Strange kinetics: conflict between density and trajectory description

Bologna, Mauro; Grigolini, Paolo; West, Bruce J.

doi:10.1016/s0301-0104(02)00543-8

Cited by 25 publications

(42 citation statements)

References 31 publications

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“…(36) and, consequently, that this expression for the aging correlation function rests on the same approximation, Eq. (20), as that yielding the major result of this paper-namely, Eq. (23): Equations (43) and (20) share the property of being exact, if referred to a single trajectory, and become approximate when used to make predictions on an ensemble of distinct trajectories.…”

Section: Agingmentioning

confidence: 70%

“…(20), as that yielding the major result of this paper-namely, Eq. (23): Equations (43) and (20) share the property of being exact, if referred to a single trajectory, and become approximate when used to make predictions on an ensemble of distinct trajectories. The exact expression for the aging correlation function can be found in the important and rigorous work of Ref.…”

Section: Agingmentioning

confidence: 70%

“…(8). This violation of the factorization property seems to be a satisfactory explanation as to why the GDE [20] does not yield the proper Lévy diffusion in the asympotic limit. On the other hand, using the results of this section we recover the results of the numerical calculations and theoretical prediction of the fourth moments obtained by Allegrini et al [27] and, independently, by other groups [28].…”

Section: ͒͘ ͑24͒mentioning

confidence: 96%

“…(23)-namely, Eq. (20). To make this fact more transparent, let us define a further condition, called C, as the occurrence of a random event at t 0 .…”

Section: Agingmentioning

confidence: 99%

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Non-Poisson dichotomous noise: Higher-order correlation functions and aging

et al. 2004

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We study a two-state symmetric noise, with a given waiting time distribution ͑ ͒, and focus our attention on the connection between the four-time and two-time correlation functions. The transition of ͑ ͒ from the exponential to the nonexponential condition yields the breakdown of the usual factorization condition of high-order correlation functions, as well as the birth of aging effects. We discuss the subtle connections between these two properties and establish the condition that the Liouville-like approach has to satisfy in order to produce a correct description of the resulting diffusion process.

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Section: Agingmentioning

confidence: 70%

Section: Agingmentioning

confidence: 70%

Section: ͒͘ ͑24͒mentioning

confidence: 96%

“…(23)-namely, Eq. (20). To make this fact more transparent, let us define a further condition, called C, as the occurrence of a random event at t 0 .…”

Section: Agingmentioning

confidence: 99%

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Non-Poisson dichotomous noise: Higher-order correlation functions and aging

et al. 2004

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“…[21], this is the limit for u → 0 of the Laplace transform of a function of time, which for t → ϱ is proportional to 1 / t 2− D . By comparison with Eq.…”

Section: ͑5͒mentioning

confidence: 99%

Random growth of interfaces as a subordinated process

et al. 2004

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We study the random growth of surfaces from within the perspective of a single column, namely, the fluctuation of the column height around the mean value, y͑t͒ϵh͑t͒ − ͗h͑t͒͘, which is depicted as being subordinated to a standard fluctuation-dissipation process with friction ␥. We argue that the main properties of Kardar-Parisi-Zhang theory, in one dimension, are derived by identifying the distribution of return times to y͑0͒ = 0, which is a truncated inverse power law, with the distribution of subordination times. The agreement of the theoretical prediction with the numerical treatment of the ͑1+1͒-dimensional model of ballistic deposition is remarkably good, in spite of the finite-size effects affecting this model. is an example of self-organization: As pointed out by Family [7], a growing surface spontaneously evolving into a steady state with universal fractal properties is similar to the mechanism of self-organized criticality [8]. The columns of the material growing due to the deposition of particles can be thought of as the individuals of a society. The joint action of the randomness driving the particle deposition and the interaction among columns results in the emergence of anomalous scaling coefficients, which can be interpreted as the signature of cooperation. However, only a little attention has been devoted so far to studying the dynamics of the single individuals of this society, namely, the single growing columns of the sample under study. Usually the authors of this field of research study the correlation among distinct columns [9] without paying attention to the dynamics of an individual. Yet, a single column is expected to carry information about cooperation.The single column perspective was recently adopted by Merikoski et al.[10] to study combustion fronts in paper. The individual property under observation iswhere h͑t͒ denotes the height of a single column at time t and ͗h͑t͒͘ the average over the heights of the columns of the whole sample. The authors of Ref.[10] record the times at which the variable y͑t͒ changes sign and builds up the corresponding time series t i so as to create the new time series The coefficient ␤ refers to the interface growth prior to saturation, a physical condition where the standard deviation of all L columns, the interface widthgrows as w͑L , t͒ ϰ t ␤ . Equation (2) establishes a connection between a single column property, D , and a collective property, ␤, thereby playing an important role for the perspective adopted in this paper. The theoretical foundation for this important relation is given in earlier papers [11][12][13][14] and has been more recently discussed by Majumdar [15].In this paper we prove that the KPZ condition emerges from the identification of D ͑͒ with the distribution function S ͑͒, the essential ingredient of the subordination theory [16][17][18] stemming from the original work of Montroll and Weiss [19]. In the subdiffusion case, anomalous diffusion is derived from the ordinary diffusion process by assuming that the time distance between on...

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Fractal Physiology, Complexity, and the Fractional Calculus

West

2006

Fractals, Diffusion, and Relaxation in Disordered Complex Systems

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Strange kinetics: conflict between density and trajectory description

Cited by 25 publications

References 31 publications

Non-Poisson dichotomous noise: Higher-order correlation functions and aging

Non-Poisson dichotomous noise: Higher-order correlation functions and aging

Random growth of interfaces as a subordinated process

Fractal Physiology, Complexity, and the Fractional Calculus

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