45235
2016
2016
eng
19
49
article
IOP Publ. Ltd.
Bristol
1
--
--
--
A single predator charging a herd of prey: effects of self volume and predator-prey decision-making
We study the degree of success of a single predator hunting a herd of prey on a two-dimensional square lattice landscape. We explicitly consider the self volume of the prey restraining their dynamics on the lattice. The movement of both predator and prey is chosen to include an intelligent, decision making step based on their respective sighting ranges, the radius in which they can detect the other species (prey cannot recognise each other besides the self volume interaction): after spotting each other the motion of prey and predator turns from a nearest neighbour random walk into directed escape or chase, respectively. We consider a large range of prey densities and sighting ranges and compute the mean first passage time for a predator to catch a prey as well as characterise the effective dynamics of the hunted prey. We find that the prey's sighting range dominates their life expectancy and the predator profits more from a bad eyesight of the prey than from his own good eye sight. We characterise the dynamics in terms of the mean distance between the predator and the nearest prey. It turns out that effectively the dynamics of this distance coordinate can be captured in terms of a simple Ornstein–Uhlenbeck picture. Reducing the many-body problem to a simple two-body problem by imagining predator and nearest prey to be connected by an effective Hookean bond, all features of the model such as prey density and sighting ranges merge into the effective binding constant.
Journal of physics : A, Mathematical and theoretical
10.1088/1751-8113/49/22/225601
1751-8113
1751-8121
wos2016:2019
225601
WOS:000376392100006
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam Golm, Germany., rmetzler@uni-potsdam.de
Alexander von Humboldt Fellowship; ARRS Program [P1-0002]; Academy of Finland FiDiPro grant
importub
2020-03-22T16:51:01+00:00
filename=package.tar
357ecfccb10a292ef770197c7c29f4ec
Maria Schwarzl
Aljaz Godec
Gleb Oshanin
Ralf Metzler
eng
uncontrolled
first passage process
eng
uncontrolled
diffusion
eng
uncontrolled
predator-prey model
Institut für Physik und Astronomie
Referiert
Import
40371
2017
2017
eng
1
11
19
article
IOP
London
1
--
2017-10-24
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
Westudy the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
New journal of physics
10.1088/1367-2630/aa8ed9
1367-2630
Universität Potsdam, Publikationsfonds
PA 2017_54
1299.48
online registration
WOS:000413743900003
103025
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-403726">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 391</a>
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
first passage time
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
aspect ratio
eng
uncontrolled
protein search
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
Universität Potsdam
35632
2012
2012
eng
8
3
86
article
American Physical Society
College Park
1
--
--
--
First passages in bounded domains When is the mean first passage time meaningful?
We study the first passage statistics to adsorbing boundaries of a Brownian motion in bounded two-dimensional domains of different shapes and configurations of the adsorbing and reflecting boundaries. From extensive numerical analysis we obtain the probability P(omega) distribution of the random variable omega = tau(1)/(tau(1) + tau(2)), which is a measure for how similar the first passage times tau(1) and tau(2) are of two independent realizations of a Brownian walk starting at the same location. We construct a chart for each domain, determining whether P(omega) represents a unimodal, bell-shaped form, or a bimodal, M-shaped behavior. While in the former case the mean first passage time (MFPT) is a valid characteristic of the first passage behavior, in the latter case it is an insufficient measure for the process. Strikingly we find a distinct turnover between the two modes of P(omega), characteristic for the domain shape and the respective location of absorbing and reflective boundaries. Our results demonstrate that large fluctuations of the first passage times may occur frequently in two-dimensional domains, rendering quite vague the general use of the MFPT as a robust measure of the actual behavior even in bounded domains, in which all moments of the first passage distribution exist.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.86.031143
1539-3755
wos:2011-2013
031143
WOS:000309338900001
Mattos, TG (reprint author), Max Planck Inst Intelligent Syst, Heisenbergstr 3, D-70569 Stuttgart, Germany., tgmattos@is.mpg.de
European Science Foundation; Marie Curie International Research Staff
Exchange Scheme Fellowship within the 7th European Community Framework
Programme [PIRSES-GA-2010-269139]; Academy of Finland within the FiDiPro
program; ESF Research Network "Exploring the Physics of Small Devices"
Thiago G. Mattos
Carlos Mejia-Monasterio
Ralf Metzler
Gleb Oshanin
Institut für Physik und Astronomie
Referiert
46250
2017
2017
eng
11
19
article
IOP Publ. Ltd.
Bristol
1
--
--
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry-characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. A similar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA. We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters. We analyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
New journal of physics : the open-access journal for physics
10.1088/1367-2630/aa8ed9
1367-2630
wos:2017
103025
WOS:000413743900003
Grebenkov, DS (reprint author), Univ Paris Saclay, Ecole Polytech, CNRS, Lab Phys Mat Condensee,UMR7643, F-91128 Palaiseau, France.; Grebenkov, DS (reprint author), ISCP, Bolshoy Vlasyevskiy Pereulok 11, Moscow 119002, Russia., denis.grebenkov@polytechnique.edu
French National Research Agency [ANR-13-JSV5-0006-01]; Deutsche Forschungsgemeinschaft; Potsdam University
importub
2020-04-19T23:54:01+00:00
filename=package.tar
a0cdd125e124f1705eb6953da8eab0c4
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
first passage time
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
aspect ratio
eng
uncontrolled
protein search
Institut für Physik und Astronomie
Referiert
Import
43651
2019
2019
eng
16
21
article
Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
Bad Honnef und London
1
2019-07-23
2019-07-23
--
Single-trajectory spectral analysis of scaled Brownian motion
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
New Journal of Physics
10.1088/1367-2630/ab2f52
1367-2630
073043
Universität Potsdam
PA 2019_65
1618.4
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-436522">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 753</a>
false
false
Vittoria Sposini
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
power spectral analysis
eng
uncontrolled
single trajectory analysis
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
49268
2019
2019
eng
2
20
150
article
American Institute of Physics
Melville
1
2019-05-30
2019-05-30
--
Trapping of diffusing particles by periodic absorbing rings on a cylindrical tube
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.5098390
31153181
0021-9606
1089-7690
wos:2019
206101
WOS:000473301400064
Grebenkov, DS (reprint author), Univ Paris Saclay, CNRS Ecole Polytech, UMP 7643, Lab Phys Mat Condensee, F-91128 Palaiseau, France., denis.grebenkov@polytechnique.edu
Intramural Research Program of the NIH, Center for Information TechnologyUnited States Department of Health & Human ServicesNational Institutes of Health (NIH) - USA
2021-02-04T07:30:06+00:00
sword
importub
filename=package.tar
58e6c82681c0455956afabb3638dd602
Grebenkov, Denis S.
false
true
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Leonardo Dagdug
Alexander M. Berezhkovskii
Alexei T. Skvortsov
Physik
Institut für Physik und Astronomie
Referiert
Import
Green Open-Access
44287
2019
2019
eng
23
21
article
Dt. Physikalische Ges.
Bad Honnef
1
2019-12-13
2019-12-13
--
Full distribution of first exit times in the narrow escape problem
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
New Journal of Physics
10.1088/1367-2630/ab5de4
1367-2630
Universität Potsdam
PA 2019_125
1332.80
122001
<a href="https://doi.org/10.25932/publishup-44288">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 810</a>
false
false
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
narrow escape problem
eng
uncontrolled
first-passage time distribution
eng
uncontrolled
mean versus most probable reaction times
eng
uncontrolled
mixed boundary conditions
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Open Access
50401
2019
2019
eng
13
1
9
article
American Physical Society
College Park
1
2019-01-31
2019-01-31
--
Spectral Content of a Single Non-Brownian Trajectory
Time-dependent processes are often analyzed using the power spectral density (PSD) calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble average. Frequently, the available experimental datasets are too small for such ensemble averages, and hence, it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from S(f, T), the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable parametrized by frequency f and observation time T, for a broad family of anomalous diffusions-fractional Brownian motion with Hurst index H-and derive exactly its probability density function. We show that S(f, T) is proportional-up to a random numerical factor whose universal distribution we determine-to the ensemble-averaged PSD. For subdiffusion (H < 1/2), we find that S(f, T) similar to A/f(2H+1) with random amplitude A. In sharp contrast, for superdiffusion (H > 1/2) S(f, T) similar to BT2H-1/f(2) with random amplitude B. Remarkably, for H > 1/2 the PSD exhibits the same frequency dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for H > 1/2 the PSD is ageing and is dependent on T. Our predictions for both sub-and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels and by extensive simulations.
Physical review : X, Expanding access
10.1103/PhysRevX.9.011019
2160-3308
wos:2019
011019
WOS:000457704200001
Oshanin, G (reprint author), Sorbonne Univ, CNRS, Lab Phys Theor Mat Condensee, UMR 7600, 4 Pl Jussieu, F-75252 Paris 05, France., oshanin@lptmc.jussieu.fr
National Science FoundationNational Science Foundation (NSF) [1401432]; European Research Council under the European Unions Horizon 2020 Research and Innovation Program [694925]; German Research Foundation (DFG)German Research Foundation (DFG) [ME-1535/7-1]; Humboldt Polish Honorary Research Fellowship from the Foundation for Polish Science; DFG through the Collaborative Research Centre [CRC 1261]; VolkswagenStiftungVolkswagen [Az. 92738]
2021-04-19T10:41:39+00:00
sword
importub
filename=package.tar
e1a0b217f6c26c34318e5eda3adb22f3
Oshanin, Gleb
false
true
CC BY - Namensnennung, 4.0 International
Diego Krapf
Nils Lukat
Enzo Marinari
Ralf Metzler
Gleb Oshanin
Christine Selhuber-Unkel
Alessio Squarcini
Lorenz Stadler
Matthias Weiss
Xinran Xu
eng
uncontrolled
Biological Physics
eng
uncontrolled
Interdisciplinary Physics
eng
uncontrolled
Statistical Physics
Physik
Institut für Physik und Astronomie
Referiert
Import
Gold Open-Access
DOAJ gelistet
47695
2020
2020
eng
26
6
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-06-26
2020-06-26
--
Universal spectral features of different classes of random-diffusivity processes
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
New Journal of Physics
10.1088/1367-2630/ab9200
1367-2630
063056
<a href="https://doi.org/10.25932/publishup-47696">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 999</a>
Universität Potsdam
PA 2020_052
1357.79
false
false
CC BY - Namensnennung, 4.0 International
Vittoria Sposini
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
50396
2020
2021
eng
23
23
article
Dt. Physikalische Ges.
Bad Honnef
1
2021-04-19
2021-04-19
--
Exact distributions of the maximum and range of random diffusivity processes
We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
New Journal of Physics
10.1088/1367-2630/abd313
1367-2630
Universität Potsdam
PA 2021_006
1260.81
023014
<a href="https://doi.org/10.25932/publishup-50397">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1142</a>
false
false
CC BY - Namensnennung, 4.0 International
Denis S. Grebenkov
Vittoria Sposini
Ralf Metzler
Gleb Oshanin
Flavio Seno
eng
uncontrolled
random diffusivity
eng
uncontrolled
extremal values
eng
uncontrolled
maximum and range
eng
uncontrolled
diffusion
eng
uncontrolled
Brownian motion
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
48404
2020
2020
eng
28
22
article
Dt. Physikalische Ges.
Bad Honnef
1
2020-10-02
2020-10-02
--
From single-particle stochastic kinetics to macroscopic reaction rates
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
New Journal of Physics
fastest first-passage time of N random walkers
10.1088/1367-2630/abb1de
1367-2630
Universität Potsdam
PA 2020_095
1418.10
103004
<a href="https://doi.org/10.25932/publishup-48405">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1018</a>
false
false
CC BY - Namensnennung, 4.0 International
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
42299
2018
2018
eng
12
1
article
Macmillan Publishers Limited
London
1
2018-12-13
2018-12-13
--
Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants—the inverse of the mean-first-passage-time to the reaction-event. In contradiction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly solvable model we study the effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delineated by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.
Communications Chemistry
10.1038/s42004-018-0096-x
2399-3669
96
Universität Potsdam
PA 2018_82
1785.00
<a href="http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-422989">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 527</a>
CC BY - Namensnennung, 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Chemie und zugeordnete Wissenschaften
open_access
Referiert
Publikationsfonds der Universität Potsdam
Open Access
52194
2021
2021
eng
20
postprint
1
2021-09-02
2021-06-08
--
A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-52194
urn:nbn:de:kobv:517-opus4-521942
1866-8372
<a href="http://publishup.uni-potsdam.de/52193">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
093004
Denis S Grebenkov et al 2021 New J. Phys. 23 093004
true
true
CC BY - Namensnennung, 4.0 International
Denis Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1159
eng
uncontrolled
diffusion
eng
uncontrolled
reaction cascade
eng
uncontrolled
first passage time
Astronomie und zugeordnete Wissenschaften
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/52194/pmnr1159.pdf
52193
2021
2021
eng
18
23
article
IOP - Institute of Physics Publishing
Bristol
1
2021-09-02
2021-06-08
--
A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes
We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.
New Journal of Physics (NJP)
1367-2630
10.1088/1367-2630/ac1e42
Universität Potsdam
PA 2021_095
1931.47
<a href="https://doi.org/10.25932/publishup-52194">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1159</a>
093004
false
false
CC BY - Namensnennung, 4.0 International
Denis Grebenkov
Ralf Metzler
Gleb Oshanin
eng
uncontrolled
diffusion
eng
uncontrolled
reaction cascade
eng
uncontrolled
first passage time
Astronomie und zugeordnete Wissenschaften
Physik
Institut für Physik und Astronomie
Referiert
Publikationsfonds der Universität Potsdam
Gold Open-Access
48405
2020
2020
eng
29
1018
postprint
1
2020-11-24
2020-11-24
--
From single-particle stochastic kinetics to macroscopic reaction rates
We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
fastest first-passage time of N random walkers
10.25932/publishup-48405
urn:nbn:de:kobv:517-opus4-484059
1866-8372
New Journal of Physics 22 (2020) Art. 103004 DOI: 10.1088/1367-2630/abb1de
103004
<a href="http://publishup.uni-potsdam.de/48404">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
1018
eng
uncontrolled
diffusion
eng
uncontrolled
first-passage
eng
uncontrolled
fastest first-passage time of N walkers
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/48405/pmnr1018.pdf
50397
2020
2021
eng
24
1142
postprint
1
2021-02-09
2021-02-09
--
Exact distributions of the maximum and range of random diffusivity processes
We study the extremal properties of a stochastic process xt defined by the Langevin equation ẋₜ =√2Dₜ ξₜ, in which ξt is a Gaussian white noise with zero mean and Dₜ is a stochastic‘diffusivity’, defined as a functional of independent Brownian motion Bₜ.We focus on threechoices for the random diffusivity Dₜ: cut-off Brownian motion, Dₜt ∼ Θ(Bₜ), where Θ(x) is the Heaviside step function; geometric Brownian motion, Dₜ ∼ exp(−Bₜ); and a superdiffusive process based on squared Brownian motion, Dₜ ∼ B²ₜ. For these cases we derive exact expressions for the probability density functions of the maximal positive displacement and of the range of the process xₜ on the time interval ₜ ∈ (0, T).We discuss the asymptotic behaviours of the associated probability density functions, compare these against the behaviour of the corresponding properties of standard Brownian motion with constant diffusivity (Dₜ = D0) and also analyse the typical behaviour of the probability density functions which is observed for a majority of realisations of the stochastic diffusivity process.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-50397
urn:nbn:de:kobv:517-opus4-503976
1866-8372
New Journal of Physics 23 (2021) Art. 023014 DOI: 10.1088/1367-2630/abd313
023014
<a href="http://publishup.uni-potsdam.de/50396">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC BY - Namensnennung, 4.0 International
Denis S. Grebenkov
Vittoria Sposini
Ralf Metzler
Gleb Oshanin
Flavio Seno
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
1142
eng
uncontrolled
random diffusivity
eng
uncontrolled
extremal values
eng
uncontrolled
maximum and range
eng
uncontrolled
diffusion
eng
uncontrolled
Brownian motion
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/50397/pmnr1142.pdf
52711
2018
2018
eng
16393
16401
9
24
20
article
Royal Society of Chemistry
Cambridge
1
2018-05-21
2018-05-21
--
Towards a full quantitative description of single-molecule reaction kinetics in biological cells
The first-passage time (FPT), i.e., the moment when a stochastic process reaches a given threshold value for the first time, is a fundamental mathematical concept with immediate applications. In particular, it quantifies the statistics of instances when biomolecules in a biological cell reach their specific binding sites and trigger cellular regulation. Typically, the first-passage properties are given in terms of mean first-passage times. However, modern experiments now monitor single-molecular binding-processes in living cells and thus provide access to the full statistics of the underlying first-passage events, in particular, inherent cell-to-cell fluctuations. We here present a robust explicit approach for obtaining the distribution of FPTs to a small partially reactive target in cylindrical-annulus domains, which represent typical bacterial and neuronal cell shapes. We investigate various asymptotic behaviours of this FPT distribution and show that it is typically very broad in many biological situations, thus, the mean FPT can differ from the most probable FPT by orders of magnitude. The most probable FPT is shown to strongly depend only on the starting position within the geometry and to be almost independent of the target size and reactivity. These findings demonstrate the dramatic relevance of knowing the full distribution of FPTs and thus open new perspectives for a more reliable description of many intracellular processes initiated by the arrival of one or few biomolecules to a small, spatially localised region inside the cell.
Physical chemistry, chemical physics : a journal of European Chemical Societies
10.1039/c8cp02043d
29873351
1463-9076
1463-9084
wos:2018
WOS:000436032900009
Grebenkov, DS (reprint author), Univ Paris Saclay, CNRS, Ecole Polytech, Lab Phys Mat Condensee,UMR 7643, F-91128 Palaiseau, France., denis.grebenkov@polytechnique.edu; rmetzler@uni-potsdam.de; oshanin@lptmc.jussieu.fr
Deutsche ForschungsgemeinschaftGerman Research Foundation (DFG) [ME 1535/7-1, ME 1535/6-1]; French National Research AgencyFrench National Research Agency (ANR) [ANR-13-JSV5-0006-01]; Foundation for Polish Science within an Alexander von Humboldt Polish Honorary Research Fellowship
2021-11-17T15:40:03+00:00
sword
importub
filename=package.tar
211bd2cc5c276e08e819a7a0dcd26c25
Grebenkov, Denis S.
false
true
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Physik
Institut für Physik und Astronomie
Referiert
Import
Green Open-Access
42298
2019
2019
eng
12
527
postprint
1
2019-01-15
2019-01-15
--
Strong defocusing of molecular reaction times results from an interplay of geometry and reaction control
Textbook concepts of diffusion-versus kinetic-control are well-defined for reaction-kinetics involving macroscopic concentrations of diffusive reactants that are adequately described by rate-constants—the inverse of the mean-first-passage-time to the reaction-event. In contradiction, an open important question is whether the mean-first-passage-time alone is a sufficient measure for biochemical reactions that involve nanomolar reactant concentrations. Here, using a simple yet generic, exactly solvable model we study the effect of diffusion and chemical reaction-limitations on the full reaction-time distribution. We show that it has a complex structure with four distinct regimes delineated by three characteristic time scales spanning a window of several decades. Consequently, the reaction-times are defocused: no unique time-scale characterises the reaction-process, diffusion- and kinetic-control can no longer be disentangled, and it is imperative to know the full reaction-time distribution. We introduce the concepts of geometry- and reaction-control, and also quantify each regime by calculating the corresponding reaction depth.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-42298
urn:nbn:de:kobv:517-opus4-422989
1866-8372
Communications Chemistry 1 (2018) Art. 96 DOI: 10.1038/s42004-018-0096-x
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/42299">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
true
true
CC BY - Namensnennung, 4.0 International
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
527
Chemie und zugeordnete Wissenschaften
open_access
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/42298/pmnr527.pdf
40372
2017
2017
eng
11
postprint
1
--
2017-11-16
--
Effects of the target aspect ratio and intrinsic reactivity onto diffusive search in bounded domains
We study the mean first passage time (MFPT) to a reaction event on a specific site in a cylindrical geometry—characteristic, for instance, for bacterial cells, with a concentric inner cylinder representing the nuclear region of the bacterial cell. Asimilar problem emerges in the description of a diffusive search by a transcription factor protein for a specific binding region on a single strand of DNA.We develop a unified theoretical approach to study the underlying boundary value problem which is based on a self-consistent approximation of the mixed boundary condition. Our approach permits us to derive explicit, novel, closed-form expressions for the MFPT valid for a generic setting with an arbitrary relation between the system parameters.Weanalyse this general result in the asymptotic limits appropriate for the above-mentioned biophysical problems. Our investigation reveals the crucial role of the target aspect ratio and of the intrinsic reactivity of the binding region, which were disregarded in previous studies. Theoretical predictions are confirmed by numerical simulations.
urn:nbn:de:kobv:517-opus4-403726
online registration
New journal of physics 19 (2017). - DOI: 10.1088/1367-2630/aa8ed9
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/40371">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
Denis S. Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
391
eng
uncontrolled
aspect ratio
eng
uncontrolled
cylindrical geometry
eng
uncontrolled
first passage time
eng
uncontrolled
protein search
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/40372/pmnr391_online.pdf
43652
2019
2019
eng
16
753
postprint
1
2019-10-15
2019-10-15
--
Single-trajectory spectral analysis of scaled Brownian motion
Astandard approach to study time-dependent stochastic processes is the power spectral density (PSD), an ensemble-averaged property defined as the Fourier transform of the autocorrelation function of the process in the asymptotic limit of long observation times, T → ∞. In many experimental situations one is able to garner only relatively few stochastic time series of finite T, such that practically neither an ensemble average nor the asymptotic limit T → ∞ can be achieved. To accommodate for a meaningful analysis of such finite-length data we here develop the framework of single-trajectory spectral analysis for one of the standard models of anomalous diffusion, scaled Brownian motion.Wedemonstrate that the frequency dependence of the single-trajectory PSD is exactly the same as for standard Brownian motion, which may lead one to the erroneous conclusion that the observed motion is normal-diffusive. However, a distinctive feature is shown to be provided by the explicit dependence on the measurement time T, and this ageing phenomenon can be used to deduce the anomalous diffusion exponent.Wealso compare our results to the single-trajectory PSD behaviour of another standard anomalous diffusion process, fractional Brownian motion, and work out the commonalities and differences. Our results represent an important step in establishing singletrajectory PSDs as an alternative (or complement) to analyses based on the time-averaged mean squared displacement.
Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-43652
urn:nbn:de:kobv:517-opus4-436522
1866-8372
073043
New Journal of Physics 21 (2019) Art. 073043 DOI: 10.1088/1367-2630/ab2f52
<a href="http://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/index/docId/43651">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
Vittoria Sposini
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
753
eng
uncontrolled
diffusion
eng
uncontrolled
anomalous diffusion
eng
uncontrolled
power spectral analysis
eng
uncontrolled
single trajectory analysis
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/43652/pmnr753.pdf
44288
2019
2020
eng
24
810
postprint
1
2020-01-20
2020-01-20
--
Full distribution of first exit times in the narrow escape problem
In the scenario of the narrow escape problem (NEP) a particle diffuses in a finite container and eventually leaves it through a small 'escape window' in the otherwise impermeable boundary, once it arrives to this window and crosses an entropic barrier at the entrance to it. This generic problem is mathematically identical to that of a diffusion-mediated reaction with a partially-reactive site on the container's boundary. Considerable knowledge is available on the dependence of the mean first-reaction time (FRT) on the pertinent parameters. We here go a distinct step further and derive the full FRT distribution for the NEP. We demonstrate that typical FRTs may be orders of magnitude shorter than the mean one, thus resulting in a strong defocusing of characteristic temporal scales. We unveil the geometry-control of the typical times, emphasising the role of the initial distance to the target as a decisive parameter. A crucial finding is the further FRT defocusing due to the barrier, necessitating repeated escape or reaction attempts interspersed with bulk excursions. These results add new perspectives and offer a broad comprehension of various features of the by-now classical NEP that are relevant for numerous biological and technological systems.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-44288
urn:nbn:de:kobv:517-opus4-442883
1866-8372
New Journal of Physics 21 (2019) DOI: 10.1088/1367-2630/ab5de4
122001
<a href="http://publishup.uni-potsdam.de/44287">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
false
true
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
810
eng
uncontrolled
narrow escape problem
eng
uncontrolled
first-passage time distribution
eng
uncontrolled
mean versus most probable reaction times
eng
uncontrolled
mixed boundary conditions
Physik
open_access
Institut für Physik und Astronomie
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/44288/pmnr810.pdf
47696
2020
2020
eng
27
999
postprint
1
2020-09-22
2020-09-22
--
Universal spectral features of different classes of random-diffusivity processes
Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
10.25932/publishup-47696
urn:nbn:de:kobv:517-opus4-476960
1866-8372
063056
<a href="http://publishup.uni-potsdam.de/47695">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
New Journal of Physics 22 (2020) 6, 063056 DOI: 10.1088/1367-2630/ab9200
false
true
CC BY - Namensnennung, 4.0 International
Vittoria Sposini
Denis S Grebenkov
Ralf Metzler
Gleb Oshanin
Flavio Seno
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
999
eng
uncontrolled
diffusion
eng
uncontrolled
power spectrum
eng
uncontrolled
random diffusivity
eng
uncontrolled
single trajectories
Physik
open_access
Institut für Physik und Astronomie
Referiert
Green Open-Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/47696/pmnr999.pdf
42429
2018
2019
eng
31
655
postprint
1
2019-02-27
2019-02-27
--
Power spectral density of a single Brownian trajectory
The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.
Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
what one can and cannot learn from it
10.25932/publishup-42429
urn:nbn:de:kobv:517-opus4-424296
1866-8372
online registration
023029
New Journal of Physics 20 (2018), Art. 023029 DOI 10.1088/1367-2630/aaa67c
<a href="http://publishup.uni-potsdam.de/53576">Bibliographieeintrag der Originalveröffentlichung/Quelle</a>
CC BY - Namensnennung, 4.0 International
Diego Krapf
Enzo Marinari
Ralf Metzler
Gleb Oshanin
Xinran Xu
Alessio Squarcini
Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
655
eng
uncontrolled
power spectral density
eng
uncontrolled
single-trajectory analysis
eng
uncontrolled
probability density function
eng
uncontrolled
exact results
Physik
open_access
Mathematisch-Naturwissenschaftliche Fakultät
Referiert
Open Access
Universität Potsdam
https://publishup.uni-potsdam.de/files/42429/pmnr655.pdf
53576
2018
2018
eng
30
20
article
IOP Publ. Ltd.
Bristol
1
2018-02-09
2018-02-09
--
Power spectral density of a single Brownian trajectory
The power spectral density (PSD) of any time-dependent stochastic processX (t) is ameaningful feature of its spectral content. In its text-book definition, the PSD is the Fourier transform of the covariance function of X-t over an infinitely large observation timeT, that is, it is defined as an ensemble-averaged property taken in the limitT -> infinity. Alegitimate question is what information on the PSD can be reliably obtained from single-trajectory experiments, if one goes beyond the standard definition and analyzes the PSD of a single trajectory recorded for a finite observation timeT. In quest for this answer, for a d-dimensional Brownian motion (BM) we calculate the probability density function of a single-trajectory PSD for arbitrary frequency f, finite observation time T and arbitrary number k of projections of the trajectory on different axes. We show analytically that the scaling exponent for the frequency-dependence of the PSD specific to an ensemble of BM trajectories can be already obtained from a single trajectory, while the numerical amplitude in the relation between the ensemble-averaged and single-trajectory PSDs is afluctuating property which varies from realization to realization. The distribution of this amplitude is calculated exactly and is discussed in detail. Our results are confirmed by numerical simulations and single-particle tracking experiments, with remarkably good agreement. In addition we consider a truncated Wiener representation of BM, and the case of a discrete-time lattice random walk. We highlight some differences in the behavior of a single-trajectory PSD for BM and for the two latter situations. The framework developed herein will allow for meaningful physical analysis of experimental stochastic trajectories.
New journal of physics : the open-access journal for physics
what one can and cannot learn from it
10.1088/1367-2630/aaa67c
1367-2630
wos:2018
023029
WOS:000424670300003
Oshanin, G (reprint author), Sorbonne Univ, Lab Phys Theor Matiere Condensee, CNRS UMR 7600, 4 Pl Jussieu, F-75252 Paris 05, France., oshanin@lptmc.jussieu.fr
NSFNational Science Foundation (NSF) [1401432]; European Research Council (ERC) under the European Union Horizon research and innovation program [694925]
2022-01-24T13:02:05+00:00
sword
importub
filename=package.tar
a3468766259e30e33649f7aaeba64334
<a href="https://doi.org/10.25932/publishup-42429">Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 655 </a>
false
true
Diego Krapf
Enzo Marinari
Ralf Metzler
Gleb Oshanin
Xinran Xu
Alessio Squarcini
eng
uncontrolled
power spectral density
eng
uncontrolled
single-trajectory analysis
eng
uncontrolled
probability density function
eng
uncontrolled
exact results
Physik
Institut für Physik und Astronomie
Referiert
Import
Gold Open-Access
DOAJ gelistet