Lévy walks

Asymptotic densities of ballistic Lévy walks

(2015) D. Froemberg et al.   PHYSICAL REVIEW E

Uncovering the Mechanism of Trapping and Cell Orientation during Neisseria gonorrhoeae Twitching Motility

(2014) Vasily Zaburdaev et al.   BIOPHYSICAL JOURNAL

Nonlinear Fluctuating Hydrodynamics for Anharmonic Chains

(2014) Herbert Spohn   JOURNAL OF STATISTICAL PHYSICS

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

(2014) Ralf Metzler et al.   PHYSICAL CHEMISTRY CHEMICAL PHYSICS

Walk dimension for light in complex disordered media

(2014) Romolo Savo et al.   PHYSICAL REVIEW A

Thermal interfacial transport in the presence of ballistic heat modes

(2014) Bjorn Vermeersch et al.   PHYSICAL REVIEW B

Signatures of Lévy flights with annealed disorder

(2014) Q. Baudouin et al.   PHYSICAL REVIEW E

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards

(2014) Giampaolo Cristadoro et al.   PHYSICAL REVIEW E

Infinite densities for Lévy walks

(2014) A. Rebenshtok et al.   PHYSICAL REVIEW E

Numerical test of hydrodynamic fluctuation theory in the Fermi-Pasta-Ulam chain

(2014) Suman G. Das et al.   PHYSICAL REVIEW E

Equilibrium time-correlation functions for one-dimensional hard-point systems

(2014) Christian B. Mendl et al.   PHYSICAL REVIEW E

Non-Normalizable Densities in Strong Anomalous Diffusion: Beyond the Central Limit Theorem

(2014) Adi Rebenshtok et al.   PHYSICAL REVIEW LETTERS

Anomalous Heat Diffusion

(2014) Sha Liu et al.   PHYSICAL REVIEW LETTERS

Tunable transport with broken space–time symmetries

(2014) Sergey Denisov et al.   PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS

How the Motility Pattern of Bacteria Affects Their Dispersal and Chemotaxis

(2014) Johannes Taktikos et al.   PLoS One

Leatherback Turtle Movements, Dive Behavior, and Habitat Characteristics in Ecoregions of the Northwest Atlantic Ocean

(2014) Kara L. Dodge et al.   PLoS One

Anomalous diffusion and multifractality enhance mating encounters in the ocean

(2014) Laurent Seuront et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Levy flights do not always optimize random blind search for sparse targets

(2014) V. V. Palyulin et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Hierarchical random walks in trace fossils and the origin of optimal search behavior

(2014) D. W. Sims et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Scaling laws of ambush predator 'waiting' behaviour are tuned to a common ecology

(2014) V. J. Wearmouth et al.   PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES

Colloquium: Fractional calculus view of complexity: A tutorial

(2014) Bruce J. West   REVIEWS OF MODERN PHYSICS

Bacterial twitching motility is coordinated by a two-dimensional tug-of-war with directional memory

(2014) Rahul Marathe et al.   Nature Communications

From the Area under the Bessel Excursion to Anomalous Diffusion of Cold Atoms

(2014) E. Barkai et al.   Physical Review X

Scaling Green-Kubo Relation and Application to Three Aging Systems

(2014) A. Dechant et al.   Physical Review X

Aging Renewal Theory and Application to Random Walks

(2014) Johannes H. P. Schulz et al.   Physical Review X

Random walk analysis of ranging patterns of sympatric langurs in a complex resource landscape

(2013) Rajnish Vandercone et al.   AMERICAN JOURNAL OF PRIMATOLOGY

Recurrent patterning in the daily foraging routes of hamadryas baboons (Papio hamadryas): Spatial memory in large-scale versus small-scale space

(2013) Amy L. Schreier et al.   AMERICAN JOURNAL OF PRIMATOLOGY

Spatial foraging in free ranging bearded sakis: Traveling salesmen or Lévy walkers?

(2013) Christopher A. Shaffer   AMERICAN JOURNAL OF PRIMATOLOGY

A Bacterial Swimmer with Two Alternating Speeds of Propagation

(2013) Matthias Theves et al.   BIOPHYSICAL JOURNAL

Random walk modeling of adult Leuctra ferruginea (stonefly) dispersal

(2013) James Knighton et al.   Ecological Informatics

Random time averaged diffusivities for Lévy walks

(2013) D. Froemberg et al.   EUROPEAN PHYSICAL JOURNAL B

The Lévy flight foraging hypothesis in a pelagic seabird

(2013) Stefano Focardi et al.   JOURNAL OF ANIMAL ECOLOGY

Does the Australian desert ant Melophorus bagoti approximate a Lévy search by an intrinsic bi-modal walk?

(2013) Andy M. Reynolds et al.   JOURNAL OF THEORETICAL BIOLOGY

Beyond Boltzmann–Gibbs statistical mechanics in optical lattices

(2013) Eric Lutz et al.   Nature Physics

Time-averaged Einstein relation and fluctuating diffusivities for the Lévy walk

(2013) D. Froemberg et al.   PHYSICAL REVIEW E

Linear response, fluctuation-dissipation, and finite-system-size effects in superdiffusion

(2013) Aljaž Godec et al.   PHYSICAL REVIEW E

Exact solution of a Lévy walk model for anomalous heat transport

(2013) Abhishek Dhar et al.   PHYSICAL REVIEW E

Finite-Time Effects and Ultraweak Ergodicity Breaking in Superdiffusive Dynamics

(2013) Aljaž Godec et al.   PHYSICAL REVIEW LETTERS

Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories

(2013) Yasmine Meroz et al.   PHYSICAL REVIEW LETTERS

Flow Intermittency, Dispersion, and Correlated Continuous Time Random Walks in Porous Media

(2013) Pietro de Anna et al.   PHYSICAL REVIEW LETTERS

Space-Time Velocity Correlation Function for Random Walks

(2013) V. Zaburdaev et al.   PHYSICAL REVIEW LETTERS

Fractional motions

(2013) Iddo I. Eliazar et al.   PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS

Scavengers on the Move: Behavioural Changes in Foraging Search Patterns during the Annual Cycle

(2013) Pascual López-López et al.   PLoS One

Constructing a Stochastic Model of Bumblebee Flights from Experimental Data

(2013) Friedrich Lenz et al.   PLoS One

Evidence of Levy walk foraging patterns in human hunter-gatherers

(2013) D. A. Raichlen et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

The Hidden Geometry of Complex, Network-Driven Contagion Phenomena

(2013) D. Brockmann et al.   SCIENCE

Optimisation and mathematical explanation: doing the Lévy Walk

(2013) Sam Baron   SYNTHESE

A new approach for objective identification of turns and steps in organism movement data relevant to random walk modelling

(2013) Nicolas E. Humphries et al.   Methods in Ecology and Evolution

Movement patterns of Tenebrio beetles demonstrate empirically that correlated-random-walks have similitude with a Lévy walk

(2013) Andy M. Reynolds et al.   Scientific Reports

Finding food: outbound searching behavior in the Australian desert ant Melophorus bagoti

(2012) Patrick Schultheiss et al.   BEHAVIORAL ECOLOGY

Anomalous heat conduction and anomalous diffusion in low dimensional nanoscale systems

(2012) S. Liu et al.   EUROPEAN PHYSICAL JOURNAL B

On the Critical Delays of Mobile Networks Under Lévy Walks and Lévy Flights

(2012) Kyunghan Lee et al.   IEEE-ACM TRANSACTIONS ON NETWORKING

Langevin Picture of Lévy Walks and Their Extensions

(2012) Marcin Magdziarz et al.   JOURNAL OF STATISTICAL PHYSICS

Frigatebird behaviour at the ocean-atmosphere interface: integrating animal behaviour with multi-satellite data

(2012) S. De Monte et al.   Journal of the Royal Society Interface

Generalized Lévy walks and the role of chemokines in migration of effector CD8+ T cells

(2012) Tajie H. Harris et al.   NATURE

Langevin description of superdiffusive Lévy processes

(2012) S. Eule et al.   PHYSICAL REVIEW E

Lévy walks with velocity fluctuations

(2012) S. Denisov et al.   PHYSICAL REVIEW E

Anomalous diffusion in run-and-tumble motion

(2012) Felix Thiel et al.   PHYSICAL REVIEW E

Erratum: Perturbation Spreading in Many-Particle Systems: A Random Walk Approach [Phys. Rev. Lett.106, 180601 (2011)]

(2012) V. Zaburdaev et al.   PHYSICAL REVIEW LETTERS

Weak Localization of Light in Superdiffusive Random Systems

(2012) Matteo Burresi et al.   PHYSICAL REVIEW LETTERS

Distributional Response to Biases in Deterministic Superdiffusion

(2012) Takuma Akimoto   PHYSICAL REVIEW LETTERS

Optimizing Persistent Random Searches

(2012) Vincent Tejedor et al.   PHYSICAL REVIEW LETTERS

Theory of Fractional Lévy Kinetics for Cold Atoms Diffusing in Optical Lattices

(2012) David A. Kessler et al.   PHYSICAL REVIEW LETTERS

Exact Results for Anomalous Transport in One-Dimensional Hamiltonian Systems

(2012) Henk van Beijeren   PHYSICAL REVIEW LETTERS

Observation of Anomalous Diffusion and Fractional Self-Similarity in One Dimension

(2012) Yoav Sagi et al.   PHYSICAL REVIEW LETTERS

Lévy walk description of suprathermal ion transport

(2012) K. Gustafson et al.   PHYSICS OF PLASMAS

Dance of the microswimmers

(2012) Eric Lauga et al.   PHYSICS TODAY

Foraging success of biological Levy flights recorded in situ

(2012) N. E. Humphries et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

High-throughput lensfree 3D tracking of human sperms reveals rare statistics of helical trajectories

(2012) T.-W. Su et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Comment on "Levy Walks Evolve Through Interaction Between Movement and Environmental Complexity"

(2012) V. A. A. Jansen et al.   SCIENCE

Fractional governing equations for coupled random walks

(2011) A. Jurlewicz et al.   COMPUTERS & MATHEMATICS WITH APPLICATIONS

On the Levy-Walk Nature of Human Mobility

(2011) Injong Rhee et al.   IEEE-ACM TRANSACTIONS ON NETWORKING

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

(2011) Ring T. Cardé et al.   JOURNAL OF ANIMAL ECOLOGY

Local and average behaviour in inhomogeneous superdiffusive media

(2011) Alessandro Vezzani et al.   PHILOSOPHICAL MAGAZINE

Transport and scaling in quenched two- and three-dimensional Lévy quasicrystals

(2011) P. Buonsante et al.   PHYSICAL REVIEW E

Fractional Feynman-Kac equation for weak ergodicity breaking

(2011) Shai Carmi et al.   PHYSICAL REVIEW E

Density profiles in open superdiffusive systems

(2011) Stefano Lepri et al.   PHYSICAL REVIEW E

In VivoAnomalous Diffusion and Weak Ergodicity Breaking of Lipid Granules

(2011) Jae-Hyung Jeon et al.   PHYSICAL REVIEW LETTERS

Perturbation Spreading in Many-Particle Systems: A Random Walk Approach

(2011) V. Zaburdaev et al.   PHYSICAL REVIEW LETTERS

Langevin Dynamics Deciphers the Motility Pattern of Swimming Parasites

(2011) Vasily Zaburdaev et al.   PHYSICAL REVIEW LETTERS

On the Origin and Characteristics of Noise-Induced Lévy Walks of E. Coli

(2011) Franziska Matthäus et al.   PLoS One

Variation in individual walking behavior creates the impression of a Levy flight

(2011) S. Petrovskii et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis

(2011) L. Xie et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Ergodic and nonergodic processes coexist in the plasma membrane as observed by single-molecule tracking

(2011) A. V. Weigel et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Bacteria use type-IV pili to slingshot on surfaces

(2011) F. Jin et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

High activity and Levy searches: jellyfish can search the water column like fish

(2011) G. C. Hays et al.   PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES

Intermittent search strategies

(2011) O. Bénichou et al.   REVIEWS OF MODERN PHYSICS

Levy Walks Evolve Through Interaction Between Movement and Environmental Complexity

(2011) M. de Jager et al.   SCIENCE

Engineering Disorder in Superdiffusive Lévy Glasses

(2010) Jacopo Bertolotti et al.   ADVANCED FUNCTIONAL MATERIALS

Role of quenching on superdiffusive transport in two-dimensional random media

(2010) Pierre Barthelemy et al.   PHYSICAL REVIEW E

Lévy walks and scaling in quenched disordered media

(2010) Raffaella Burioni et al.   PHYSICAL REVIEW E

Poincaré recurrences in Hamiltonian systems with a few degrees of freedom

(2010) D. L. Shepelyansky   PHYSICAL REVIEW E

Experimental evidence of strong anomalous diffusion in living cells

(2010) Naama Gal et al.   PHYSICAL REVIEW E

Bacterial strategies for chemotaxis response

(2010) A. Celani et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Bacteria Use Type IV Pili to Walk Upright and Detach from Surfaces: Fig. 1

(2010) Maxsim L. Gibiansky et al.   SCIENCE

Lagging and leading coupled continuous time random walks, renewal times and their joint limits

(2010) P. Straka et al.   STOCHASTIC PROCESSES AND THEIR APPLICATIONS

Sampling rate and misidentification of Lévy and non-Lévy movement paths

(2009) Michael J. Plank et al.   ECOLOGY

Random searching

(2009) Michael F Shlesinger   Journal of Physics A-Mathematical and Theoretical

Lévy-taxis: a novel search strategy for finding odor plumes in turbulent flow-dominated environments

(2009) Zohar Pasternak et al.   Journal of Physics A-Mathematical and Theoretical

On moments and scaling regimes in anomalous random walks

(2009) Michael Schmiedeberg et al.   JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Non-local observables and lightcone-averaging in relativistic thermodynamics

(2009) Jörn Dunkel et al.   Nature Physics

Lévy flights of photons in hot atomic vapours

(2009) N. Mercadier et al.   Nature Physics

Nonalgebraic length dependence of transmission through a chain of barriers with a Lévy spacing distribution

(2009) C. W. J. Beenakker et al.   PHYSICAL REVIEW B

Continuous-time multidimensional Markovian description of Lévy walks

(2009) Ihor Lubashevsky et al.   PHYSICAL REVIEW E

Realization of Lévy walks as Markovian stochastic processes

(2009) Ihor Lubashevsky et al.   PHYSICAL REVIEW E

Universality of Algebraic Laws in Hamiltonian Systems

(2009) Roberto Venegeroles   PHYSICAL REVIEW LETTERS

Fractional Feynman-Kac Equation for Non-Brownian Functionals

(2009) Lior Turgeman et al.   PHYSICAL REVIEW LETTERS

Fractional Brownian Motion Versus the Continuous-Time Random Walk: A Simple Test for Subdiffusive Dynamics

(2009) Marcin Magdziarz et al.   PHYSICAL REVIEW LETTERS

Relativistic Brownian motion

(2009) Jörn Dunkel et al.   PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS

Beyond quantum jumps: Blinking nanoscale light emitters

(2009) Fernando D. Stefani et al.   PHYSICS TODAY

Adaptive Lévy Walks in Foraging Fallow Deer

(2009) Stefano Focardi et al.   PLoS One

Power-Law Distributions in Empirical Data

(2009) Aaron Clauset et al.   SIAM REVIEW

Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems

(2008) Bruno Nachtergaele et al.   COMMUNICATIONS IN MATHEMATICAL PHYSICS

Cell motility as random motion: A review

(2008) D. Selmeczi et al.   European Physical Journal-Special Topics

Anomalous transport in a one-dimensional Lorentz gas model

(2008) S. Eule et al.   JOURNAL OF CHEMICAL PHYSICS

Microscopic Approach to Random Walks

(2008) Vasily Yu. Zaburdaev   JOURNAL OF STATISTICAL PHYSICS

Weakly Non-Ergodic Statistical Physics

(2008) A. Rebenshtok et al.   JOURNAL OF STATISTICAL PHYSICS

Anomalous diffusion of heterogeneous populations characterized by normal diffusion at the individual level

(2008) S. Hapca et al.   Journal of the Royal Society Interface

Ecological modelling: The mathematical mirror to animal nature

(2008) Mark Buchanan   NATURE

Scaling laws of marine predator search behaviour

(2008) David W. Sims et al.   NATURE

Understanding individual human mobility patterns

(2008) Marta C. González et al.   NATURE

A Lévy flight for light

(2008) Pierre Barthelemy et al.   NATURE

Random walks with random velocities

(2008) Vasily Zaburdaev et al.   PHYSICAL REVIEW E

Universality of Algebraic Decays in Hamiltonian Systems

(2008) G. Cristadoro et al.   PHYSICAL REVIEW LETTERS

Nonergodicity Mimics Inhomogeneity in Single Particle Tracking

(2008) Ariel Lubelski et al.   PHYSICAL REVIEW LETTERS

Random Time-Scale Invariant Diffusion and Transport Coefficients

(2008) Y. He et al.   PHYSICAL REVIEW LETTERS

Persistent Cell Motion in the Absence of External Signals: A Search Strategy for Eukaryotic Cells

(2008) Liang Li et al.   PLoS One

Functional Analysis of Spontaneous Cell Movement under Different Physiological Conditions

(2008) Hiroaki Takagi et al.   PLoS One

Fractal Materials and Their Functional Properties

(2008) Kaoru Tsujii   POLYMER JOURNAL

Anomalous dynamics of cell migration

(2008) P. Dieterich et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Levy strategies in intermittent search processes are advantageous

(2008) M. A. Lomholt et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA