35545
2012
2012
eng
5
5
86
article
IOP Publ. Ltd.
Bristol
1
--
--
--
The role of ergodicity in anomalous stochastic processes - analysis of single-particle trajectories
Single-particle experiments produce time series x(t) of individual particle trajectories, frequently revealing anomalous diffusion behaviour. Typically, individual x(t) are evaluated in terms of time-averaged quantities instead of ensemble averages. Here we discuss the behaviour of the time-averaged mean squared displacement of different stochastic processes giving rise to anomalous diffusion. In particular, we pay attention to the ergodic properties of these processes, i.e. the (non)equivalence of time and ensemble averages.
Physica scripta : an international journal for experimental and theoretical physics
10.1088/0031-8949/86/05/058510
0031-8949
wos:2011-2013
058510
WOS:000310910000035
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, D-14476 Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme); European Science Foundation
Ralf Metzler
Jae-Hyung Jeon
Institut für Physik und Astronomie
Referiert
35441
2012
2012
eng
9
23
137
article
American Institute of Physics
Melville
1
--
--
--
The RARE model a generalized approach to random relaxation processes in disordered systems
This paper introduces and analyses a general statistical model, termed the RAndom RElaxations (RARE) model, of random relaxation processes in disordered systems. The model considers excitations that are randomly scattered around a reaction center in a general embedding space. The model's input quantities are the spatial scattering statistics of the excitations around the reaction center, and the chemical reaction rates between the excitations and the reaction center as a function of their mutual distance. The framework of the RARE model is versatile and a detailed stochastic analysis of the random relaxation processes is established. Analytic results regarding the duration and the range of the random relaxation processes, as well as the model's thermodynamic limit, are obtained in closed form. In particular, the case of power-law inputs, which turn out to yield stretched exponential relaxation patterns and asymptotically Paretian relaxation ranges, is addressed in detail.
The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
10.1063/1.4770266
0021-9606
1089-7690
wos:2011-2013
234106
WOS:000312780300008
Eliazar, I (reprint author), Holon Inst Technol, POB 305, IL-58102 Holon, Israel., eliazar@post.tau.ac.il; rmetzler@uni-potsdam.de
Academy of Finland (FiDiPro scheme)
Iddo Eliazar
Ralf Metzler
eng
uncontrolled
chemical relaxation
eng
uncontrolled
Pareto analysis
eng
uncontrolled
reaction kinetics theory
eng
uncontrolled
reaction rate constants
eng
uncontrolled
stochastic processes
Institut für Physik und Astronomie
Referiert
35689
2012
2012
eng
426
450
25
3
15
article
Versita
Warsaw
1
--
--
--
Velocity and displacement correlation functions for fractional generalized Langevin equations
We study analytically a generalized fractional Langevin equation. General formulas for calculation of variances and the mean square displacement are derived. Cases with a three parameter Mittag-Leffler frictional memory kernel are considered. Exact results in terms of the Mittag-Leffler type functions for the relaxation functions, average velocity and average particle displacement are obtained. The mean square displacement and variances are investigated analytically. Asymptotic behaviors of the particle in the short and long time limit are found. The model considered in this paper may be used for modeling anomalous diffusive processes in complex media including phenomena similar to single file diffusion or possible generalizations thereof. We show the importance of the initial conditions on the anomalous diffusive behavior of the particle.
Fractional calculus and applied analysis : an international journal for theory and applications
10.2478/s13540-012-0031-2
1311-0454
wos:2011-2013
WOS:000305912000007
Sandev, T (reprint author), Radiat Safety Directorate, Partizanski Odredi 143,POB 22, Skopje 1020, Macedonia., trifce.sandev@drs.gov.mk; rmetzler@uni-potsdam.de; tomovski@pmf.ukim.mk
Ministry of Education and Science of the Republic of Macedonia; NWO
Trifce Sandev
Ralf Metzler
Zivorad Tomovski
eng
uncontrolled
fractional generalized Langevin equation
eng
uncontrolled
frictional memory kernel
eng
uncontrolled
variances
eng
uncontrolled
mean square displacement
eng
uncontrolled
anomalous diffusion
Institut für Physik und Astronomie
Referiert
36362
2012
2012
eng
6
2
97
article
EDP Sciences
Mulhouse
1
--
--
--
A solution to the subdiffusion-efficiency paradox inactive states enhance reaction efficiency at subdiffusion conditions in living cells
Macromolecular crowding in living biological cells effects subdiffusion of larger biomolecules such as proteins and enzymes. Mimicking this subdiffusion in terms of random walks on a critical percolation cluster, we here present a case study of EcoRV restriction enzymes involved in vital cellular defence. We show that due to its so far elusive propensity to an inactive state the enzyme avoids non-specific binding and remains well-distributed in the bulk cytoplasm of the cell. Despite the reduced volume exploration capability of subdiffusion processes, this mechanism guarantees a high efficiency of the enzyme. By variation of the non-specific binding constant and the bond occupation probability on the percolation network, we demonstrate that reduced nonspecific binding are beneficial for efficient subdiffusive enzyme activity even in relatively small bacteria cells. Our results corroborate a more local picture of cellular regulation.
epl : a letters journal exploring the frontiers of physics
10.1209/0295-5075/97/20008
0295-5075
wos:2011-2013
20008
WOS:000300259100008
Sereshki, LE (reprint author), Tech Univ Munich, Dept Phys, James Franck Str, D-85747 Garching, Germany., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Center for Nanoscience; Academy of
Finland; Danish National Research Foundation
L. E. Sereshki
M. A. Lomholt
Ralf Metzler
Institut für Physik und Astronomie
Referiert
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
35613
2012
2012
eng
11
4
86
article
American Physical Society
College Park
1
--
--
--
Bulk-mediated diffusion on a planar surface full solution
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.86.041101
1539-3755
wos:2011-2013
041101
WOS:000309350400001
Chechkin, AV (reprint author), Inst Theoret Phys NSC KIPT, Akad Skaya St 1, UA-61108 Kharkov, Ukraine.
Academy of Finland within FiDiPro scheme
Aleksei V. Chechkin
Irwin M. Zaid
Michael A. Lomholt
Igor M. Sokolov
Ralf Metzler
Institut für Physik und Astronomie
Referiert