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 - https://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 - 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 Levy flights and Levy walks JF - New journal of physics : the open-access journal for physics 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. KW - Levy flights KW - Levy walks KW - first-passage time KW - first-hitting time Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab41bb SN - 1367-2630 VL - 21 IS - 10 PB - IOP Publ. Ltd. CY - Bristol 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 - 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 - 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 - 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 - 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 - https://doi.org/10.1088/1742-5468/2012/03/L03001 SN - 1742-5468 IS - 1 PB - IOP Publ. Ltd. CY - Bristol 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 - https://doi.org/10.1088/1742-5468/2014/11/P11031 SN - 1742-5468 PB - IOP Publ. Ltd. CY - Bristol 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 - https://doi.org/10.1039/c4sm01819b SN - 1744-683X SN - 1744-6848 VL - 10 IS - 45 SP - 9016 EP - 9037 PB - Royal Society of Chemistry CY - Cambridge ER - 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 - 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 - 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 JF - New Journal of Physics 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. KW - Lévy flights KW - Lévy walks KW - first-passage time KW - first-hitting time Y1 - 2019 U6 - https://doi.org/10.1088/1367-2630/ab41bb SN - 1367-2630 VL - 21 PB - Dt. Physikalische Ges. CY - Bad Honnef 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 -