35271
2013
2013
eng
5
2
110
article
American Physical Society
College Park
1
--
--
--
Aging effects and population splitting in single-particle trajectoryaverages
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.
Physical review letters
10.1103/PhysRevLett.110.020602
0031-9007 (print)
1079-7114 (online)
wos:2011-2013
020602
WOS:000313336500003
Schulz, JHP (reprint author), Tech Univ Munich, Phys Dept T30G, D-85747 Garching, Germany.
CompInt graduate school; Academy of Finland (FiDiPro scheme); Israel
Science Foundation
Johannes H. P. Schulz
Eli Barkai
Ralf Metzler
Institut für Physik und Astronomie
Referiert
34877
2013
2013
eng
11
11
1
7
66
other
AMER INST PHYSICS
MELVILLE
1
--
--
--
Electrostatic effects in living cells Reply
PHYSICS TODAY
0031-9228
(print)
1945-0699
(online)
wos:2011-2013
WOS:000327027700008
Barkai, E (reprint author), Bar Ilan Univ, Ramat Gan, Israel.
, rmetzler@uni-potsdam.de
Eli Barkai
Yuval Garini
Ralf Metzler
38041
2014
2014
eng
24
1
4
article
American Physical Society
College Park
1
--
--
--
Aging renewal theory and application to random walks
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.
Physical review : X, Expanding access
10.1103/PhysRevX.4.011028
2160-3308 (print)
wos:2014
011028
WOS:000332161500001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam Golm, Germany., rmetzler@uni-potsdam.de
Elitenetzwerk Bayern; Academy of Finland (FiDiPro scheme); Israel
Science Foundation
Johannes H. P. Schulz
Eli Barkai
Ralf Metzler
Institut für Physik und Astronomie
Referiert
Open Access
37299
2014
2014
eng
10
49
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Localisation and universal fluctuations in ultraslow diffusion processes
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.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/49/492002
1751-8113 (print)
1751-8121 (online)
wos:2014
492002
WOS:000346266400002
Godec, A (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); Alexander von Humboldt Foundation;
Berlin Mathematical Society; Israel Science Foundation
Aljaz Godec
Aleksei V. Chechkin
Eli Barkai
Holger Kantz
Ralf Metzler
eng
uncontrolled
Sinai diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
quenched energy landscape
Institut für Physik und Astronomie
Referiert
35732
2012
2012
eng
29
35
7
8
65
article
American Institute of Physics
Melville
1
--
--
--
Strange Kinetics of single molecules in living cells
Physics today
0031-9228 (print)
wos:2011-2013
WOS:000307614600020
Barkai, E (reprint author), Bar Ilan Univ, Ramat Gan, Israel.
Israel Science Foundation; Academy of Finland
Eli Barkai
Yuval Garini
Ralf Metzler
Institut für Physik und Astronomie
Referiert
38215
2014
2014
eng
24128
24164
37
44
16
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
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.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c4cp03465a
25297814
1463-9076 (print)
1463-9084 (online)
wos:2014
WOS:000344249400001
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland; Israel Science Foundation; Deutsche
Forschungsgemeinschaft [CH 707/5-1]
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Institut für Chemie
Referiert
34723
2013
2013
eng
15
12
139
article
American Institute of Physics
Melville
1
--
--
--
Noisy continuous time random walks
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.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4816635
0021-9606 (print)
1089-7690 (online)
wos:2011-2013
WOS:000325392000019
Jeon, JH (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., jae-hyung.jeon@tut.fi; barkaie@mail.biu.ac.il; rmetzler@uni-potsdam.de
Academy of Finland within the Finland Distinguished Professor (FiDiPro)
scheme; Israel Science Foundation
Jae-Hyung Jeon
Eli Barkai
Ralf Metzler
Institut für Physik und Astronomie
Referiert
7443
2014
2014
eng
24128
24164
37
16
2014
article
1
--
2014-09-22
--
Anomalous diffusion models and their properties
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.
physical chemistry, chemical physics : PCCP
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
10.1039/c4cp03465a
1463-9076 (print), 1463-9084 (online)
online registration
Au-006611
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74448">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 174</a>
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
time random-walks
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
weak ergodicity breaking
eng
uncontrolled
flight search patterns
eng
uncontrolled
levy flights
Chemie und zugeordnete Wissenschaften
Institut für Chemie
Referiert
Open Access
RSC
Universität Potsdam
7444
2014
2014
eng
24128
24164
37
postprint
1
2015-03-26
2014-09-22
--
Anomalous diffusion models and their properties
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.
non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
urn:nbn:de:kobv:517-opus4-74448
online registration
Au-006611
Physical Chemistry, Chemical Physics (2014) 16, S. 24128-24164. - DOI: 10.1039/c4cp03465a
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7443">Bibliographieeintrag der Originalveröffentlichung/Quelle</a
Ralf Metzler
Jae-Hyung Jeon
Andrey G. Cherstvy
Eli Barkai
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
paper 174
eng
uncontrolled
Fokker-Planck equations
eng
uncontrolled
flight search patterns
eng
uncontrolled
fluctuation-dissipation theorem
eng
uncontrolled
fluorescence photobleaching recovery
eng
uncontrolled
fractional dynamics approach
eng
uncontrolled
intermittent chaotic systems
eng
uncontrolled
levy flights
eng
uncontrolled
photon-counting statistics
eng
uncontrolled
time random-walks
deu
uncontrolled
weak ergodicity breaking
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/opus4-ubp/files/7444/pmnr174.pdf