Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow

Solomon, Tom; Weeks, Eric R.; Swinney, Harry L.

doi:10.1103/physrevlett.71.3975

Cited by 729 publications

(531 citation statements)

References 23 publications

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“…[70]. Lévy flights define one of the most paradigmatic models of anomalous dynamics with wide applications, for example, in fluid dynamics [71], in the foraging of biological organisms [72] and in glassy optical material [44], to highlight only a few cases. It can be shown that the position PDF ̺(x, t) characterizing the process defined by…”

Section: Lévy Flightsmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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Abstract. We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: Lévy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.

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Section: Lévy Flightsmentioning

confidence: 99%

Anomalous Fluctuation Relations

Klages

Chechkin

Dieterich

2013

Nonequilibrium Statistical Physics of Small Systems

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“…For instance such a behavior has been observed for fluids in a rotating annulus [15]. Tracer particles stick temporar ily to eddies and after release they are temporarily locked in a mode of laminar motion.…”

Section: Coexistence Of Modes Of Localization and Of Laminaritymentioning

confidence: 92%

“…One finds diffusion anomalies in numerical studies of one-dimensional maps [4,5,9], of the Chirikov-Taylor standard map [1,2,10,11], of stochastic webs [7], and of conservative motion in two-dimensional potential surfaces [6,12]. Experimentally, anomalies have been observed for tracer diffusion in flow systems [13][14][15].…”

Section: Introductionmentioning

confidence: 93%

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From Dispersion to Laminarity in Dynamical Systems

Zumofen¹,

Klafter

1994

Zeitschrift Für Naturforschung A

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We study transport in dynamical systems characterized by intermittent chaotic behavior with coexistence of dispersive motion due to periods of localization, and of enhanced diffusion due to periods of laminar motion. This transport is discussed within the continuous-time random walk approach which applies to both dispersive and enhanced motions. We analyze the coexistence for the standard map and for a one-dimensional map.

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“…Socio-economical and biological systems display these general features, and have been treated by physicists. Scaling power laws [7,8] have been found in many biological [9][10][11], physical [2,[12][13][14][15][16][17][18][19][20] and socio-economical systems [21][22][23][24][25][26][27][28][29], and they are now considered as an important property of these systems.…”

Section: Introductionmentioning

confidence: 99%

Power-law distributions for the citation index of scientific publications and scientists

Gupta¹,

Campanha²,

Pesce³

2005

Braz. J. Phys.

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The number of citations of a scientific publication or of an individual scientist has become an important factor of quality assessment in science. We report a study of the statistical distribution of the citation index of both scientific publications and scientists. We give numerical evidence that Tsallis (power law) statistics explains the entire distribution over eight orders of magnitude (10 −4 to 10 4 ). Also, we draw Zipf plots in order to analyze the statistical distribution of the citation index of Brazilian and international physicists and chemists. The relatively small group of Brazilian scientists seems more adequate to explain the dynamics of the citation index. In this case, we find that the distribution of the citation index can also be explained by a gradually truncated power law with similar parameters. We finally discuss possible mechanisms behind the citation index of scientists and scientific publications.

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Observation of anomalous diffusion and Lévy flights in a two-dimensional rotating flow

Cited by 729 publications

References 23 publications

Anomalous Fluctuation Relations

Anomalous Fluctuation Relations

From Dispersion to Laminarity in Dynamical Systems

Power-law distributions for the citation index of scientific publications and scientists

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