35967
2012
2012
eng
2527
2542
16
8
391
article
Elsevier
Amsterdam
1
--
--
--
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
35732
2012
2012
eng
29
35
7
8
65
article
American Institute of Physics
Melville
1
--
--
--
Strange Kinetics of single molecules in living cells
Physics today
0031-9228 (print)
wos:2011-2013
WOS:000307614600020
Barkai, E (reprint author), Bar Ilan Univ, Ramat Gan, Israel.
Israel Science Foundation; Academy of Finland
Eli Barkai
Yuval Garini
Ralf Metzler
Institut für Physik und Astronomie
Referiert
36288
2012
2012
eng
8651
8658
8
33
8
article
Royal Society of Chemistry
Cambridge
1
--
--
--
Quantifying supercoiling-induced denaturation bubbles in DNA
In both eukaryotic and prokaryotic DNA sequences of 30-100 base-pairs rich in AT base-pairs have been identified at which the double helix preferentially unwinds. Such DNA unwinding elements are commonly associated with origins for DNA replication and transcription, and with chromosomal matrix attachment regions. Here we present a quantitative study of local DNA unwinding based on extensive single DNA plasmid imaging. We demonstrate that long-lived single-stranded denaturation bubbles exist in negatively supercoiled DNA, at the expense of partial twist release. Remarkably, we observe a linear relation between the degree of supercoiling and the bubble size, in excellent agreement with statistical modelling. Furthermore, we obtain the full distribution of bubble sizes and the opening probabilities at varying salt and temperature conditions. The results presented herein underline the important role of denaturation bubbles in negatively supercoiled DNA for biological processes such as transcription and replication initiation in vivo.
Soft matter
10.1039/c2sm26089a
1744-683X (print)
wos:2011-2013
WOS:000307021300014
Metzler, R (reprint author), Tampere Univ Technol, Dept Phys, FI-33101 Tampere, Finland., rmetzler@uni-potsdam.de
Deutsche Forschungsgemeinschaft; Academy of Finland
Jozef Adamcik
Jae-Hyung Jeon
Konrad J. Karczewski
Ralf Metzler
Giovanni Dietler
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 (print)
1089-7690 (online)
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
35910
2012
2012
eng
5
5
85
article
American Physical Society
College Park
1
--
--
--
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
--
--
--
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
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 (print)
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
35899
2012
2012
eng
2321
2330
10
10
102
article
Cell Press
Cambridge
1
--
--
--
Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states
Transcription factors (TFs) such as the lac repressor find their target sequence on DNA at remarkably high rates. In the established Berg-von Hippel model for this search process, the TF alternates between three-dimensional diffusion in the bulk solution and one-dimensional sliding along the DNA chain. To overcome the so-called speed-stability paradox, in similar models the TF was considered as being present in two conformations (search state and recognition state) between which it switches stochastically. Combining both the facilitated diffusion model and alternating states, we obtain a generalized model. We explicitly treat bulk excursions for rodlike chains arranged in parallel and consider a simplified model for coiled DNA. Compared to previously considered facilitated diffusion models, corresponding to limiting cases of our generalized model, we surprisingly find a reduced target search rate. Moreover, at optimal conditions there is no longer an equipartition between the time spent by the protein on and off the DNA chain.
Biophysical journal
10.1016/j.bpj.2012.04.008
0006-3495 (print)
wos:2011-2013
WOS:000304091100011
Metzler, R (reprint author), Univ Potsdam, Inst Phys & Astron, Potsdam, Germany., rmetzler@uni-potsdam.de
Academy of Finland
Maximilian Bauer
Ralf Metzler
Institut für Physik und Astronomie
Referiert
36072
2012
2012
eng
10
1
article
IOP Publ. Ltd.
Bristol
1
--
--
--
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
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 (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