49348
2021
2020
eng
22
23
article
Dt. Physikalische Ges. ; IOP
Bad Honnef ; London
1
2021-01-20
2020-07-03
--
Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.
New Journal of Physics
10.1088/1367-2630/abd50e
1367-2630
013008
<a href="https://doi.org/10.25932/publishup-49349">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1118</a>
Universität Potsdam
PA 2021_005
1418.10
CC-BY - Namensnennung 4.0 International
Samudrajit Thapa
Agnieszka Wyłomańska
Grzegorz Sikora
Caroline E. Wagner
Diego Krapf
Holger Kantz
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
large-deviation statistic
eng
uncontrolled
time-averaged mean squared displacement
eng
uncontrolled
Chebyshev inequality
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
50460
2018
2018
eng
22
1
52
article
IOP Publ. Ltd.
Bristol
1
--
2018-11-30
--
Generalized diffusion-wave equation with memory kernel
We study generalized diffusion-wave equation in which the second order time derivative is replaced by an integro-differential operator. It yields time fractional and distributed order time fractional diffusion-wave equations as particular cases. We consider different memory kernels of the integro-differential operator, derive corresponding fundamental solutions, specify the conditions of their non-negativity and calculate the mean squared displacement for all cases. In particular, we introduce and study generalized diffusion-wave equations with a regularized Prabhakar derivative of single and distributed orders. The equations considered can be used for modeling the broad spectrum of anomalous diffusion processes and various transitions between different diffusion regimes.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8121/aaefa3
1751-8113
1751-8121
wos:2019
015201
WOS:000452486200001
Sandev, T (reprint author), Radiat Safety Directorate, Partizanski Odredi 143,POB 22, Skopje 1020, North Macedonia.; Sandev, T (reprint author), Ss Cyril & Methodius Univ, Inst Phys, Fac Nat Sci & Math, Arhimedova 3, Skopje 1000, North Macedonia.; Sandev, T (reprint author), Macedonian Acad Sci & Arts, Res Ctr Comp Sci & Informat Technol, Bul Krste Misirkov 2, Skopje 1000, North Macedonia., trifce.sandev@drs.gov.mk
NWONetherlands Organization for Scientific Research (NWO) [040.11.629]; Foundation (DFG) [ME 1535/6-1]
2021-04-21T11:52:24+00:00
sword
importub
filename=package.tar
d7d154dbb1574ab32a62a690764d9aa5
false
true
Trifce Sandev
Zivorad Tomovski
Johan L. A. Dubbeldam
Aleksei V. Chechkin
eng
uncontrolled
diffusion-wave equation
eng
uncontrolled
Mittag-Leffler function
eng
uncontrolled
anomalous diffusion
Physik
Institut für Physik und Astronomie
Referiert
Import
Green Open-Access
7400
2014
2014
eng
1591
1601
11
10
2014
article
Royal Society of Chemistry
1
--
2014-01-02
--
Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
Soft matter
10.1039/c3sm52846d
2046-2069
online registration
Au-006605
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-74021">Zweitveröffentlichung als Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 168</a>
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
intracellular-transport
eng
uncontrolled
adenoassociated virus
eng
uncontrolled
infection pathway
eng
uncontrolled
escherichia-coli
eng
uncontrolled
endosomal escape
eng
uncontrolled
living cells
eng
uncontrolled
trafficking
eng
uncontrolled
cytoplasm
eng
uncontrolled
models
Chemie und zugeordnete Wissenschaften
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
RSC
7402
2014
2014
eng
1591
1601
11
168
postprint
1
2015-03-20
2014-01-02
--
Particle invasion, survival, and non-ergodicity in 2D diffusion processes with space-dependent diffusivity
We study the thermal Markovian diffusion of tracer particles in a 2D medium with spatially varying diffusivity D(r), mimicking recently measured, heterogeneous maps of the apparent diffusion coefficient in biological cells. For this heterogeneous diffusion process (HDP) we analyse the mean squared displacement (MSD) of the tracer particles, the time averaged MSD, the spatial probability density function, and the first passage time dynamics from the cell boundary to the nucleus. Moreover we examine the non-ergodic properties of this process which are important for the correct physical interpretation of time averages of observables obtained from single particle tracking experiments. From extensive computer simulations of the 2D stochastic Langevin equation we present an in-depth study of this HDP. In particular, we find that the MSDs along the radial and azimuthal directions in a circular domain obey anomalous and Brownian scaling, respectively. We demonstrate that the time averaged MSD stays linear as a function of the lag time and the system thus reveals a weak ergodicity breaking. Our results will enable one to rationalise the diffusive motion of larger tracer particles such as viruses or submicron beads in biological cells.
urn:nbn:de:kobv:517-opus4-74021
online registration
Au-006605
Soft Matter, 2014, 10, S. 1591-1601 - DOI: 10.1039/c3sm52846d
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7400">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
paper 168
eng
uncontrolled
adenoassociated virus
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
cytoplasm
eng
uncontrolled
endosomal escape
eng
uncontrolled
escherichia-coli
eng
uncontrolled
infection pathway
eng
uncontrolled
intracellular-transport
eng
uncontrolled
living cells
eng
uncontrolled
models
eng
uncontrolled
trafficking
Chemie und zugeordnete Wissenschaften
open_access
Institut für Chemie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/7402/pmnr168.pdf
50178
2019
2019
eng
27
9
52
article
IOP Publ. Ltd.
Bristol
1
2019-02-01
2019-02-01
--
Finite-energy Levy-type motion through heterogeneous ensemble of Brownian particles
Complex systems are known to display anomalous diffusion, whose signature is a space/time scaling x similar to t(delta) with delta not equal 1/2 in the probability density function (PDF). Anomalous diffusion can emerge jointly with both Gaussian, e.g. fractional Brownian motion, and power-law decaying distributions, e.g. Levy Flights or Levy Walks (LWs). Levy flights get anomalous scaling, but, being jumps of any size allowed even at short times, have infinite position variance, infinite energy and discontinuous paths. LWs, which are based on random trapping events, overcome these limitations: they resemble a Levy-type power-law distribution that is truncated in the large displacement range and have finite moments, finite energy and, even with discontinuous velocity, they are continuous. However, LWs do not take into account the role of strong heterogeneity in many complex systems, such as biological transport in the crowded cell environment. In this work we propose and discuss a model describing a heterogeneous ensemble of Brownian particles (HEBP). Velocity of each single particle obeys a standard underdamped Langevin equation for the velocity, with linear friction term and additive Gaussian noise. Each particle is characterized by its own relaxation time and velocity diffusivity. We show that, for proper distributions of relaxation time and velocity diffusivity, the HEBP resembles some LW statistical features, in particular power-law decaying PDF, long-range correlations and anomalous diffusion, at the same time keeping finite position moments and finite energy. The main differences between the HEBP model and two different LWs are investigated, finding that, even when both velocity and position PDFs are similar, they differ in four main aspects: (i) LWs are biscaling, while HEBP is monoscaling; (ii) a transition from anomalous (delta = 1/2) to normal (delta = 1/2) diffusion in the long-time regime is seen in the HEBP and not in LWs; (iii) the power-law index of the position PDF and the space/time diffusion scaling are independent in the HEBP, while they both depend on the scaling of the interevent time PDF in LWs; (iv) at variance with LWs, our HEBP model obeys a fluctuation-dissipation theorem.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8121/aafe90
1751-8113
1751-8121
wos:2019
095601
WOS:000457540700001
Paradisi, P (reprint author), BCAM, Alameda Mazarredo 14, E-48009 Bilbao, Basque Country, Spain.; Paradisi, P (reprint author), ISTI CNR Inst Informat Sci & Technol A Faedo, Via G Moruzzi 1, I-56124 Pisa, Italy., paolo.paradisi@cnr.it; gpagnini@bcamath.org
Basque Government through the BERC 2014-2017 programBasque Government; Basque Government through the BERC 2018-2021 programBasque Government; Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation [SEV-2013-0323, SEV-2017-0718]; Spanish Ministry of Economy and Competitiveness MINECO [MTM2016-76016-R Bizkaia Talent; European Commission through COFUND scheme, 2015 Financial Aid Program for Researchers [AYD-000-252]; Deutsche (DFG) [ME 1535/6-1]
2021-04-06T09:40:46+00:00
sword
importub
filename=package.tar
3534c3e0b917c07dae09bacf4802a873
Paradisi, Paolo
Oleksii Yu Sliusarenko
Silvia Vitali
Vittoria Sposini
Paolo Paradisi
Aleksei V. Chechkin
Gastone Castellani
Gianni Pagnini
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
heterogeneous ensemble of Brownian particles
eng
uncontrolled
biological transport
eng
uncontrolled
Langevin equation
eng
uncontrolled
Gaussian processes
eng
uncontrolled
fractional diffusion
eng
uncontrolled
Levy walk
Physik
Institut für Physik und Astronomie
Referiert
Import
53605
2018
2018
eng
10
28
19
1
21
article
De Gruyter
Berlin
1
2018-03-13
2018-03-23
--
From continuous time random walks to the generalized diffusion equation
We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density function and mean squared displacement for different forms of the equation are explicitly calculated. We show examples of generalized diffusion equations in normal or Caputo form that encode the same probability distribution functions as those obtained from the generalized diffusion equation in modified form. The obtained equations are general and many known fractional diffusion equations are included as special cases.
Fractional calculus and applied analysis : an international journal for theory and applications
10.1515/fca-2018-0002
1311-0454
1314-2224
wos:2018
8th International Conference on Transform Methods and Special Functions (TMSF)
AUG 27-31, 2017
WOS:000427936000002
Bulgarian Acad Sci, Inst Math & Informat, Sofia, BULGARIA, Bulgarian Acad Sci, Inst Math & Informat
Sandev, T (reprint author), Radiat Safety Directorate, Partizanski Odredi 143,POB 22, Skopje 1020, Macedonia.; Sandev, T (reprint author), Ss Cyril & Methodius Univ Skopje, Fac Nat Sci & Math, Inst Phys, POB 162, Skopje 1001, Macedonia.; Sandev, T (reprint author), Macedonian Acad Sci & Arts, Res Ctr Comp Sci & Informat Technol, Bul Krste Misirkov 2, Skopje 1000, Macedonia., trifce.sandev@drs.gov.mk; rmetzler@uni-potsdam.de; achechkin@kipt.kharkov.ua
Deutsche Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [ME 1535/6-1]
2022-01-25T11:40:38+00:00
sword
importub
filename=package.tar
dac93ec76f9381760f4200b38d11133c
Sandev, Trifce
Metzler, Ralf
Chechkin, Aleksei
false
true
Trifce Sandev
Ralf Metzler
Aleksei V. Chechkin
eng
uncontrolled
continuous time random walk (CTRW)
eng
uncontrolled
generalized diffusion equation
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
anomalous diffusion
Astronomie und zugeordnete Wissenschaften
Physik
Institut für Physik und Astronomie
Referiert
Import
Bronze Open-Access
56949
2020
2020
eng
34
47
53
article
IOP Publ. Ltd.
Bristol
1
2020-11-04
2020-11-04
--
Fractional Brownian motion with random diffusivity
Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.
Journal of physics : A, Mathematical and theoretical
emerging residual nonergodicity below the correlation time
10.1088/1751-8121/aba467
1751-8113
1751-8121
outputup:dataSource:WoS:2020
474001
WOS:000588562400001
Metzler, R (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Golm, Germany., rmetzler@uni-potsdam.de
Chinese Council Scholarship [201806830031]; Deutscher Akademischer; Austauschdienst (DAAD)Deutscher Akademischer Austausch Dienst (DAAD); [57214224]; National Natural Science Foundation of China (NNSFC)National; Natural Science Foundation of China (NSFC) [11472126, 11232007]; Priority Academic Programme Development of Jiangsu Higher Education; Institutions (PAPD); Deutsche Forschungsgemeinschaft (DFG)German; Research Foundation (DFG) [ME 1535/7-1]; Foundation for Polish Science; (Fundacja na rzecz Nauki Polskiej); Alexander von Humboldt Polish; Honorary Research Scholarship; Department of Physics and Astronomy of; Padua University [191017]
Metzler, Ralf
2022-12-02T09:46:26+00:00
sword
importub
filename=package.tar
c06f993682e35c525e876aabe1a17402
1363010-6
false
true
CC-BY - Namensnennung 4.0 International
Wei Wang
Andrey G. Cherstvy
Aleksei V. Chechkin
Samudrajit Thapa
Flavio Seno
Xianbin Liu
Ralf Metzler
eng
uncontrolled
stochastic processes
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
fractional Brownian motion
eng
uncontrolled
diffusing diffusivity
eng
uncontrolled
weak ergodicity breaking
Astronomie und zugeordnete Wissenschaften
Physik
Institut für Physik und Astronomie
Referiert
Import
Hybrid Open-Access
38814
2015
2015
eng
16
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ultraslow scaled Brownian motion
We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form D(t) similar or equal to 1/t. For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/6/063038
1367-2630
wos:2015
063038
WOS:000358930400003
Bodrova, AS (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
EUIRSES DCP-PhysBio [N269139]; Academy of Finland (Suomen Akatemia,
Finland Distinguished Professorship); Berlin Mathematical Society;
Deutsche Forschungsgemeinschaft (DFG) [CH707/5-1]; Open Access
Publication Fund of the University of Potsdam
Anna S. Bodrova
Aleksei V. Chechkin
Andrey G. Cherstvy
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
ageing
Institut für Physik und Astronomie
Referiert
Open Access
38753
2015
2015
eng
14
17
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Fluctuation relations for anomalous dynamics generated by time-fractional Fokker-Planck equations
Anomalous dynamics characterized by non-Gaussian probability distributions (PDFs) and/or temporal long-range correlations can cause subtle modifications of conventional fluctuation relations (FRs). As prototypes we study three variants of a generic time-fractional Fokker-Planck equation with constant force. Type A generates superdiffusion, type B subdiffusion and type C both super-and subdiffusion depending on parameter variation. Furthermore type C obeys a fluctuation-dissipation relation whereas A and B do not. We calculate analytically the position PDFs for all three cases and explore numerically their strongly non-Gaussian shapes. While for type C we obtain the conventional transient work FR, type A and type B both yield deviations by featuring a coefficient that depends on time and by a nonlinear dependence on the work. We discuss possible applications of these types of dynamics and FRs to experiments.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/7/075004
1367-2630
wos:2015
075004
WOS:000359128100001
Klages, R (reprint author), Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England., peter.dieterich@tu-dresden.de; r.klages@qmul.ac.uk; chechkin@pks.mpg.de
Peter Dieterich
Rainer Klages
Aleksei V. Chechkin
eng
uncontrolled
fluctuation relations
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
stochastic thermodynamics
eng
uncontrolled
Fokker-Planck equations
Institut für Physik und Astronomie
Referiert
Open Access
38715
2015
2015
eng
1006
1038
33
4
18
article
De Gruyter
Berlin
1
--
--
--
Diffusion and fokker-planck-smoluchowski equations with generalized memory kernel
We consider anomalous stochastic processes based on the renewal continuous time random walk model with different forms for the probability density of waiting times between individual jumps. In the corresponding continuum limit we derive the generalized diffusion and Fokker-Planck-Smoluchowski equations with the corresponding memory kernels. We calculate the qth order moments in the unbiased and biased cases, and demonstrate that the generalized Einstein relation for the considered dynamics remains valid. The relaxation of modes in the case of an external harmonic potential and the convergence of the mean squared displacement to the thermal plateau are analyzed.
Fractional calculus and applied analysis : an international journal for theory and applications
10.1515/fca-2015-0059
1311-0454
1314-2224
wos:2015
WOS:000359161800010
Sandev, T (reprint author), Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany., sandev@pks.mpg.de; chechkin@pks.mpg.de; kantz@pks.mpg.de; rmetzler@uni-potsdam.de
IMU Berlin Einstein Foundation; Academy of Finland within the FiDiPro
programme
Trifce Sandev
Aleksei V. Chechkin
Holger Kantz
Ralf Metzler
eng
uncontrolled
continuous time random walk (CTRW)
eng
uncontrolled
Fokker-Planck-Smoluchowski equation
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
multi-scaling
Institut für Physik und Astronomie
Referiert
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
1751-8121
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
37307
2014
2014
eng
18
48
47
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Ageing and confinement in non-ergodic heterogeneous diffusion processes
We study the effects of ageing-the time delay between initiation of the physical process at t = 0 and start of observation at some time t(a) > 0-and spatial confinement on the properties of heterogeneous diffusion processes (HDPs) with deterministic power-law space-dependent diffusivities, D(x) = D-0 vertical bar x vertical bar(alpha). From analysis of the ensemble and time averaged mean squared displacements and the ergodicity breaking parameter quantifying the inherent degree of irreproducibility of individual realizations of the HDP we obtain striking similarities to ageing subdiffusive continuous time random walks with scale-free waiting time distributions. We also explore how both processes can be distinguished. For confined HDPs we study the long-time saturation of the ensemble and time averaged particle displacements as well as the magnitude of the inherent scatter of time averaged displacements and contrast the outcomes to the results known for other anomalous diffusion processes under confinement.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/47/48/485002
1751-8113
1751-8121
wos:2014
485002
WOS:000345229100004
Cherstvy, AG (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft (DFG) [CH 707/5-1]; Berlin Mathematical
Society; Academy of Finland (Suomen Akatemia)
Andrey G. Cherstvy
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
stochastic processes
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
ageing
eng
uncontrolled
weak ergodicity breaking
Institut für Physik und Astronomie
Referiert
7860
2015
2015
eng
063038
17
article
Dt. Physikalische Ges., IOP
Bad Honnef, London
1
--
2015-06-29
--
Ultraslow scaled Brownian motion
We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/17/6/063038
1367-2630
Universität Potsdam, Publikationsfonds
PA 2015_12
1113.84
online registration
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-78618">Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 188</a>
Ralf Metzler
Andrey G. Cherstvy
Aleksei V. Chechkin
Anna S. Bodrova
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
ageing
Physik
Transport processes
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
7861
2015
eng
postprint
1
--
--
--
Ultraslow scaled Brownian motion
We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations.
New journal of physics : the open-access journal for physics
urn:nbn:de:kobv:517-opus4-78618
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/7860">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Ralf Metzler
Andrey G. Cherstvy
Aleksei V. Chechkin
Anna S. Bodrova
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
188
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic processes
eng
uncontrolled
ageing
Physik
Transport processes
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/7861/pmnr188.pdf
49349
2021
2021
eng
24
1118
postprint
1
2021-02-10
2021-02-10
--
Leveraging large-deviation statistics to decipher the stochastic properties of measured trajectories
Extensive time-series encoding the position of particles such as viruses, vesicles, or individualproteins are routinely garnered insingle-particle tracking experiments or supercomputing studies.They contain vital clues on how viruses spread or drugs may be delivered in biological cells.Similar time-series are being recorded of stock values in financial markets and of climate data.Such time-series are most typically evaluated in terms of time-averaged mean-squareddisplacements (TAMSDs), which remain random variables for finite measurement times. Theirstatistical properties are different for differentphysical stochastic processes, thus allowing us toextract valuable information on the stochastic process itself. To exploit the full potential of thestatistical information encoded in measured time-series we here propose an easy-to-implementand computationally inexpensive new methodology, based on deviations of the TAMSD from itsensemble average counterpart. Specifically, we use the upper bound of these deviations forBrownian motion (BM) to check the applicability of this approach to simulated and real data sets.By comparing the probability of deviations fordifferent data sets, we demonstrate how thetheoretical bound for BM reveals additional information about observed stochastic processes. Weapply the large-deviation method to data sets of tracer beads tracked in aqueous solution, tracerbeads measured in mucin hydrogels, and of geographic surface temperature anomalies. Ouranalysis shows how the large-deviation properties can be efficiently used as a simple yet effectiveroutine test to reject the BM hypothesis and unveil relevant information on statistical propertiessuch as ergodicity breaking and short-time correlations.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-49349
urn:nbn:de:kobv:517-opus4-493494
1866-8372
013008
<a href="http://publishup.uni-potsdam.de/49348">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
New Journal of Physics 23 (2021) 013008 DOI:10.1088/1367-2630/abd50e
CC-BY - Namensnennung 4.0 International
Samudrajit Thapa
Agnieszka Wyłomańska
Grzegorz Sikora
Caroline E. Wagner
Diego Krapf
Holger Kantz
Aleksei V. Chechkin
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1118
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
large-deviation statistic
eng
uncontrolled
time-averaged mean squared displacement
eng
uncontrolled
Chebyshev inequality
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/49349/pmnr1118.pdf
58684
2021
2021
eng
17
29
54
article
IOP Publ. Ltd.
Bristol
1
2021-06-14
2021-06-14
--
Fractional Brownian motion in superharmonic potentials and non-Boltzmann stationary distributions
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise (FGN) in a superharmonic external potential of the form U(x) proportional to x(2n) (n is an element of N). When the noise is considered to be external, the resulting overdamped motion is described by the non-Markovian Langevin equation for fractional Brownian motion. For this case we show the existence of long time, stationary probability density functions (PDFs) the shape of which strongly deviates from the naively expected Boltzmann PDF in the confining potential U(x). We analyse in detail the temporal approach to stationarity as well as the shape of the non-Boltzmann stationary PDF. A typical characteristic is that subdiffusive, antipersistent (with negative autocorrelation) motion tends to effect an accumulation of probability close to the origin as compared to the corresponding Boltzmann distribution while the opposite trend occurs for superdiffusive (persistent) motion. For this latter case this leads to distinct bimodal shapes of the PDF. This property is compared to a similar phenomenon observed for Markovian Levy flights in superharmonic potentials. We also demonstrate that the motion encoded in the fractional Langevin equation driven by FGN always relaxes to the Boltzmann distribution, as in this case the fluctuation-dissipation theorem is fulfilled.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8121/ac019b
1751-8113
1751-8121
outputup:dataSource:WoS:2021
29LT01
WOS:000661636400001
Metzler, R (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
German Research Foundation (DFG)German Research Foundation (DFG) [ME 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNP)
Metzler, Ralf
2023-04-03T11:09:13+00:00
sword
importub
filename=package.tar
b1c2636b498750422907ee3fcc68b6d7
1363010-6
209217-7
false
true
CC-BY - Namensnennung 4.0 International
Tobias Guggenberger
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
Boltzmann distribution
eng
uncontrolled
non-Gaussian distribution
Physik
Institut für Physik und Astronomie
Referiert
Import
Hybrid Open-Access
45794
2016
2016
eng
18
33
16
11
article
EDP Sciences
Les Ulis
1
--
--
--
Comb Model with Slow and Ultraslow Diffusion
We consider a generalized diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyze the probability distribution functions and we derive the mean squared displacement in x and y directions. Different forms of the memory kernels (Dirac delta, power-law, and distributed order) are considered. It is shown that anomalous diffusion may occur along both x and y directions. Ultraslow diffusion and some more general diffusive processes are observed as well. We give the corresponding continuous time random walk model for the considered two dimensional diffusion-like equation on a comb, and we derive the probability distribution functions which subordinate the process governed by this equation to the Wiener process.
Mathematical modelling of natural phenomena
10.1051/mmnp/201611302
0973-5348
1760-6101
wos2016:2019
WOS:000378279200002
Chechkin, A (reprint author), Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, D-01187 Dresden, Germany.; Chechkin, A (reprint author), Akhiezer Inst Theoret Phys, UA-61108 Kharkov, Ukraine.; Chechkin, A (reprint author), Univ Padua, Dept Phys & Astron, Galileo Galilei DFA, I-35131 Padua, Italy., chechkin@pks.mpg.de
Israel Science Foundation [ISF-1028]; Academy of Finland within the Finland Distinguished Professor programme
importub
2020-03-22T21:30:01+00:00
filename=package.tar
04e2b577aaacb3efc39d148569f70c94
T. Sandev
Alexander Iomin
Holger Kantz
Ralf Metzler
Aleksei V. Chechkin
eng
uncontrolled
comb-like model
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
mean squared displacement
eng
uncontrolled
probability density function
Institut für Physik und Astronomie
Referiert
Import
35363
2013
2013
eng
114
126
13
2
8
article
EDP Sciences
Les Ulis
1
--
--
--
Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
Mathematical modelling of natural phenomena
10.1051/mmnp/20138208
0973-5348
wos:2011-2013
WOS:000318215200008
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme)
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-415480">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 593</a>
Aleksei V. Chechkin
I. M. Zaid
M. A. Lomholt
Igor M. Sokolov
Ralf Metzler
eng
uncontrolled
Bulk-mediated diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
Levy flights
eng
uncontrolled
stochastic processes
Institut für Chemie
Referiert
48003
2020
2020
eng
17
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-08-14
2020-08-14
--
Unexpected crossovers in correlated random-diffusivity processes
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.
New Journal of Physics
10.1088/1367-2630/aba390
1367-2630
Universität Potsdam
PA 2020_077
1323.56
083041
<a href="https://doi.org/10.25932/publishup-48004">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1006</a>
false
false
CC-BY - Namensnennung 4.0 International
Wei Wang
Flavio Seno
Igor M. Sokolov
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
non-Gaussianity
eng
uncontrolled
fractional Brownian motion
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
48004
2020
2020
eng
18
1006
postprint
1
2020-10-23
2020-10-23
--
Unexpected crossovers in correlated random-diffusivity processes
The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by 'viscoelastic' anomalous diffusion, in which the increments of the motion feature long-ranged negative and positive correlations. While viscoelastic anomalous diffusion is typically modelled by a Gaussian process with correlated increments, so-called fractional Gaussian noise, an increasing number of systems are reported, in which viscoelastic anomalous diffusion is paired with non-Gaussian displacement distributions. Following recent advances in Brownian yet non-Gaussian diffusion we here introduce and discuss several possible versions of random-diffusivity models with long-ranged correlations. While all these models show a crossover from non-Gaussian to Gaussian distributions beyond some correlation time, their mean squared displacements exhibit strikingly different behaviours: depending on the model crossovers from anomalous to normal diffusion are observed, as well as a priori unexpected dependencies of the effective diffusion coefficient on the correlation exponent. Our observations of the non-universality of random-diffusivity viscoelastic anomalous diffusion are important for the analysis of experiments and a better understanding of the physical origins of 'viscoelastic yet non-Gaussian' diffusion.
10.25932/publishup-48004
urn:nbn:de:kobv:517-opus4-480049
1866-8372
New Journal of Physics 22 (2020) 083041 DOI: 10.1088/1367-2630/aba390
083041
<a href="http://publishup.uni-potsdam.de/48003">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
CC-BY - Namensnennung 4.0 International
Wei Wang
Flavio Seno
Igor M. Sokolov
Aleksei V. Chechkin
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1006
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
non-Gaussianity
eng
uncontrolled
fractional Brownian motion
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/48004/pmnr1006.pdf
41548
2013
2013
eng
114
126
13
593
postprint
1
2019-02-12
2019-02-12
--
Bulk-mediated surface diffusion on a cylinder in the fast exchange limit
In various biological systems and small scale technological applications particles transiently bind to a cylindrical surface. Upon unbinding the particles diffuse in the vicinal bulk before rebinding to the surface. Such bulk-mediated excursions give rise to an effective surface translation, for which we here derive and discuss the dynamic equations, including additional surface diffusion. We discuss the time evolution of the number of surface-bound particles, the effective surface mean squared displacement, and the surface propagator. In particular, we observe sub- and superdiffusive regimes. A plateau of the surface mean-squared displacement reflects a stalling of the surface diffusion at longer times. Finally, the corresponding first passage problem for the cylindrical geometry is analysed.
Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
10.25932/publishup-41548
urn:nbn:de:kobv:517-opus4-415480
1866-8372
online registration
Mathematical modelling of natural phenomena 8 (2013) 2, pp.114–126 DOI 10.1051/mmnp/20138208
<a href="http://publishup.uni-potsdam.de/frontdoor/index/index/docId/35363">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Keine öffentliche Lizenz: Unter Urheberrechtsschutz
Aleksei V. Chechkin
Irwin M. Zaid
Michael A. Lomholt
Igor M. Sokolov
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
593
eng
uncontrolled
Bulk-mediated diffusion;
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
Levy flights
eng
uncontrolled
stochastic processes
Mathematik
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
Cambridge University Press (CUP)
Universität Potsdam
https://publishup.uni-potsdam.de/files/41548/pmnr593.pdf
38596
2015
2015
eng
18
37
48
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Quantifying the non-ergodicity of scaled Brownian motion
We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form D(t) similar or equal to t(alpha-1). We compute the ergodicity breaking parameter EB in the entire range of scaling exponents a, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Delta the EB parameter as function of the scaling exponent a has no divergence at alpha - 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/48/37/375002
1751-8113
1751-8121
wos:2015
375002
WOS:000361551700004
Safdari, H (reprint author), Shahid Beheshti Univ, Dept Phys, GC, Tehran 19839, Iran., rmetzler@uni-potsdam.de
Academy of Finland (Suomen Akatemia, Finland Distinguished
Professorship); Deutsche Forschungsgemeinschaft; IMU Berlin Einstein
Foundation
Hadiseh Safdari
Andrey G. Cherstvy
Aleksei V. Chechkin
Felix Thiel
Igor M. Sokolov
Ralf Metzler
eng
uncontrolled
scaled Brownian motion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
ageing
Institut für Physik und Astronomie
Referiert
42259
2019
2019
eng
28
507
postprint
1
2019-01-15
2019-01-15
--
Crossover from anomalous to normal diffusion
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 noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
truncated power-law noise correlations and applications to dynamics in lipid bilayers
10.25932/publishup-42259
urn:nbn:de:kobv:517-opus4-422590
1866-8372
103027
New Journal of Physics 20 (2018) Art. 103027 DOI: 10.1088/1367-2630/aae4b2
103027
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/42260">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC-BY - Namensnennung 4.0 International
Daniel Molina-Garcia
Trifce Sandev
Hadiseh Safdari
Gianni Pagnini
Aleksei V. Chechkin
Ralf Metzler
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
507
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
truncated power-law correlated noise
eng
uncontrolled
lipid bilayer membrane dynamics
Physik
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/42259/pmnr507.pdf
42260
2018
2018
eng
28
20
article
IOP Publishing Ltd
London und Bad Honnef
1
2018-10-18
2018-10-18
--
Crossover from anomalous to normal diffusion
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 noise, that is noise with Gaussian amplitude and power-law correlations, which are cut off at some mesoscopic time scale. Concretely we consider such noise with built-in exponential or power-law tempering, driving an overdamped Langevin equation (fractional Brownian motion) and fractional Langevin equation motion. We derive explicit expressions for the mean squared displacement and correlation functions, including different shapes of the crossover behaviour depending on the concrete tempering, and discuss the physical meaning of the tempering. In the case of power-law tempering we also find a crossover behaviour from faster to slower superdiffusion and slower to faster subdiffusion. As a direct application of our model we demonstrate that the obtained dynamics quantitatively describes the subdiffusion–diffusion and subdiffusion–subdiffusion crossover in lipid bilayer systems. We also show that a model of tempered fractional Brownian motion recently proposed by Sabzikar and Meerschaert leads to physically very different behaviour with a seemingly paradoxical ballistic long time scaling.
New Journal of Physics
truncated power-law noise correlations and applications to dynamics in lipid bilayers
10.1088/1367-2630/aae4b2
1367-2630
103027
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-422590">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 507</a>
CC-BY - Namensnennung 4.0 International
Daniel Molina-Garcia
Trifce Sandev
Hadiseh Safdari
Gianni Pagnini
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
truncated power-law correlated noise
eng
uncontrolled
lipid bilayer membrane dynamics
Physik
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access