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
OPUS4-8518 Wissenschaftlicher Artikel Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf Quantifying non-ergodic dynamics of force-free granular gases Brownianmotion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann- Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent (viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles. 2015 8 Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies 17 21791 21798 10.1039/C5CP02824H Institut für Chemie
OPUS4-8520 misc Bodrova, Anna; Chechkin, Aleksei V.; Cherstvy, Andrey G.; Metzler, Ralf Quantifying non-ergodic dynamics of force-free granular gases Brownianmotion is ergodic in the Boltzmann-Khinchin sense that long time averages of physical observables such as the mean squared displacement provide the same information as the corresponding ensemble average, even at out-of-equilibrium conditions. This property is the fundamental prerequisite for single particle tracking and its analysis in simple liquids. We study analytically and by event-driven molecular dynamics simulations the dynamics of force-free cooling granular gases and reveal a violation of ergodicity in this Boltzmann-Khinchin sense as well as distinct ageing of the system. Such granular gases comprise materials such as dilute gases of stones, sand, various types of powders, or large molecules, and their mixtures are ubiquitous in Nature and technology, in particular in Space. We treat—depending on the physical-chemical properties of the inter-particle interaction upon their pair collisions—both a constant and a velocity-dependent (viscoelastic) restitution coefficient e. Moreover we compare the granular gas dynamics with an effective single particle stochastic model based on an underdamped Langevin equation with time dependent diffusivity. We find that both models share the same behaviour of the ensemble mean squared displacement (MSD) and the velocity correlations in the limit of weak dissipation. Qualitatively, the reported non-ergodic behaviour is generic for granular gases with any realistic dependence of e on the impact velocity of particles. 2015 urn:nbn:de:kobv:517-opus4-85200 Institut für Chemie
OPUS4-8523 Wissenschaftlicher Artikel Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf Geometry controlled anomalous diffusion in random fractal geometries We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided. Weinheim Wiley-VCH Verl. 2015 13 Physical chemistry, chemical physics : PCCP ; a journal of European Chemical Societies 17 30134 30147 10.1039/c5cp03548a Institut für Chemie
OPUS4-8524 misc Mardoukhi, Yousof; Jeon, Jae-Hyung; Metzler, Ralf Geometry controlled anomalous diffusion in random fractal geometries We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law BT� h with h o 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided. 2015 urn:nbn:de:kobv:517-opus4-85247 Institut für Chemie
OPUS4-8955 Wissenschaftlicher Artikel de Carvalho, Sidney J.; Metzler, Ralf; Cherstvy, Andrey G. Inverted critical adsorption of polyelectrolytes in confinement What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption-desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids. London Royal Society of Chemistry 2015 13 Soft matter 11 4430 4443 10.1039/C5SM00635J Institut für Chemie
OPUS4-8956 misc de Carvalho, Sidney J.; Metzler, Ralf; Cherstvy, Andrey G. Inverted critical adsorption of polyelectrolytes in confinement What are the fundamental laws for the adsorption of charged polymers onto oppositely charged surfaces, for convex, planar, and concave geometries? This question is at the heart of surface coating applications, various complex formation phenomena, as well as in the context of cellular and viral biophysics. It has been a long-standing challenge in theoretical polymer physics; for realistic systems the quantitative understanding is however often achievable only by computer simulations. In this study, we present the findings of such extensive Monte-Carlo in silico experiments for polymer-surface adsorption in confined domains. We study the inverted critical adsorption of finite-length polyelectrolytes in three fundamental geometries: planar slit, cylindrical pore, and spherical cavity. The scaling relations extracted from simulations for the critical surface charge density sc—defining the adsorption-desorption transition—are in excellent agreement with our analytical calculations based on the ground-state analysis of the Edwards equation. In particular, we confirm the magnitude and scaling of sc for the concave interfaces versus the Debye screening length 1/k and the extent of confinement a for these three interfaces for small ka values. For large ka the critical adsorption condition approaches the known planar limit. The transition between the two regimes takes place when the radius of surface curvature or half of the slit thickness a is of the order of 1/k. We also rationalize how sc(k) dependence gets modified for semi-flexible versus flexible chains under external confinement. We examine the implications of the chain length for critical adsorption—the effect often hard to tackle theoretically—putting an emphasis on polymers inside attractive spherical cavities. The applications of our findings to some biological systems are discussed, for instance the adsorption of nucleic acids onto the inner surfaces of cylindrical and spherical viral capsids. 2015 13 4430 4443 urn:nbn:de:kobv:517-opus4-89562 Institut für Chemie
OPUS4-39421 Wissenschaftlicher Artikel Ghosh, Surya K.; Cherstvy, Andrey G.; Metzler, Ralf Non-universal tracer diffusion in crowded media of non-inert obstacles We study the diffusion of a tracer particle, which moves in continuum space between a lattice of excluded volume, immobile non-inert obstacles. In particular, we analyse how the strength of the tracer-obstacle interactions and the volume occupancy of the crowders alter the diffusive motion of the tracer. From the details of partitioning of the tracer diffusion modes between trapping states when bound to obstacles and bulk diffusion, we examine the degree of localisation of the tracer in the lattice of crowders. We study the properties of the tracer diffusion in terms of the ensemble and time averaged mean squared displacements, the trapping time distributions, the amplitude variation of the time averaged mean squared displacements, and the non-Gaussianity parameter of the diffusing tracer. We conclude that tracer-obstacle adsorption and binding triggers a transient anomalous diffusion. From a very narrow spread of recorded individual time averaged trajectories we exclude continuous type random walk processes as the underlying physical model of the tracer diffusion in our system. For moderate tracer-crowder attraction the motion is found to be fully ergodic, while at stronger attraction strength a transient disparity between ensemble and time averaged mean squared displacements occurs. We also put our results into perspective with findings from experimental single-particle tracking and simulations of the diffusion of tagged tracers in dense crowded suspensions. Our results have implications for the diffusion, transport, and spreading of chemical components in highly crowded environments inside living cells and other structured liquids. Cambridge Royal Society of Chemistry 2015 12 Physical chemistry, chemical physics : a journal of European Chemical Societies 17 3 1847 1858 10.1039/c4cp03599b Institut für Physik und Astronomie
OPUS4-7861 misc Metzler, Ralf; Cherstvy, Andrey G.; Chechkin, Aleksei V.; Bodrova, Anna S. Ultraslow scaled Brownian motion We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined motion the mean squared displacement (MSD) of USBM exhibits an ultraslow, logarithmic growth as function of time, in contrast to the conventional scaled Brownian motion. In a harmonic potential the MSD of USBM does not saturate but asymptotically decays inverse-proportionally to time, reflecting the highly non-stationary character of the process. We show that the process is weakly non-ergodic in the sense that the time averaged MSD does not converge to the regular MSD even at long times, and for unconfined motion combines a linear lag time dependence with a logarithmic term. The weakly non-ergodic behaviour is quantified in terms of the ergodicity breaking parameter. The USBM process is also shown to be ageing: observables of the system depend on the time gap between initiation of the test particle and start of the measurement of its motion. Our analytical results are shown to agree excellently with extensive computer simulations. 2015 New journal of physics : the open-access journal for physics urn:nbn:de:kobv:517-opus4-78618 Institut für Physik und Astronomie
OPUS4-39009 Wissenschaftlicher Artikel Blavatska, Viktoria; Metzler, Ralf Conformational properties of complex polymers: rosette versus star-like structures Multiple loop formation in polymer macromolecules is an important feature of the chromatin organization and DNA compactification in the nuclei. We analyse the size and shape characteristics of complex polymer structures, containing in general f(1) loops (petals) and f(2) linear chains (branches). Within the frames of continuous model of Gaussian macromolecule, we apply the path integration method and obtain the estimates for gyration radius R-g and asphericity (A) over cap of typical conformation as functions of parameters f(1), f(2). In particular, our results qualitatively reveal the extent of anisotropy of star-like topologies as compared to the rosette structures of the same total molecular weight. Bristol IOP Publ. Ltd. 2015 14 Journal of physics : A, Mathematical and theoretical 48 13 10.1088/1751-8113/48/13/135001 Institut für Physik und Astronomie
OPUS4-7910 Wissenschaftlicher Artikel Metzler, Ralf; Bauer, Maximilian; Rasmussen, Emil S.; Lomholt, Michael A. Real sequence effects on the search dynamics of transcription factors on DNA Recent experiments show that transcription factors (TFs) indeed use the facilitated diffusion mechanism to locate their target sequences on DNA in living bacteria cells: TFs alternate between sliding motion along DNA and relocation events through the cytoplasm. From simulations and theoretical analysis we study the TF-sliding motion for a large section of the DNA-sequence of a common E. coli strain, based on the two-state TF-model with a fast-sliding search state and a recognition state enabling target detection. For the probability to detect the target before dissociating from DNA the TF-search times self-consistently depend heavily on whether or not an auxiliary operator (an accessible sequence similar to the main operator) is present in the genome section. Importantly, within our model the extent to which the interconversion rates between search and recognition states depend on the underlying nucleotide sequence is varied. A moderate dependence maximises the capability to distinguish between the main operator and similar sequences. Moreover, these auxiliary operators serve as starting points for DNA looping with the main operator, yielding a spectrum of target detection times spanning several orders of magnitude. Auxiliary operators are shown to act as funnels facilitating target detection by TFs. London Nature Publishing Group 2015 Scientific Reports 5 10072 10.1038/srep10072 Institut für Physik und Astronomie