56040
2022
2022
eng
1
28
28
postprint
Universitätsverlag Potsdam
Potsdam
1
2022-09-13
2022-09-13
--
Stochastic harmonic trapping of a Lévy walk: transport and first-passage dynamics under soft resetting strategies
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-56040
urn:nbn:de:kobv:517-opus4-560402
1866-8372
033003
Version of record
Metzler, Ralf
Deng, Weihua
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/56039">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC-BY - Namensnennung 4.0 International
Pengbo Xu
Tian Zhou
Ralf Metzler
Weihua Deng
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1262
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic resetting
eng
uncontrolled
Levy walks
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/56040/pmnr1262.pdf
56039
2022
2022
eng
1
28
28
3
24
article
Deutsche Physikalische Gesellschaft
Bad Honnef
1
2022-03-08
2022-03-08
--
Stochastic harmonic trapping of a Lévy walk
We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
transport and first-passage dynamics under soft resetting strategies
10.1088/1367-2630/ac5282
1367-2630
033003
<a href="https://doi.org/10.25932/publishup-56040">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1262</a>
Metzler, Ralf
Deng, Weihua
WOS:000766357100001
Deng, Weihua (corresponding author), Lanzhou Univ, Gansu Key Lab Appl Math & Complex Syst, Sch Math & Stat, Lanzhou 730000, Peoples R China.; Metzler, Ralf (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany.
1464444-7
National Natural Science Foundation of China [12071195]
12071195
AI and Big Data; Funds [2019620005000775]
2019620005000775
German Science Foundation (DFG) [ME; 1535/12-1]
ME; 1535/12-1
Fundacja na rzecz Nauki; Polskiej, FNP
China Postdoctoral Science Foundation [8206300491]
8206300491
German Research Foundation
Potsdam University
CC-BY - Namensnennung 4.0 International
Pengbo Xu
Tian Zhou
Ralf Metzler
Weihua Deng
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
stochastic resetting
eng
uncontrolled
Levy walks
Physik
Institut für Physik und Astronomie
Extern
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
61765
2022
2022
eng
14
192
19
article
Royal Society
London
1
2022-07-06
2022-07-06
--
Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.
Interface : journal of the Royal Society
10.1098/rsif.2022.0233
35857918
1742-5689
1742-5662
outputup:dataSource:WoS:2022
20220233
WOS:000821277200001
Metzler, R (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
German Science Foundation (DFG) [ME 1535/12-1]; Polish National Agency; for Academic Exchange(NAWA)
Metzler, Ralf
2023-12-08T07:51:45+00:00
sword
importub
filename=package.tar
2b9418dd63fd97bf9a2b38a3e32651ab
2156283-0
2197250-3
false
true
Timo J. Doerries
Aleksei V. Chechkin
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
mobile-immobile model
eng
uncontrolled
tau proteins
Physik
Institut für Physik und Astronomie
Referiert
Import
62098
2022
2022
eng
18
7
24
article
Dt. Physikalische Ges.
[Bad Honnef]
1
2022-07-07
2022-07-07
--
Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials
We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/ac7b3c
1367-2630
outputup:dataSource:WoS:2022
073006
WOS:000821434200001
Metzler, Ralf (corresponding author), Wroclaw Univ Sci & Technol, Hugo Steinhaus Ctr, Fac Pure & Appl Math, Wyspianskiego 27, PL-50370 Wroclaw, Poland., rmetzler@uni-potsdam.de
German Science Foundation (DFG) [ME 1535/12-1]; Polish National Agency; for Academic Exchange (NAWA); German Research Foundation (DFG); [491466077]
Metzler, Ralf
2024-01-11T12:01:03+00:00
sword
importub
filename=package.tar
dac404b50671d21178fa3267d69634c1
1464444-7
false
true
CC-BY - Namensnennung 4.0 International
Tobias Guggenberger
Aleksei Chechkin
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
Boltzmann distribution
eng
uncontrolled
fractional Brownian motion
Mathematik
Physik
Institut für Physik und Astronomie
Referiert
Import
Gold Open-Access
DOAJ gelistet
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
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
61153
2021
eng
31
29
54
article
IOP Publ. Ltd.
Bristol
1
2021-06-29
2021-06-29
--
Characterising stochastic motion in heterogeneous media driven by coloured non-Gaussian noise
We study the stochastic motion of a test particle in a heterogeneous medium in terms of a position dependent diffusion coefficient mimicking measured deterministic diffusivity gradients in biological cells or the inherent heterogeneity of geophysical systems. Compared to previous studies we here investigate the effect of the interplay of anomalous diffusion effected by position dependent diffusion coefficients and coloured non-Gaussian noise. The latter is chosen to be distributed according to Tsallis' q-distribution, representing a popular example for a non-extensive statistic. We obtain the ensemble and time averaged mean squared displacements for this generalised process and establish its non-ergodic properties as well as analyse the non-Gaussian nature of the associated displacement distribution. We consider both non-stratified and stratified environments.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8121/abfba6
1751-8113
1751-8121
outputup:dataSource:WoS:2021
295002
WOS:000667489900001
Xu, Y; Li, YG (corresponding author), Northwestern Polytech Univ, Sch Math & Stat, Xian 710072, Peoples R China.; Metzler, R (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de; hsux3@nwpu.edu.cn; liyonge@nwpu.edu.cn; <br /> rmetzler@uni-potsdam.de
NSF of ChinaNational Natural Science Foundation of China (NSFC) [11772255, 11902118]; National Key Research and Development Program of China [2018AAA0102201]; Research Funds for Interdisciplinary Subject of Northwestern Poly-technical University; Shaanxi Project for Distinguished Young Scholars; Shaanxi Provincial Key RD Program [2020KW-013, 2019TD-010]; German Research Foundation (DFG)German Research Foundation (DFG) [ME 1535/12-1]; Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNP) within an Alexander von Humboldt Honorary Polish Research Scholarship
Xu, Y
Li, YG
Metzler, Ralf
2023-10-26T07:16:08+00:00
sword
importub
filename=package.tar
d3d74bc4a4cdfee3a6e9f450fff93b23
1363010-6
209217-7
Erratum: <a href="https://doi.org/10.1088/1751-8121/ac14da">https://doi.org/10.1088/1751-8121/ac14da</a>
false
true
CC-BY - Namensnennung 4.0 International
Nicholas Mwilu Mutothya
Yong Xu
Yongge Li
Ralf Metzler
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
non-extensive statistics
eng
uncontrolled
coloured
eng
uncontrolled
noise
eng
uncontrolled
heterogeneous diffusion process
Physik
Institut für Physik und Astronomie
Referiert
Import
Hybrid Open-Access
55754
2021
2022
eng
1
23
23
postprint
Universitätsverlag Potsdam
Potsdam
1
2022-07-25
2022-07-25
--
Distribution of first-reaction times with target regions on boundaries of shell-like domains
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-55754
urn:nbn:de:kobv:517-opus4-557542
1866-8372
Version of record
123049
Grebenkov, Denis S
Metzler, Ralf
<a href="http://publishup.uni-potsdam.de/55755">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
CC-BY - Namensnennung 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1255
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage time
eng
uncontrolled
first-reaction time
eng
uncontrolled
shell-like geometries
eng
uncontrolled
approximate methods
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/55754/pmnr1255.pdf
55755
2021
2021
eng
1
23
23
23
2021
article
IOP Publishing
London
1
2021-12-29
2021-12-29
--
Distribution of first-reaction times with target regions on boundaries of shell-like domains
We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
New Journal of Physics (NJP)
10.1088/1367-2630/ac4282
1367-2630
123049
Grebenkov, Denis S
Metzler, Ralf
<a href="https://doi.org/10.25932/publishup-55754">Zweitveröffentlichung in der Schriftenreihe Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1255</a>
false
false
CC-BY - Namensnennung 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage time
eng
uncontrolled
first-reaction time
eng
uncontrolled
shell-like geometries
eng
uncontrolled
approximate methods
Physik
Institut für Physik und Astronomie
Extern
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
61642
2021
2021
eng
24
2
article
IOP Publishing
Bristol
1
2021-11-23
2021-11-23
--
First passage dynamics of stochastic motion in heterogeneous media driven by correlated white Gaussian and coloured non-Gaussian noises
We study the first passage dynamics for a diffusing particle experiencing a spatially varying diffusion coefficient while driven by correlated additive Gaussian white noise and multiplicative coloured non-Gaussian noise. We consider three functional forms for position dependence of the diffusion coefficient: power-law, exponential, and logarithmic. The coloured non-Gaussian noise is distributed according to Tsallis' q-distribution. Tracks of the non-Markovian systems are numerically simulated by using the fourth-order Runge-Kutta algorithm and the first passage times (FPTs) are recorded. The FPT density is determined along with the mean FPT (MFPT). Effects of the noise intensity and self-correlation of the multiplicative noise, the intensity of the additive noise, the cross-correlation strength, and the non-extensivity parameter on the MFPT are discussed.
Journal of physics. Complexity
10.1088/2632-072X/ac35b5
2632-072X
outputup:dataSource:WoS:2021
045012
WOS:000721581200001
Metzler, Ralf (corresponding author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Foundation for Polish Science (Fundacja na rzecz Nauki Polskiej, FNP) within an Alexander von Humboldt Polish Honorary Research Scholarship; German Science Foundation (DFG)German Research Foundation (DFG) [ME 1535/12-1]; National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [12072264, 11902118]; Key International (Regional) Joint Research Program of NSF of China [12120101002]; Research Funds for Interdisciplinary Subject of Northwestern PolytechnicalUniversity, Shaanxi ProvincialKeyR D Program [2020KW-013, 2019TD-010]; Foundation of Key Laboratory of Structural Mechanics and Intelligent Materials of Hebei Province
2023-11-30T06:37:31+00:00
sword
importub
filename=package.tar
0939cbfdd4f3003795f4108714b2df16
Metzler, Ralf
3034619-8
CC-BY - Namensnennung 4.0 International
Nicholas Mwilu Mutothya
Yong Xu
Yongge Li
Ralf Metzler
Nicholas Muthama Mutua
eng
uncontrolled
first passage
eng
uncontrolled
diffusion
eng
uncontrolled
non-Gaussian
eng
uncontrolled
correlated noise
Physik
Institut für Physik und Astronomie
Referiert
Import
Gold Open-Access
DOAJ gelistet