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 - http://dx.doi.org/10.1088/1751-8113/47/3/032002
SN - 1751-8113 (print)
SN - 1751-8121 (online)
VL - 47
IS - 3
PB - IOP Publ. Ltd.
CY - Bristol
ER -
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 - http://dx.doi.org/10.1088/1742-5468/2012/03/L03001
SN - 1742-5468 (print)
IS - 1
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Mantsevich, Vladimir N.
A1 - Klages, Rainer
A1 - Metzler, Ralf
A1 - Chechkin, Aleksei V.
T1 - Comparison of pure and combined search strategies for single and multiple targets
JF - The European physical journal : B, Condensed matter and complex systems
N2 - 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.
Y1 - 2017
U6 - http://dx.doi.org/10.1140/epjb/e2017-80372-4
SN - 1434-6028
SN - 1434-6036
VL - 90
SP - 20
EP - 37
PB - Springer
CY - New York
ER -
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 - http://dx.doi.org/10.1073/pnas.1320424111
SN - 0027-8424 (print)
VL - 111
IS - 8
SP - 2931
EP - 2936
PB - National Acad. of Sciences
CY - Washington
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Chechkin, Aleksei V.
A1 - Metzler, Ralf
T1 - Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - driven diffusive systems (theory)
KW - fluctuations (theory)
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2014
U6 - http://dx.doi.org/10.1088/1742-5468/2014/11/P11031
SN - 1742-5468 (print)
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 - http://dx.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 -
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 - Postprints 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 -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Ala-Nissila, Tapio
A1 - Metzler, Ralf
ED - Metzler, Ralf
T1 - Polymer translocation: the first two decades and the recent diversification
JF - Soft matter
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.
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-opus4-76266
SN - 1744-683X
VL - 45
IS - 10
SP - 9016
EP - 9037
PB - the Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Ala-Nissila, Tapio
A1 - Metzler, Ralf
T1 - Polymer translocation: the first two decades and the recent diversification
JF - Soft matter
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.
Y1 - 2014
U6 - http://dx.doi.org/10.1039/c4sm01819b
SN - 1744-683X (print)
SN - 1744-6848 (online)
VL - 10
IS - 45
SP - 9016
EP - 9037
PB - Royal Society of Chemistry
CY - Cambridge
ER -
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 - Postprints 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 -