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 - 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 - 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 - 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 -