35967
2012
2012
eng
2527
2542
16
8
391
article
Elsevier
Amsterdam
1
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Generalized space-time fractional diffusion equation with composite fractional time derivative
We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
Physica : europhysics journal ; A, Statistical mechanics and its applications
10.1016/j.physa.2011.12.035
0378-4371 (print)
1873-2119 (online)
wos:2011-2013
WOS:000301209400003
Tomovski, Z (reprint author), St Cyril & Methodius Univ, Fac Nat Sci & Math, Inst Math, Skopje 1000, Macedonia., tomovski@pmf.ukim.mk; trifce.sandev@drs.gov.mk; metz@ph.tum.de; j.l.a.dubbeldam@tudelft.nl
DAAD; NWO; Academy of Finland; Ministry of Education and Science of the
Republic of Macedonia
Zivorad Tomovski
Trifce Sandev
Ralf Metzler
Johan Dubbeldam
eng
uncontrolled
Fractional diffusion equation
eng
uncontrolled
Composite fractional derivative
eng
uncontrolled
Riesz-Feller fractional derivative
eng
uncontrolled
Mittag-Leffler functions
eng
uncontrolled
Fox H-function
eng
uncontrolled
Fractional moments
eng
uncontrolled
Asymptotic expansions
eng
uncontrolled
Grunwald-Letnikov approximation
Institut für Physik und Astronomie
Referiert
36362
2012
2012
eng
6
2
97
article
EDP Sciences
Mulhouse
1
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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 (print)
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
35689
2012
2012
eng
426
450
25
3
15
article
Versita
Warsaw
1
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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 (print)
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
36072
2012
2012
eng
10
1
article
IOP Publ. Ltd.
Bristol
1
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How a finite potential barrier decreases the mean first-passage time
We consider the mean first-passage time of a random walker moving in a potential landscape on a finite interval, the starting and end points being at different potentials. From analytical calculations and Monte Carlo simulations we demonstrate that the mean first-passage time for a piecewise linear curve between these two points is minimized by the introduction of a potential barrier. Due to thermal fluctuations, this barrier may be crossed. It turns out that the corresponding expense for this activation is less severe than the gain from an increased slope towards the end point. In particular, the resulting mean first-passage time is shorter than for a linear potential drop between the two points.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2012/03/L03001
1742-5468 (print)
wos:2011-2013
L03001
WOS:000302246400002
Palyulin, VV (reprint author), Tech Univ Munich, Dept Phys, D-85747 Garching, Germany., vladimir.palyulin@tum.de; rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Academy of Finland
Vladimir V. Palyulin
Ralf Metzler
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
35545
2012
2012
eng
5
5
86
article
IOP Publ. Ltd.
Bristol
1
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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 (print)
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
35632
2012
2012
eng
8
3
86
article
American Physical Society
College Park
1
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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 (print)
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
35910
2012
2012
eng
5
5
85
article
American Physical Society
College Park
1
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Correlated continuous-time random walks in external force fields
We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T-i is equal to the previous waiting time Ti-1 plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.
Physical review : E, Statistical, nonlinear and soft matter physics
10.1103/PhysRevE.85.051103
1539-3755 (print)
1550-2376 (online)
wos:2011-2013
051103
WOS:000306440100001
Magdziarz, M (reprint author), Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, Wyspianskiego 27, PL-50370 Wroclaw, Poland., marcin.magdziarz@pwr.wroc.pl; rmetzler@uni-potsdam.de; wladyslaw.szczotka@math.uni.wroc.pl; piotr.zebrowski@math.uni.wroc.pl
Marcin Magdziarz
Ralf Metzler
Wladyslaw Szczotka
Piotr Zebrowski
Institut für Physik und Astronomie
Referiert
35980
2012
2012
eng
18
article
IOP Publ. Ltd.
Bristol
1
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Correlated continuous-time random walks-scaling limits and Langevin picture
In this paper we analyze correlated continuous-time random walks introduced recently by Tejedor and Metzler (2010 J. Phys. A: Math. Theor. 43 082002). We obtain the Langevin equations associated with this process and the corresponding scaling limits of their solutions. We prove that the limit processes are self-similar and display anomalous dynamics. Moreover, we extend the model to include external forces. Our results are confirmed by Monte Carlo simulations.
Journal of statistical mechanics: theory and experiment
10.1088/1742-5468/2012/04/P04010
1742-5468 (print)
wos:2011-2013
P04010
WOS:000303545700012
Magdziarz, M (reprint author), Wroclaw Univ Technol, Inst Math & Comp Sci, Hugo Steinhaus Ctr, Wyspianskiego 27, PL-50370 Wroclaw, Poland., Marcin.Magdziarz@pwr.wroc.pl; rmetzler@uni-potsdam.de; Wladyslaw.Szczotka@math.uni.wroc.pl; Piotr.Zebrowski@math.uni.wroc.pl
Academy of Finland (FiDiPro)
Marcin Magdziarz
Ralf Metzler
Wladyslaw Szczotka
Piotr Zebrowski
eng
uncontrolled
stochastic processes (theory)
eng
uncontrolled
diffusion
Institut für Physik und Astronomie
Referiert
35989
2012
2012
eng
75
84
10
1
204
article
Springer
Heidelberg
1
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Diffusion inside living human cells
Naturally occurring lipid granules diffuse in the cytoplasm and can be used as tracers to map out the viscoelastic landscape inside living cells. Using optical trapping and single particle tracking we found that lipid granules exhibit anomalous diffusion inside human umbilical vein endothelial cells. For these cells the exact diffusional pattern of a particular granule depends on the physiological state of the cell and on the localization of the granule within the cytoplasm. Granules located close to the actin rich periphery of the cell move less than those located towards to the center of the cell or within the nucleus. Also, granules in cells which are stressed by intense laser illumination or which have attached to a surface for a long period of time move in a more restricted fashion than those within healthy cells. For granules diffusing in healthy cells, in regions away from the cell periphery, occurrences of weak ergodicity breaking are observed, similar to the recent observations inside living fission yeast cells [1].
European physical journal special topics
10.1140/epjst/e2012-01553-y
1951-6355 (print)
wos:2011-2013
WOS:000302814400007
Leijnse, N (reprint author), Univ Copenhagen, Niels Bohr Inst, Blegdamsvej 17, DK-2100 Copenhagen O, Denmark., oddershede@nbi.dk
Lundbeck Foundation 'Center for Biomembranes in Nanomedicine';
University of Copenhagen; Academy of Finland
N. Leijnse
J. -H. Jeon
S. Loft
Ralf Metzler
L. B. Oddershede
Institut für Physik und Astronomie
Referiert
35571
2012
2012
eng
5
18
109
article
American Physical Society
College Park
1
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Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical compositions with single-trajectory analyses, we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than 4 orders of magnitude in time, clearly stretching into the submicrosecond domain. The lipid motion depends on the lipid chemistry, the lipid phase, and especially the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases, including the gel phase, and in the presence of cholesterol. The results underline the relevance of anomalous diffusion in lipid bilayers and the strong effects of the membrane composition.
Physical review letters
10.1103/PhysRevLett.109.188103
0031-9007 (print)
wos:2011-2013
188103
WOS:000310434400041
Jeon, JH (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland.
Academy of Finland
Jae-Hyung Jeon
Hector Martinez-Seara Monne
Matti Javanainen
Ralf Metzler
Institut für Physik und Astronomie
Referiert