2018
DOI: 10.1088/1367-2630/aae4b2
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Crossover from anomalous to normal diffusion: truncated power-law noise correlations and applications to dynamics in lipid bilayers

Abstract: The emerging diffusive dynamics in many complex systems show a characteristic crossover behaviour from anomalous to normal diffusion which is otherwise fitted by two independent power-laws. A prominent example for a subdiffusive-diffusive crossover are viscoelastic systems such as lipid bilayer membranes, while superdiffusive-diffusive crossovers occur in systems of actively moving biological cells. We here consider the general dynamics of a stochastic particle driven by so-called tempered fractional Gaussian … Show more

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Cited by 102 publications
(76 citation statements)
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References 80 publications
(240 reference statements)
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“…A more detailed study of such processes will be of interest. Similarly, it should be analysed how the relaxation behaviour of both the MSD and the probability density function looks like when we introduce hard or soft cutoffs to the FGN, as recently studied in [49]. Finally, it will be interesting to see how corresponding stochastic processes fuelled by FGN but with distributed (superstatistical) diffusivities [50] behave under confinement.…”
Section: Resultsmentioning
confidence: 94%
“…A more detailed study of such processes will be of interest. Similarly, it should be analysed how the relaxation behaviour of both the MSD and the probability density function looks like when we introduce hard or soft cutoffs to the FGN, as recently studied in [49]. Finally, it will be interesting to see how corresponding stochastic processes fuelled by FGN but with distributed (superstatistical) diffusivities [50] behave under confinement.…”
Section: Resultsmentioning
confidence: 94%
“…Also, the trajectories of growing axons are likely to show long-range temporal correlations that are an inherent property of FBM (in addition to other useful properties reviewed in the Introduction; here we assume ≠ 1/2). It should be noted that the long-range correlations in FBM extend to arbitrarily large distances (Biagini et al, 2010), which may exceed biological reality, but a possible theoretical refinement may be provided by stochastic processes in which the long-range correlations are cut off at a large but finite distance (Molina-Garcia et al, 2018). In addition, branching FBM-like processes may offer insights into how the bifurcation or arborization of serotonergic fibers can affect their steady state distribution.…”
Section: Discussionmentioning
confidence: 99%
“…Of course, in each particular application of these models the physical background should be discussed, for example, the existence of a relevant continuous time random walk description, or the particular form of the second initial condition as discussed in Section 4. We note that a very different model based on the Langevin equation with generalized memory kernel has been studied very recently, which also leads to different crossovers between the diffusion regimes [47]. It would be of interest to study the case with distributed order memory kernel of the form η(t) = Table 1.…”
Section: Discussionmentioning
confidence: 99%