Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen
OPUS4-35967 Wissenschaftlicher Artikel Tomovski, Zivorad; Sandev, Trifce; Metzler, Ralf; Dubbeldam, Johan 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). Amsterdam Elsevier 2012 16 Physica : europhysics journal ; A, Statistical mechanics and its applications 391 8 2527 2542 10.1016/j.physa.2011.12.035 Institut für Physik und Astronomie
OPUS4-35732 Wissenschaftlicher Artikel Barkai, Eli; Garini, Yuval; Metzler, Ralf Strange Kinetics of single molecules in living cells Melville American Institute of Physics 2012 7 Physics today 65 8 29 35 Institut für Physik und Astronomie
OPUS4-36288 Wissenschaftlicher Artikel Adamcik, Jozef; Jeon, Jae-Hyung; Karczewski, Konrad J.; Metzler, Ralf; Dietler, Giovanni 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. Cambridge Royal Society of Chemistry 2012 8 Soft matter 8 33 8651 8658 10.1039/c2sm26089a Institut für Physik und Astronomie
OPUS4-35441 Wissenschaftlicher Artikel Eliazar, Iddo; Metzler, Ralf 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. Melville American Institute of Physics 2012 9 The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr 137 23 10.1063/1.4770266 Institut für Physik und Astronomie
OPUS4-35910 Wissenschaftlicher Artikel Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr 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. College Park American Physical Society 2012 5 Physical review : E, Statistical, nonlinear and soft matter physics 85 5 10.1103/PhysRevE.85.051103 Institut für Physik und Astronomie
OPUS4-35980 Wissenschaftlicher Artikel Magdziarz, Marcin; Metzler, Ralf; Szczotka, Wladyslaw; Zebrowski, Piotr 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. Bristol IOP Publ. Ltd. 2012 18 Journal of statistical mechanics: theory and experiment 10.1088/1742-5468/2012/04/P04010 Institut für Physik und Astronomie
OPUS4-35613 Wissenschaftlicher Artikel Chechkin, Aleksei V.; Zaid, Irwin M.; Lomholt, Michael A.; Sokolov, Igor M.; Metzler, Ralf 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. College Park American Physical Society 2012 11 Physical review : E, Statistical, nonlinear and soft matter physics 86 4 10.1103/PhysRevE.86.041101 Institut für Physik und Astronomie
OPUS4-35899 Wissenschaftlicher Artikel Bauer, Maximilian; Metzler, Ralf 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. Cambridge Cell Press 2012 10 Biophysical journal 102 10 2321 2330 10.1016/j.bpj.2012.04.008 Institut für Physik und Astronomie
OPUS4-36072 Wissenschaftlicher Artikel Palyulin, Vladimir V.; Metzler, Ralf 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. Bristol IOP Publ. Ltd. 2012 10 Journal of statistical mechanics: theory and experiment 1 10.1088/1742-5468/2012/03/L03001 Institut für Physik und Astronomie
OPUS4-35689 Wissenschaftlicher Artikel Sandev, Trifce; Metzler, Ralf; Tomovski, Zivorad 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. Warsaw Versita 2012 25 Fractional calculus and applied analysis : an international journal for theory and applications 15 3 426 450 10.2478/s13540-012-0031-2 Institut für Physik und Astronomie