@article{SchulzBarkaiMetzler2013,
author = {Schulz, Johannes H. P. and Barkai, Eli and Metzler, Ralf},
title = {Aging effects and population splitting in single-particle trajectoryaverages},
series = {Physical review letters},
volume = {110},
journal = {Physical review letters},
number = {2},
publisher = {American Physical Society},
address = {College Park},
issn = {0031-9007 (print)},
doi = {10.1103/PhysRevLett.110.020602},
pages = {5},
year = {2013},
abstract = {We study time averages of single particle trajectories in scale-free anomalous diffusion processes, in which the measurement starts at some time t(a) > 0 after initiation of the process at t = 0. Using aging renewal theory, we show that for such nonstationary processes a large class of observables are affected by a unique aging function, which is independent of boundary conditions or the external forces. Moreover, we discuss the implications of aging induced population splitting: with growing age ta of the process, an increasing fraction of particles remains motionless in a measurement of fixed duration. Consequences for single biomolecule tracking in live cells are discussed.},
language = {en}
}
@misc{BarkaiGariniMetzler2013,
author = {Barkai, Eli and Garini, Yuval and Metzler, Ralf},
title = {Electrostatic effects in living cells Reply},
series = {PHYSICS TODAY},
volume = {66},
journal = {PHYSICS TODAY},
number = {7},
publisher = {AMER INST PHYSICS},
address = {MELVILLE},
issn = {0031-9228 (print)},
pages = {11 -- 11},
year = {2013},
language = {en}
}
@article{SchulzBarkaiMetzler2014,
author = {Schulz, Johannes H. P. and Barkai, Eli and Metzler, Ralf},
title = {Aging renewal theory and application to random walks},
series = {Physical review : X, Expanding access},
volume = {4},
journal = {Physical review : X, Expanding access},
number = {1},
publisher = {American Physical Society},
address = {College Park},
issn = {2160-3308 (print)},
doi = {10.1103/PhysRevX.4.011028},
pages = {24},
year = {2014},
abstract = {We discuss a renewal process in which successive events are separated by scale-free waiting time periods. Among other ubiquitous long-time properties, this process exhibits aging: events counted initially in a time interval [0, t] statistically strongly differ from those observed at later times [t(a,) t(a) + t]. The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. In complex, disordered media, processes with scale-free waiting times play a particularly prominent role. We set up a unified analytical foundation for such anomalous dynamics by discussing in detail the distribution of the aging renewal process. We analyze its half-discrete, half-continuous nature and study its aging time evolution. These results are readily used to discuss a scale-free anomalous diffusion process, the continuous-time random walk. By this, we not only shed light on the profound origins of its characteristic features, such as weak ergodicity breaking, along the way, we also add an extended discussion on aging effects. In particular, we find that the aging behavior of time and ensemble averages is conceptually very distinct, but their time scaling is identical at high ages. Finally, we show how more complex motion models are readily constructed on the basis of aging renewal dynamics.},
language = {en}
}
@article{GodecChechkinBarkaietal.2014,
author = {Godec, Aljaz and Chechkin, Aleksei V. and Barkai, Eli and Kantz, Holger and Metzler, Ralf},
title = {Localisation and universal fluctuations in ultraslow diffusion processes},
series = {Journal of physics : A, Mathematical and theoretical},
volume = {47},
journal = {Journal of physics : A, Mathematical and theoretical},
number = {49},
publisher = {IOP Publ. Ltd.},
address = {Bristol},
issn = {1751-8113 (print)},
doi = {10.1088/1751-8113/47/49/492002},
pages = {10},
year = {2014},
abstract = {We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) < x(2)(t)> similar or equal to log(gamma)t. Comparison of annealed (renewal) continuous time random walks (CTRWs) with logarithmic waiting time distribution psi(tau) similar or equal to 1/(tau log(1+gamma)tau) and Sinai diffusion in quenched random landscapes reveals striking similarities, despite the great differences in their physical nature. In particular, they exhibit a weakly non-ergodic disparity of the time-averaged and ensemble-averaged MSDs. Remarkably, for the CTRW we observe that the fluctuations of time averages become universal, with an exponential suppression of mobile trajectories. We discuss the fundamental connection between the Golosov localization effect and non-ergodicity in the sense of the disparity between ensemble-averaged MSD and time-averaged MSD.},
language = {en}
}
@article{BarkaiGariniMetzler2012,
author = {Barkai, Eli and Garini, Yuval and Metzler, Ralf},
title = {Strange Kinetics of single molecules in living cells},
series = {Physics today},
volume = {65},
journal = {Physics today},
number = {8},
publisher = {American Institute of Physics},
address = {Melville},
issn = {0031-9228 (print)},
pages = {29 -- 35},
year = {2012},
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: 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{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{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}
}