@article{MetzlerJeonCherstvyetal.2014,
author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli},
title = {Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking},
series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
volume = {16},
journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
number = {44},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1463-9076 (print)},
doi = {10.1039/c4cp03465a},
pages = {24128 -- 24164},
year = {2014},
abstract = {Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.},
language = {en}
}
@article{JeonChechkinMetzler2014,
author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
volume = {16},
journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
number = {30},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1463-9076 (print)},
doi = {10.1039/c4cp02019g},
pages = {15811 -- 15817},
year = {2014},
abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM), a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is < x(2)(t) similar or equal to 2K(t)t with K(t) similar or equal to t(alpha-1) for 0 < alpha < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion, for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely, we demonstrate that under confinement, the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments, in particular, under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
language = {en}
}
@article{MardoukhiJeonMetzler2015,
author = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Metzler, Ralf},
title = {Geometry controlled anomalous diffusion in random fractal geometries},
series = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies},
journal = {Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies},
number = {17},
publisher = {Wiley-VCH Verl.},
address = {Weinheim},
issn = {1439-7641 (online)},
doi = {10.1039/c5cp03548a},
pages = {30134 -- 30147},
year = {2015},
abstract = {We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.},
language = {en}
}
@misc{MardoukhiJeonMetzler2015,
author = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Metzler, Ralf},
title = {Geometry controlled anomalous diffusion in random fractal geometries},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-85247},
year = {2015},
abstract = {We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.},
language = {en}
}
@article{MetzlerJeonCherstvyetal.2014,
author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli},
title = {Anomalous diffusion models and their properties},
series = {physical chemistry, chemical physics : PCCP},
volume = {2014},
journal = {physical chemistry, chemical physics : PCCP},
number = {16},
issn = {1463-9076 (print), 1463-9084 (online)},
doi = {10.1039/c4cp03465a},
pages = {24128 -- 24164},
year = {2014},
abstract = {Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.},
language = {en}
}
@misc{MetzlerJeonCherstvyetal.2014,
author = {Metzler, Ralf and Jeon, Jae-Hyung and Cherstvy, Andrey G. and Barkai, Eli},
title = {Anomalous diffusion models and their properties},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448},
pages = {24128 -- 24164},
year = {2014},
abstract = {Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.},
language = {en}
}
@article{AdamcikJeonKarczewskietal.2012,
author = {Adamcik, Jozef and Jeon, Jae-Hyung and Karczewski, Konrad J. and Metzler, Ralf and Dietler, Giovanni},
title = {Quantifying supercoiling-induced denaturation bubbles in DNA},
series = {Soft matter},
volume = {8},
journal = {Soft matter},
number = {33},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1744-683X (print)},
doi = {10.1039/c2sm26089a},
pages = {8651 -- 8658},
year = {2012},
abstract = {In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.},
language = {en}
}
@article{JavanainenHammarenMonticellietal.2013,
author = {Javanainen, Matti and Hammaren, Henrik and Monticelli, Luca and Jeon, Jae-Hyung and Miettinen, Markus S. and Martinez-Seara, Hector and Metzler, Ralf and Vattulainen, Ilpo},
title = {Anomalous and normal diffusion of proteins and lipids in crowded lipid membranes},
series = {Faraday discussions},
volume = {161},
journal = {Faraday discussions},
number = {1},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1359-6640 (print)},
doi = {10.1039/c2fd20085f},
pages = {397 -- 417},
year = {2013},
abstract = {Lateral diffusion plays a crucial role in numerous processes that take place in cell membranes, yet it is quite poorly understood in native membranes characterized by, e.g., domain formation and large concentration of proteins. In this article, we use atomistic and coarse-grained simulations to consider how packing of membranes and crowding with proteins affect the lateral dynamics of lipids and membrane proteins. We find that both packing and protein crowding have a profound effect on lateral diffusion, slowing it down. Anomalous diffusion is observed to be an inherent property in both protein-free and protein-rich membranes, and the time scales of anomalous diffusion and the exponent associated with anomalous diffusion are found to strongly depend on packing and crowding. Crowding with proteins also has a striking effect on the decay rate of dynamical correlations associated with lateral single-particle motion, as the transition from anomalous to normal diffusion is found to take place at macroscopic time scales: while in protein-poor conditions normal diffusion is typically observed in hundreds of nanoseconds, in protein-rich conditions the onset of normal diffusion is tens of microseconds, and in the most crowded systems as large as milliseconds. The computational challenge which results from these time scales is not easy to deal with, not even in coarse-grained simulations. We also briefly discuss the physical limits of protein motion. Our results suggest that protein concentration is anything but constant in the plane of cell membranes. Instead, it is strongly dependent on proteins' preference for aggregation.},
language = {en}
}
@article{JeonLeijnseOddershedeetal.2013,
author = {Jeon, Jae-Hyung and Leijnse, Natascha and Oddershede, Lene B. and Metzler, Ralf},
title = {Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions},
series = {New journal of physics : the open-access journal for physics},
volume = {15},
journal = {New journal of physics : the open-access journal for physics},
number = {4},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1367-2630 (print)},
doi = {10.1088/1367-2630/15/4/045011},
pages = {16},
year = {2013},
abstract = {We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 mu m after short-time normal diffusion turn over to perform anomalous diffusion of the form < r(2)(t)> similar or equal to t(alpha) with alpha approximate to 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.},
language = {en}
}
@article{JeonChechkinMetzler2014,
author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
series = {Physical chemistry, chemical physics : PCCP},
volume = {30},
journal = {Physical chemistry, chemical physics : PCCP},
number = {16},
publisher = {The Royal Society of Chemistry},
address = {Cambridge},
doi = {10.1039/C4CP02019G},
pages = {15811 -- 15817},
year = {2014},
abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
language = {en}
}
@misc{JeonChechkinMetzler2014,
author = {Jeon, Jae-Hyung and Chechkin, Aleksei V. and Metzler, Ralf},
title = {Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion},
url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-76302},
pages = {15811 -- 15817},
year = {2014},
abstract = {Anomalous diffusion is frequently described by scaled Brownian motion (SBM){,} a Gaussian process with a power-law time dependent diffusion coefficient. Its mean squared displacement is ?x2(t)? [similar{,} equals] 2K(t)t with K(t) [similar{,} equals] t[small alpha]-1 for 0 < [small alpha] < 2. SBM may provide a seemingly adequate description in the case of unbounded diffusion{,} for which its probability density function coincides with that of fractional Brownian motion. Here we show that free SBM is weakly non-ergodic but does not exhibit a significant amplitude scatter of the time averaged mean squared displacement. More severely{,} we demonstrate that under confinement{,} the dynamics encoded by SBM is fundamentally different from both fractional Brownian motion and continuous time random walks. SBM is highly non-stationary and cannot provide a physical description for particles in a thermalised stationary system. Our findings have direct impact on the modelling of single particle tracking experiments{,} in particular{,} under confinement inside cellular compartments or when optical tweezers tracking methods are used.},
language = {en}
}
@article{RevereyJeonBaoetal.2015,
author = {Reverey, Julia F. and Jeon, Jae-Hyung and Bao, Han and Leippe, Matthias and Metzler, Ralf and Selhuber-Unkel, Christine},
title = {Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii},
series = {Scientific reports},
volume = {5},
journal = {Scientific reports},
publisher = {Nature Publ. Group},
address = {London},
issn = {2045-2322 (print)},
doi = {10.1038/srep11690},
pages = {14},
year = {2015},
abstract = {Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.},
language = {en}
}
@article{JeonBarkaiMetzler2013,
author = {Jeon, Jae-Hyung and Barkai, Eli and Metzler, Ralf},
title = {Noisy continuous time random walks},
series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
volume = {139},
journal = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
number = {12},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0021-9606 (print)},
doi = {10.1063/1.4816635},
pages = {15},
year = {2013},
abstract = {Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time random walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time random walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time random walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time random walks may appear ergodic, while the bare continuous time random walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.},
language = {en}
}
@article{JeonMonneJavanainenetal.2012,
author = {Jeon, Jae-Hyung and Monne, Hector Martinez-Seara and Javanainen, Matti and Metzler, Ralf},
title = {Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins},
series = {Physical review letters},
volume = {109},
journal = {Physical review letters},
number = {18},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007 (print)},
doi = {10.1103/PhysRevLett.109.188103},
pages = {5},
year = {2012},
abstract = {Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.},
language = {en}
}
@article{MetzlerJeon2012,
author = {Metzler, Ralf and Jeon, Jae-Hyung},
title = {The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories},
series = {Physica scripta : an international journal for experimental and theoretical physics},
volume = {86},
journal = {Physica scripta : an international journal for experimental and theoretical physics},
number = {5},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {0031-8949 (print)},
doi = {10.1088/0031-8949/86/05/058510},
pages = {5},
year = {2012},
abstract = {Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.},
language = {en}
}
@article{MardoukhiJeonMetzler2015,
author = {Mardoukhi, Yousof and Jeon, Jae-Hyung and Metzler, Ralf},
title = {Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster},
series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
volume = {17},
journal = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
number = {44},
publisher = {Royal Society of Chemistry},
address = {Cambridge},
issn = {1463-9076 (print)},
doi = {10.1039/c5cp03548a},
pages = {30134 -- 30147},
year = {2015},
abstract = {We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law similar to T-h with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.},
language = {en}
}
@article{JeonMetzler2012,
author = {Jeon, Jae-Hyung and Metzler, Ralf},
title = {Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement},
series = {Physical review : E, Statistical, nonlinear and soft matter physics},
volume = {85},
journal = {Physical review : E, Statistical, nonlinear and soft matter physics},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {1539-3755 (print)},
doi = {10.1103/PhysRevE.85.021147},
pages = {8},
year = {2012},
abstract = {Single-particle tracking has become a standard tool for the investigation of diffusive properties, especially in small systems such as biological cells. Usually the resulting time series are analyzed in terms of time averages over individual trajectories. Here we study confined normal as well as anomalous diffusion, modeled by fractional Brownian motion and the fractional Langevin equation, and show that even for such ergodic systems time-averaged quantities behave differently from their ensemble-averaged counterparts, irrespective of how long the measurement time becomes. Knowledge of the exact behavior of time averages is therefore fundamental for the proper physical interpretation of measured time series, in particular, for extraction of the relaxation time scale from data.},
language = {en}
}