Lévy flight search patterns of wandering albatrosses

Viswanathan, G. M.; Afanasyev, Vsevolod; Buldyrev, Sergey V.; Murphy, Eugene J.; Prince, P. A.; Stanley, H. Eugene

doi:10.1038/381413a0

Cited by 1,273 publications

(1,087 citation statements)

References 21 publications

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“…Varying α allows us to work with a "tunable" distribution. These distributions' "fat" power-law tails lead to diverging moments (which is why they are used to describe super-diffusive behavior seen in biological foraging [42,43,44,45,46,47], and quite recently, in the diffusion of bank-notes across the United States, [48]). Specifically, the ensemble-averaged contour length of the loop is well defined only at α > 4 (L = N ℓ sin (3π/α)/ sin (4πα)), mean squared gyration radius exists at α > 5, and σ only exists at α > 7, in which case it is equal to…”

Section: Modelsmentioning

confidence: 99%

The abundance of unknots in various models of polymer loops

Moore

Grosberg

2006

J. Phys. A: Math. Gen.

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Abstract. A veritable zoo of different knots is seen in the ensemble of looped polymer chains, whether created computationally or observed in vitro. At short loop lengths, the spectrum of knots is dominated by the trivial knot (unknot). The fractional abundance of this topological state in the ensemble of all conformations of the loop of N segments follows a decaying exponential form, ∼ exp (−N/N 0 ), where N 0 marks the crossover from a mostly unknotted (ie topologically simple) to a mostly knotted (ie topologically complex) ensemble. In the present work we use computational simulation to look closer into the variation of N 0 for a variety of polymer models. Among models examined, N 0 is smallest (about 240) for the model with all segments of the same length, it is somewhat larger (305) for Gaussian distributed segments, and can be very large (up to many thousands) when the segment length distribution has a fat power law tail.

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Section: Modelsmentioning

confidence: 99%

The abundance of unknots in various models of polymer loops

Moore

Grosberg

2006

J. Phys. A: Math. Gen.

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“…Viswanathan and his colleagues found a scale-free fractal-like pattern in the data 1 , just what a Lévy flight ought to produce. Three years C. BERRIE…”

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confidence: 96%

Ecological modelling: The mathematical mirror to animal nature

Buchanan¹

2008

Nature

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“…However, except from a general understanding that climate variability is nonlinear in origin, a clear formulation of its nature remains elusive. Here, we provide unique insights about climate variability by employing global temperature data and time series analysis using 'random walk' methods (Hurst et al 1965; Tsonis and Eisner 1995; Viswanathan et al 1996). The mathematical principles and physics behind these methods are fundamental to our work and as such we need first to familiarize the reader with the underlying details.…”

Section: Introduction and Theoretical Backgroundmentioning

confidence: 99%

A characteristic time scale in the global temperature record

Tsonis

Roebber

Elsner

1998

Geophysical Research Letters

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Abstract. Using modem time series analysis we discover a characteristic time scale in the global temperature record. This time scale corresponds to about 20 months and separates processes that promote a trend in the past from processes that reverse this tendency. This characteristic scale has important implications one of which might be that the E1 Nifio/La Nifia cycle may act as a mechanism countering the tendency of shorter time scale events to organize a positive or a negative temperature trend.

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Lévy flight search patterns of wandering albatrosses

Cited by 1,273 publications

References 21 publications

The abundance of unknots in various models of polymer loops

The abundance of unknots in various models of polymer loops

Ecological modelling: The mathematical mirror to animal nature

A characteristic time scale in the global temperature record

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