Memory-induced anomalous dynamics: Emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

Kumar, Niraj; Harbola, Upendra; Lindenberg, Katja

doi:10.1103/physreve.82.021101

Cited by 85 publications

(92 citation statements)

References 22 publications

(29 reference statements)

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“…(27). Consistently with the analysis, each curve (for ∆ < t) can be very well fitted by the approximation (32), that is, a linear behavior in ∆ is observed. In Fig.…”

Section: A Asymptotic Randomnesssupporting

confidence: 81%

“…It is known that globally correlated stochastic dynamics lead to anomalous diffusion processes [27][28][29][30][31][32][33][34][35]. On the other hand, we remark that the interplay between memory effects and weak ergodicity breaking was study previously such as for example in correlated continuous-time random walk models [36,37], single-file diffusion [38], and fractional Brownian-Langevin motion [39].…”

Section: Introductionmentioning

confidence: 63%

“…(32) and (33) define the random values (written in terms of f ± ) that assume the time-averaged moments (27) in the long time limit. In order to check these results, in Fig.…”

Section: A Asymptotic Randomnessmentioning

confidence: 99%

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Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

Budini

2016

Phys. Rev. E

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We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this "inhomogeneous diffusion" feature the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long time regime they remain random objects. While their average over realizations recover the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.

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“…(27). Consistently with the analysis, each curve (for ∆ < t) can be very well fitted by the approximation (32), that is, a linear behavior in ∆ is observed. In Fig.…”

Section: A Asymptotic Randomnesssupporting

confidence: 81%

Section: Introductionmentioning

confidence: 63%

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Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

Budini

2016

Phys. Rev. E

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“…Due to its simpleness, the microscopic memory effect, the key origin of anomalous diffusion, was easily applied to other models, among which Cressoni et al suggested that the loss of recent memory rather than the distant past can induce persistence, which is related to the repetitive behaviors and psychological symptoms of Alzheimer's disease [30]. In [31], it was shown that, by adding a possibility that a walker does not move at all in the model of [29], diffusive, superdiffusive, and subdiffusive behaviors can exhibit in different parameter regimes. It has the advantage to describe the anomalous diffusion within a single model just by changing the parameters; however, in this case, the subdiffusive property may be caused by the staying behavior rather than the memory effect and thus superdiffusion and subdiffusion are not induced by a single origin.…”

Section: Introductionmentioning

confidence: 99%

Anomalous diffusion induced by enhancement of memory

Kim

2014

Phys. Rev. E

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We introduced simple microscopic non-Markovian walk models which describe the underlying mechanism of anomalous diffusions. In the models, we considered the competitions between randomness and memory effects of previous history by introducing the probability parameters. The memory effects were considered in two aspects: one is the perfect memory of whole history and the other is the latest memory enhanced with time. In the perfect memory model superdiffusion was induced with the relation of the Hurst exponent H to the controlling parameter p as H = p for p>1/2, while in the latest memory enhancement models, anomalous diffusions involving both superdiffusion and subdiffusion were induced with the relations H = (1+α)/2 and H = (1-α)/2 for 0 ≤ α ≤ 1, where α is the parameter controlling the degree of the latest memory enhancement. Also we found that, although the latest memory was only considered, the memory improved with time results in the long-range correlations between steps and the correlations increase as time goes on. Thus we suggest the memory enhancement as a key origin describing anomalous diffusions.

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“…In general, systems of different nature reveal asymptotically different modes of anomalous diffusion: either subor superdiffusion. 16 Only one example of a system showing anomalous as well as normal diffusion as an asymptotic state is described so far in the literature, a formal random walk model with a multi-parametric memory, 17 which, however, is too complicated to gain more insight into the physics of anomalous diffusion.…”

Section: Introductionmentioning

confidence: 99%

A gedankenexperiment for anomalous diffusion in a charge-fluctuating dusty plasma

Kopp¹,

Shchekinov²

2014

Physics of Plasmas

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Brownian motion with Gaussian-distributed step-sizes is the prototype of diffusive processes with the typical scaling of the mean-square displacement linear with time. There are, however, processes scaling slower or faster in time due to differently (e.g., power-law) distributed step-sizes, commonly referred to as sub-and superdiffusion, respectively. We address the question whether there is actually a physical reason for a discrimination between normal and anomalous diffusion or whether such processes can be regarded as a special case of normal diffusion with a complicated space-and time-dependent diffusion coefficient. In order to get to the bottom of this question, we construct a numerical gedankenexperiment, which is designed to be as simple as possible and consists of dust particles embedded as test particles into a homogeneous magnetic field that randomly changes their charge. The only parameter governing the system is the ratio of the time-scales for gyration and for recharging. By performing full-orbit simulations of such particles, we are for the first time able to (i) describe a system exhibiting sub-, normal, or superdiffusion as an asymptotic behavior, i.e., not merely as an intermediate state during the evolution of the system. We (ii) observe superdiffusion for low values of the controlling parameter, normal diffusion over a wide plateau of intermediate values, and subdiffusion for high values, i.e., we found (iii) a simple system with one single and illustrative parameter controlling whether the system exhibits super-, normal, or subdiffusion. The crucial point is (iv) a competition between ballistic (particles uncharged, extreme superdiffusion) and confined (charged, extreme subdiffusion) motions. Our system is homogeneous in space and time, so that its (v) behavior cannot be described by normal diffusion with a special diffusion coefficient, and the competition is (vi) fundamentally different from a Gaussian random walk and may be regarded as one possible prototype of anomalous diffusion. We discuss briefly possible implications to space and astrophysical dusty plasma. In particular, we show that in a plasma with polydisperse dust particles, a superposition of the three regimes of the anomalous diffusion can simultaneously come into play. V C 2014 AIP Publishing LLC. [http://dx.

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Memory-induced anomalous dynamics: Emergence of diffusion, subdiffusion, and superdiffusion from a single random walk model

Cited by 85 publications

References 22 publications

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

Inhomogeneous diffusion and ergodicity breaking induced by global memory effects

Anomalous diffusion induced by enhancement of memory

A gedankenexperiment for anomalous diffusion in a charge-fluctuating dusty plasma

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