Transient aging in fractional Brownian and Langevin-equation motion

Kursawe, Jochen; Schulz, Johannes H. P.; Metzler, Ralf

doi:10.1103/physreve.88.062124

Cited by 47 publications

(47 citation statements)

References 65 publications

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“…In the plots for the scaling exponent t b ( ) in figure 6(B) the significant spike-like signal at 1 D~is interpreted as an effect of the first collision of particles and the resulting onset of an effective confinement. We note that even in effective one-particle theories pronounced oscillations occur at the crossover point between the initial ballistic and the overdamped regime [125,126].…”

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confidence: 80%

Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

2015

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We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction f of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational-but not rotational-diffusivity of the particles D is a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law D 1with the area fraction f occupied by the crowders and the critical value . f Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.

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confidence: 80%

Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

2015

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“…To this end it is simple to set up the derivation of higher moments, but it quickly becomes difficult to maintain analytical tractability. Future work should also include non-stationary and nonergodic effects, for instance, due to confinement or underdamped fractional Langevin behavior [57]. …”

Section: Discussionmentioning

confidence: 99%

Chromosomal locus tracking with proper accounting of static and dynamic errors

2015

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The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object’s motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics (“static error”) and motion blur due to finite exposure time (“dynamic error”) on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors.

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“…Another interesting question is how the sensitivity to initial conditions translates to the time-averaged diffusivity, where, instead of averaging over an ensemble of trajectories at a given time, the mean-square displacement is computed from a time average over a single trajectory. The dependence of the time-averaged diffusivity on the initial conditions has so far only been discussed for special cases [71][72][73][74], and whether it will correspond to the stationary or nonstationary expression obtained here or to neither is an open question.…”

Section: Discussionmentioning

confidence: 99%

Scaling Green-Kubo Relation and Application to Three Aging Systems

et al. 2014

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The Green-Kubo formula relates the spatial diffusion coefficient to the stationary velocity autocorrelation function. We derive a generalization of the Green-Kubo formula that is valid for systems with longrange or nonstationary correlations for which the standard approach is no longer valid. For the systems under consideration, the velocity autocorrelation function hvðt þ τÞvðtÞi asymptotically exhibits a certain scaling behavior and the diffusion is anomalous, hx 2 ðtÞi ≃ 2D ν t ν . We show how both the anomalous diffusion coefficient D ν and the exponent ν can be extracted from this scaling form. Our scaling GreenKubo relation thus extends an important relation between transport properties and correlation functions to generic systems with scale-invariant dynamics. This includes stationary systems with slowly decaying power-law correlations, as well as aging systems, systems whose properties depend on the age of the system. Even for systems that are stationary in the long-time limit, we find that the long-time diffusive behavior can strongly depend on the initial preparation of the system. In these cases, the diffusivity D ν is not unique, and we determine its values, respectively, for a stationary or nonstationary initial state. We discuss three applications of the scaling Green-Kubo relation: free diffusion with nonlinear friction corresponding to cold atoms diffusing in optical lattices, the fractional Langevin equation with external noise recently suggested to model active transport in cells, and the Lévy walk with numerous applications, in particular, blinking quantum dots. These examples underline the wide applicability of our approach, which is able to treat very different mechanisms of anomalous diffusion.

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Transient aging in fractional Brownian and Langevin-equation motion

Cited by 47 publications

References 65 publications

Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

Chromosomal locus tracking with proper accounting of static and dynamic errors

Scaling Green-Kubo Relation and Application to Three Aging Systems

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