TY - JOUR
A1 - Tomovski, Zivorad
A1 - Sandev, Trifce
A1 - Metzler, Ralf
A1 - Dubbeldam, Johan
T1 - Generalized space-time fractional diffusion equation with composite fractional time derivative
JF - Physica : europhysics journal ; A, Statistical mechanics and its applications
N2 - 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).
KW - Fractional diffusion equation
KW - Composite fractional derivative
KW - Riesz-Feller fractional derivative
KW - Mittag-Leffler functions
KW - Fox H-function
KW - Fractional moments
KW - Asymptotic expansions
KW - Grunwald-Letnikov approximation
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.physa.2011.12.035
SN - 0378-4371 (print)
SN - 1873-2119 (online)
VL - 391
IS - 8
SP - 2527
EP - 2542
PB - Elsevier
CY - Amsterdam
ER -
TY - JOUR
A1 - Barkai, Eli
A1 - Garini, Yuval
A1 - Metzler, Ralf
T1 - Strange Kinetics of single molecules in living cells
JF - Physics today
Y1 - 2012
SN - 0031-9228 (print)
VL - 65
IS - 8
SP - 29
EP - 35
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Adamcik, Jozef
A1 - Jeon, Jae-Hyung
A1 - Karczewski, Konrad J.
A1 - Metzler, Ralf
A1 - Dietler, Giovanni
T1 - Quantifying supercoiling-induced denaturation bubbles in DNA
JF - Soft matter
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1039/c2sm26089a
SN - 1744-683X (print)
VL - 8
IS - 33
SP - 8651
EP - 8658
PB - Royal Society of Chemistry
CY - Cambridge
ER -
TY - JOUR
A1 - Eliazar, Iddo
A1 - Metzler, Ralf
T1 - The RARE model a generalized approach to random relaxation processes in disordered systems
JF - The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr
N2 - 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.
KW - chemical relaxation
KW - Pareto analysis
KW - reaction kinetics theory
KW - reaction rate constants
KW - stochastic processes
Y1 - 2012
U6 - http://dx.doi.org/10.1063/1.4770266
SN - 0021-9606 (print)
SN - 1089-7690 (online)
VL - 137
IS - 23
PB - American Institute of Physics
CY - Melville
ER -
TY - JOUR
A1 - Magdziarz, Marcin
A1 - Metzler, Ralf
A1 - Szczotka, Wladyslaw
A1 - Zebrowski, Piotr
T1 - Correlated continuous-time random walks in external force fields
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1103/PhysRevE.85.051103
SN - 1539-3755 (print)
SN - 1550-2376 (online)
VL - 85
IS - 5
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Magdziarz, Marcin
A1 - Metzler, Ralf
A1 - Szczotka, Wladyslaw
A1 - Zebrowski, Piotr
T1 - Correlated continuous-time random walks-scaling limits and Langevin picture
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - stochastic processes (theory)
KW - diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.1088/1742-5468/2012/04/P04010
SN - 1742-5468 (print)
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Chechkin, Aleksei V.
A1 - Zaid, Irwin M.
A1 - Lomholt, Michael A.
A1 - Sokolov, Igor M.
A1 - Metzler, Ralf
T1 - Bulk-mediated diffusion on a planar surface full solution
JF - Physical review : E, Statistical, nonlinear and soft matter physics
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1103/PhysRevE.86.041101
SN - 1539-3755 (print)
VL - 86
IS - 4
PB - American Physical Society
CY - College Park
ER -
TY - JOUR
A1 - Bauer, Maximilian
A1 - Metzler, Ralf
T1 - Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states
JF - Biophysical journal
N2 - 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.
Y1 - 2012
U6 - http://dx.doi.org/10.1016/j.bpj.2012.04.008
SN - 0006-3495 (print)
VL - 102
IS - 10
SP - 2321
EP - 2330
PB - Cell Press
CY - Cambridge
ER -
TY - JOUR
A1 - Palyulin, Vladimir V.
A1 - Metzler, Ralf
T1 - How a finite potential barrier decreases the mean first-passage time
JF - Journal of statistical mechanics: theory and experiment
N2 - 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.
KW - diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.1088/1742-5468/2012/03/L03001
SN - 1742-5468 (print)
IS - 1
PB - IOP Publ. Ltd.
CY - Bristol
ER -
TY - JOUR
A1 - Sandev, Trifce
A1 - Metzler, Ralf
A1 - Tomovski, Zivorad
T1 - Velocity and displacement correlation functions for fractional generalized Langevin equations
JF - Fractional calculus and applied analysis : an international journal for theory and applications
N2 - 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.
KW - fractional generalized Langevin equation
KW - frictional memory kernel
KW - variances
KW - mean square displacement
KW - anomalous diffusion
Y1 - 2012
U6 - http://dx.doi.org/10.2478/s13540-012-0031-2
SN - 1311-0454 (print)
VL - 15
IS - 3
SP - 426
EP - 450
PB - Versita
CY - Warsaw
ER -