we study the efficiency of random search processes based on Levy flights with power-law distributed jump lengths in the presence of an external drift, for instance, an underwater current, an airflow, or simply the preference of the searcher based on prior experience. While Levy flights turn out to be efficient search processes when the target is upstream relative to the starting point, in the downstream scenario, regular Brownian motion turns out to be advantageous. This is caused by the occurrence of leapovers of Levy flights, due to which Levy flights typically overshoot a point or small interval. Studying the solution of the fractional Fokker-Planck equation, we establish criteria when the combination of the external stream and the initial distance between the starting point and the target favours Levy flights over the regular Brownian search. Contrary to the common belief that Levy flights with a Levy index alpha = 1 (i.e. Cauchy flights) are optimal for sparse targets, we find that the optimal value for alpha may range in the entire interval (1, 2) and explicitly include Brownian motion as the most efficient search strategy overall.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2014/11/P11031
1742-5468 (print)
wos:2014
P11031
WOS:000345747600031
Palyulin, VV (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland within
the FiDiPro scheme; DAAD
Vladimir V. Palyulin
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
driven diffusive systems (theory)
eng
uncontrolled
fluctuations (theory)
eng
uncontrolled
stochastic processes (theory)
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
44938
2016
2016
eng
2189
2193
21
49
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Search reliability and search efficiency of combined Levy-Brownian motion: long relocations mingled with thorough local exploration
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.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/49/39/394002
1751-8113
1751-8121
wos2016:2019
394002
WOS:000383516400003
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany.; Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FIN-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Academy of Finland
importub
2020-03-22T14:21:01+00:00
filename=package.tar
da1796f72265136a5d102ef03603eb93
Vladimir V. Palyulin
Aleksei V. Chechkin
Rainer Klages
Ralf Metzler
eng
uncontrolled
random search process
eng
uncontrolled
first passage
eng
uncontrolled
first arrival
eng
uncontrolled
Levy flights
eng
uncontrolled
Brownian motion
Institut für Physik und Astronomie
Referiert
Import
7628
2014
2014
eng
9016
9037
postprint
1
2015-04-30
2014-09-19
--
Polymer translocation: the first two decades and the recent diversification
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.
urn:nbn:de:kobv:517-opus4-76287
online registration
Au-006426
Soft Matter, 2014, 10, 9016-9037. DOI: 10.1039/C4SM01819B
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7626">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Vladimir V. Palyulin
Tapio Ala-Nissila
Ralf Metzler
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
179
eng
uncontrolled
solid-state nanopores
eng
uncontrolled
single-stranded-dna
eng
uncontrolled
posttranslational protein translocation
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
monte-carlo
eng
uncontrolled
structured polynucleotides
eng
uncontrolled
dynamics simulation
eng
uncontrolled
equation approach
eng
uncontrolled
osmotic-pressure
eng
uncontrolled
membrane channel
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/7628/pmnr179.pdf
7626
2014
eng
9016
9037
22
10
45
article
the Royal Society of Chemistry
Cambridge
1
--
2014-09-19
--
Polymer translocation: the first two decades and the recent diversification
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.
Soft matter
1744-683X
urn:nbn:de:kobv:517-opus4-76266
online registration
Au-006426
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76287">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Humanwissenschaftliche Reihe ; 179 </a>
Vladimir V. Palyulin
Tapio Ala-Nissila
Ralf Metzler
eng
uncontrolled
solid-state nanopores
eng
uncontrolled
single-stranded-dna
eng
uncontrolled
posttranslational protein translocation
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
monte-carlo
eng
uncontrolled
structured polynucleotides
eng
uncontrolled
dynamics simulation
eng
uncontrolled
equation approach
eng
uncontrolled
osmotic-pressure
eng
uncontrolled
membrane channel
Physik
Institut für Physik und Astronomie
Referiert
Open Access
RSC
38210
2014
2014
eng
9016
9037
22
45
10
review
Royal Society of Chemistry
Cambridge
1
--
--
--
Polymer translocation: the first two decades and the recent diversification
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.
Soft matter
10.1039/c4sm01819b
25301107
1744-683X (print)
1744-6848 (online)
wos:2014
WOS:000344469700001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft [PA 2042/1-1]; Academy of Finland
(FiDiPro scheme); Academy of Finland through its COMP Center of
Excellence [251748]
Vladimir V. Palyulin
Tapio Ala-Nissila
Ralf Metzler
Institut für Physik und Astronomie
Referiert
43983
2019
2019
eng
25
785
postprint
1
2019-12-04
2019-12-04
--
First passage and first hitting times of Lévy flights and Lévy walks
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.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-43983
urn:nbn:de:kobv:517-opus4-439832
1866-8372
New Journal of Physics 21 (2019) 103028 DOI: 10.1088/1367-2630/ab41bb
103028
<a href="http://publishup.uni-potsdam.de/43982">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Vladimir V Palyulin
George Blackburn
Michael A Lomholt
Nicholas W Watkins
Ralf Metzler
Rainer Klages
Aleksei V. Chechkin
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
785
eng
uncontrolled
Lévy flights
eng
uncontrolled
Lévy walks
eng
uncontrolled
first-passage time
eng
uncontrolled
first-hitting time
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/43983/pmnr785.pdf