Random walks with self-similar clusters.

No abstract is available for this paper.

• Publication year

  1981

• Venue

  Proceedings of the National Academy of Sciences of the United States of America

• Publication date

  1981-06-01

• Fields of study

  Medicine, Physics, Mathematics

• Identifiers
  DOI 10.1073/PNAS.78.6.3287PMID 16593023PMCID PMC319551
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Fractals: Form, Chance and Dimension

  1978cited by this paper
• Squaring the circle and other monographs

  1969cited by this paper
• Handbook of series for scientists and engineers

  1965cited by this paper
• An Introduction to Probability Theory and Its Applications

  1959cited by this paper
• The theory and construction of non-differentiable functions

  1935cited by this paper

• Pre-asymptotic analysis of Lévy flights.

  2024cites this paper
• Change-point detection in anomalous-diffusion trajectories utilising machine-learning-based uncertainty estimates

  2024cites this paper
• Fractional Extended Diffusion Theory to capture anomalous relaxation from biased/accelerated molecular simulations.

  2024cites this paper
• A stochastic model of discussion

  2024cites this paper
• Machine-Learning Solutions for the Analysis of Single-Particle Diffusion Trajectories

  2023cites this paper
• A 2D Lévy-flight model for the complex dynamics of real-life financial markets.

  2022cites this paper
• Bayesian deep learning for error estimation in the analysis of anomalous diffusion

  2022cites this paper
• Weierstrassian Lévy walks are a by-product of crawling

  2021cites this paper
• Landscape-scaled strategies can outperform Lévy random searches.

  2021cites this paper
• (2020). Exact spatio-temporal dynamics of confined lattice random walks in arbitrary dimensions: a century after Smoluchowski and Polya. Physical

  2020cites this paper
• Tight Bounds for the Cover Times of Random Walks with Heterogeneous Step Lengths

  2020cites this paper
• On the Search Efficiency of Parallel Lévy Walks on ${\mathbb Z}^2$

  2020cites this paper
• On the Search Efficiency of Parallel Lévy Walks on Z2

  2020cites this paper
• The Difference-Quotient Turbulence Model (DQTM)

  2020cites this paper
• Exact Spatiotemporal Dynamics of Confined Lattice Random Walks in Arbitrary Dimensions: A Century after Smoluchowski and Pólya

  2020cites this paper
• Extended Poisson-Kac Theory: A Unifying Framework for Stochastic Processes with Finite Propagation Velocity

  2020cites this paper
• Lévy Walks and Path Chaos in the Dispersal of Elongated Structures Moving across Cellular Vortical Flows.

  2020cites this paper
• Active L\'evy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability

  2019cites this paper
• Hydrodynamics of Active L\'evy Matter

  2019cites this paper
• Loopy Lévy flights enhance tracer diffusion in active suspensions

  2019cites this paper
• Hydrodynamics of Active Lévy Matter

  2019cites this paper
• Lévy foraging patterns of rural humans

  2018cites this paper
• Subdiffusive continuous-time random walks with stochastic resetting.

  2018cites this paper
• Weak Galilean invariance as a selection principle for coarse-grained diffusive models

  2018cites this paper
• Nonlinear Response on External Electric Field and Nonlinear Generalization of Fluctuation-Dissipation Theorem for Levy Flights

  2018cites this paper
• Entanglement entropy on finitely ramified graphs

  2018cites this paper
• Chaotic Model for Lévy Walks in Swarming Bacteria.

  2017cites this paper
• The evolutionary origins of Lévy walk foraging

  2017cites this paper
• N-glycosylation enables high lateral mobility of GPI-anchored proteins at a molecular crowding threshold

  2016cites this paper
• Functional equation for the crossover in the model of one-dimensional Weierstrass random walks

  2016cites this paper
• Signatures of chaos in animal search patterns

  2016cites this paper
• Functional equation for the crossover in the model of one-dimensional Weierstrass random walks

  2016cites this paper
• A correspondence principle

  2016influential citation
• Understanding movements of organisms: it's time to abandon the Lévy foraging hypothesis

  2015cites this paper
• A ug 2 01 5 First-passage times in multi-scale random walks : the impact of movement scales on search efficiency

  2015cites this paper
• Long-range dispersal, stochasticity and the broken accelerating wave of advance.

  2015cites this paper
• First-passage times in multiscale random walks: The impact of movement scales on search efficiency.

  2015cites this paper
• Liberating Lévy walk research from the shackles of optimal foraging.

  2015cites this paper
• Exploring models in population biology through the simulation of species invasions, natural selection and market-mediated gene flow

  2015cites this paper
• Fluctuation Modeling of Macroscopic Cross Section with Spatial Correlation

  2014cites this paper
• Superdiffusion driven by exponentially decaying memory

  2014cites this paper
• Mussels realize Weierstrassian Lévy walks as composite correlated random walks

  2014influential citation
• Lévy flights with power-law absorption.

  2014cites this paper
• Crime Modeling with Lévy Flights

  2013cites this paper
• Geometry and field theory in multi-fractional spacetime

  2012cites this paper
• Lévy flights and multifractality in quantum critical diffusion and in classical random walks on fractals.

  2012cites this paper
• Spatial log-periodic oscillations of first-passage observables in fractals.

  2012cites this paper
• ON THE ENSEMBLE AVERAGE OF GENERALIZED TRUNCATED RANDOM WALK

  2012cites this paper
• Statistical Mechanics and Quantum Fields on Fractals

  2012cites this paper
• Evolution of optimal Lévy-flight strategies in human mental searches

  2012cites this paper
• Heat kernels and zeta functions on fractals

  2012cites this paper
• CRIME MODELLING WITH LÉVY FLIGHTS AND THE STABILITY OF HOT-SPOT PATTERNS

  2012cites this paper
• The Effects of Laminar Mixing on Reaction Fronts and Patterns

  2011cites this paper
• Rationality, Irrationality and Escalating Behavior in Lowest Unique Bid Auctions

  2011cites this paper
• Estructuras espacio-temporales en sistemas de reacción-difusión-advención

  2011cites this paper
• Competition between quenched disorder and long-range connections: a numerical study of diffusion.

  2011cites this paper
• Geometry and field theory in multi-fractional spacetime

  2011cites this paper
• Fractal Pharmacokinetics

  2010cites this paper
• Hierarchical networks of regular degree

  2010cites this paper
• The quantum Lévy walk

  2010cites this paper
• For Review O nly

  2010cites this paper
• Observation of log-periodic oscillations in the quantum dynamics of electrons on the one-dimensional Fibonacci quasicrystal

  2010cites this paper
• Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: exact results

  2009cites this paper
• Computer simulation study of the Levy flight process

  2009cites this paper
• Nonlocal transport in the reversed field pinch

  2009cites this paper
• Anomalous diffusion on the Hanoi networks

  2008cites this paper
• Superdiffusive wave front propagation in a chemical active flow

  2008cites this paper
• ON THE GENERAL RANDOM WALK FORMULATION FOR DIFFUSION IN MEDIA WITH MULTIPLE DIFFUSIVITIES

  2008cites this paper
• Geometry and dynamics for hierarchical regular networks

  2008cites this paper
• Superdiffusion in a class of networks with marginal long-range connections.

  2008cites this paper
• Random walks on the Comb model and its generalizations.

  2007cites this paper
• Non-rigid motion behaviour learning : a spectral and graphical approach

  2007cites this paper
• Fractional Kinetics in Pseudochaotic Systems and Its Applications

  2007cites this paper
• Analyse et Estimations Spectrales des Processus alpha-Stables non-Stationnaires

  2006cites this paper
• Mean number of visits to sites in Levy flights.

  2006cites this paper
• A fractal scaling law for seed hydration kinetics

  2006cites this paper
• Central limit theorem for anomalous scaling due to correlations.

  2005cites this paper
• Topological instability along invariant surfaces and pseudochaotic transport.

  2005cites this paper
• Bibliography on stable distributions, processes and related topics

  2004cites this paper
• A physical basis for fractional derivatives in constitutive equations

  2004cites this paper
• Degrees of Transience and Recurrence and Hierarchical Random Walks

  2004cites this paper
• Stochastic simulations of time series within Weierstrass–Mandelbrot walks

  2003cites this paper
• On the distribution of family names

  2003cites this paper
• Analytic expression for the mean time to absorption for a random walker on the Sierpinski gasket.

  2002cites this paper
• From gene families and genera to incomes and internet file sizes: why power laws are so common in nature.

  2002cites this paper
• Extreme events as foundation of Lévy walks with varying velocity

  2002cites this paper
• Weak mixing and anomalous kinetics along filamented surfaces.

  2001cites this paper
• Log-periodic route to fractal functions.

  2001cites this paper
• Fractional Dispersion, Lévy Motion, and the MADE Tracer Tests

  2001cites this paper
• Long-Tailed Distributions in Physics

  2000cites this paper
• Hierarchical structures in the phase space and fractional kinetics: I. Classical systems.

  2000cites this paper
• Simulating Scale-Dependent Solute Transport in Soils with the Fractional Advective–Dispersive Equation

  2000cites this paper
• Drift in a random walk along self-similar clusters

  1999cites this paper
• ABOUT NONLINEAR DRIFT VELOCITY AT RANDOM WALK BY LEVY FLIGHT : ANALYTICAL SOLUTION AND NUMERICAL SIMULATIONS

  1999cites this paper
• Chance and Stability, Stable Distributions and Their Applications

  1999cites this paper
• Above, below and beyond Brownian motion

  1999cites this paper
• Chaotic mixing of immiscible impurities in a two-dimensional flow

  1998cites this paper
• On the relation between conduction and diffusion in a random walk along self-similar clusters

  1998cites this paper
• Self-similarity, renormalization, and phase space nonuniformity of Hamiltonian chaotic dynamics.

  1997cites this paper
• Chaotic mixing by internal inertia-gravity waves

  1997cites this paper