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Eli Barkai - One of the best experts on this subject based on the ideXlab platform.

  • Large Deviations for Continuous Time Random Walks
    Entropy, 2020
    Co-Authors: Wanli Wang, Eli Barkai, Stanislav Burov
    Abstract:

    Recently observation of Random Walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time Random Walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Levy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time Random Walk model to test the large deviation theory.

  • Noisy continuous time Random Walks
    The Journal of chemical physics, 2013
    Co-Authors: Jaehyung Jeon, Eli Barkai, Ralf Metzler
    Abstract:

    Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time Random Walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time Random Walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time Random Walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time Random Walks may appear ergodic, while the bare continuous time Random Walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.

  • in vivo anomalous diffusion and weak ergodicity breaking of lipid granules
    Physical Review Letters, 2011
    Co-Authors: Jaehyung Jeon, Eli Barkai, Vincent Tejedor, Stas Burov, Christine Selhuberunkel, Kirstine Bergsorensen, Lene B Oddershede, Ralf Metzler
    Abstract:

    Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time Random Walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

  • weak ergodicity breaking in the continuous time Random Walk
    Physical Review Letters, 2005
    Co-Authors: Eli Barkai
    Abstract:

    The Continuous-Time Random Walk (CTRW) model exhibits a nonergodic phase when the average waiting time diverges. Using an analytical approach for the nonbiased and the uniformly biased CTRWs, and numerical simulations for the CTRW in a potential field, we obtain the nonergodic properties of the Random Walk which show strong deviations from Boltzmann-Gibbs theory. We derive the distribution function of occupation times in a bounded region of space which, in the ergodic phase recovers the Boltzmann-Gibbs theory, while in the nonergodic phase yields a generalized nonergodic statistical law. DOI: 10.1103/PhysRevLett.94.240602

Ralf Metzler - One of the best experts on this subject based on the ideXlab platform.

  • Noisy continuous time Random Walks
    The Journal of chemical physics, 2013
    Co-Authors: Jaehyung Jeon, Eli Barkai, Ralf Metzler
    Abstract:

    Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time Random Walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time Random Walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time Random Walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time Random Walks may appear ergodic, while the bare continuous time Random Walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.

  • in vivo anomalous diffusion and weak ergodicity breaking of lipid granules
    Physical Review Letters, 2011
    Co-Authors: Jaehyung Jeon, Eli Barkai, Vincent Tejedor, Stas Burov, Christine Selhuberunkel, Kirstine Bergsorensen, Lene B Oddershede, Ralf Metzler
    Abstract:

    Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time Random Walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Marco Dentz - One of the best experts on this subject based on the ideXlab platform.

  • 3D FLUID DEFORMATION AND MIXING VIA A CONTINUOUS TIME Random Walk
    2015
    Co-Authors: Daniel Lester, Marco Dentz, Tanguy Le Borgne, Felipe De Barros
    Abstract:

    Fluid stretching and deformation as quantified by the fluid deformation gradient tensor directly controls mixing of diffusive species in both chaotic and non-chaotic, 2D and 3D flows at the pore- and Darcy scales. Indeed, recent advances [LeBorgne et. al. PRL, 110, 204501, 2013] in the prediction of mixing and scalar dissipation require the distribution of fluid deformation rates as quantitative inputs. However, these measures are often difficult to link to medium properties or statistical heterogeneity controls. To advance this problem, we present a novel Continuous Time Random Walk (CTRW) to model stochastic evolution of the 3D fluid deformation tensor in a Protean (streamline) coordinate frame. This approach allows topological constraints imposed by the flow kinematics to be naturally obeyed, and furthermore flow features that generate non-Fickian transport can be clearly elucidated. For simple flows, this framework allows the distribution of deformation rates (and hence mixing) to be expressed in terms of heterogenenity controls, and for more complex flows, this approach clearly identifies what flow features govern anomalous transport and how their statistics can be measured as model inputs.

  • Flow intermittency, dispersion, and correlated continuous time Random Walks in porous media
    Physical Review Letters, 2013
    Co-Authors: Pietro De Anna, Marco Dentz, Diogo Bolster, Alexandre M. Tartakovsky, Tanguy Le Borgne, Perry Davy
    Abstract:

    We study the intermittency of fluid velocities in porous media and its relation to anomalous dispersion. Lagrangian velocities measured at equidistant points along streamlines are shown to form a spatial Markov process. As a consequence of this remarkable property, the dispersion of fluid particles can be described by a continuous time Random Walk with correlated temporal increments. This new dynamical picture of intermittency provides a direct link between the microscale flow, its intermittent properties, and non-Fickian dispersion.

  • Diffusion and trapping in heterogeneous media: An inhomogeneous continuous time Random Walk approach
    Advances in Water Resources, 2012
    Co-Authors: Marco Dentz, Philippe Gouze, Anna Russian, Jalal Dweik, Frederick Delay
    Abstract:

    We study diffusion in a heterogeneous medium that is characterized by spatially varying diffusion properties from a Random Walk point of view. We show that an inhomogeneous continuous time Random Walk (CTRW) with a spatially variable exponential transition time distribution solves the spatially discretized heterogeneous diffusion equation. This demonstrates the equivalence of the widely used time-domain Random Walk (TDRW) scheme and spatially inhomogeneous CTRW and at the same time provides a demonstration of the formal equivalence of the TDRW particle formulation and the heterogeneous diffusion equation. Based on this equivalence, we develop a TDRW method for heterogeneous diffusion under spatially variable multirate mass transfer properties. We discuss the implementation of these schemes and study the diffusion behavior in the presence of traps that are characterized by a truncated power-law trapping time distribution.

  • Effective pore-scale dispersion upscaling with a correlated continuous time Random Walk approach
    Water Resources Research, 2011
    Co-Authors: Tanguy Le Borgne, Marco Dentz, Diogo Bolster, Pietro De Anna, Alexandre M. Tartakovsky
    Abstract:

    We investigate the upscaling of dispersion from a pore-scale analysis of Lagrangian velocities. A key challenge in the upscaling procedure is to relate the temporal evolution of spreading to the pore-scale velocity field properties. We test the hypothesis that one can represent Lagrangian velocities at the pore scale as a Markov process in space. The resulting effective transport model is a continuous time Random Walk (CTRW) characterized by a correlated Random time increment, here denoted as correlated CTRW. We consider a simplified sinusoidal wavy channel model as well as a more complex heterogeneous pore space. For both systems, the predictions of the correlated CTRW model, with parameters defined from the velocity field properties (both distribution and correlation), are found to be in good agreement with results from direct pore-scale simulations over preasymptotic and asymptotic times. In this framework, the nontrivial dependence of dispersion on the pore boundary fluctuations is shown to be related to the competition between distribution and correlation effects. In particular, explicit inclusion of spatial velocity correlation in the effective CTRW model is found to be important to represent incomplete mixing in the pore throats.

  • Lagrangian Statistical Model for Transport in Highly Heterogeneous Velocity Fields
    Physical Review Letters, 2008
    Co-Authors: Tanguy Le Borgne, Marco Dentz, Jesus Carrera
    Abstract:

    We define an effective Lagrangian statistical model in phase space (x, t, v) for describing transport inhighly heterogeneous velocity fields with complex spatial organizations. The spatial Markovian nature (and temporal non-Markovian nature) of Lagrangian velocities leads to an effective transport description that turns out to be a correlated continuous time Random Walk. This model correctly captures the Lagrangian velocity correlation properties and is demonstrated to represent a forward model for predicting transport in highly heterogeneous porous media for different types of velocity organizations.

Jaehyung Jeon - One of the best experts on this subject based on the ideXlab platform.

  • Noisy continuous time Random Walks
    The Journal of chemical physics, 2013
    Co-Authors: Jaehyung Jeon, Eli Barkai, Ralf Metzler
    Abstract:

    Experimental studies of the diffusion of biomolecules within biological cells are routinely confronted with multiple sources of stochasticity, whose identification renders the detailed data analysis of single molecule trajectories quite intricate. Here, we consider subdiffusive continuous time Random Walks that represent a seminal model for the anomalous diffusion of tracer particles in complex environments. This motion is characterized by multiple trapping events with infinite mean sojourn time. In real physical situations, however, instead of the full immobilization predicted by the continuous time Random Walk model, the motion of the tracer particle shows additional jiggling, for instance, due to thermal agitation of the environment. We here present and analyze in detail an extension of the continuous time Random Walk model. Superimposing the multiple trapping behavior with additive Gaussian noise of variable strength, we demonstrate that the resulting process exhibits a rich variety of apparent dynamic regimes. In particular, such noisy continuous time Random Walks may appear ergodic, while the bare continuous time Random Walk exhibits weak ergodicity breaking. Detailed knowledge of this behavior will be useful for the truthful physical analysis of experimentally observed subdiffusion.

  • in vivo anomalous diffusion and weak ergodicity breaking of lipid granules
    Physical Review Letters, 2011
    Co-Authors: Jaehyung Jeon, Eli Barkai, Vincent Tejedor, Stas Burov, Christine Selhuberunkel, Kirstine Bergsorensen, Lene B Oddershede, Ralf Metzler
    Abstract:

    Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time Random Walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

J. Masoliver - One of the best experts on this subject based on the ideXlab platform.

  • the continuous time Random Walk still trendy fifty year history state of art and outlook
    European Physical Journal B, 2017
    Co-Authors: Ryszard Kutner, J. Masoliver
    Abstract:

    In this article we demonstrate the very inspiring role of the Continuous-Time Random Walk (CTRW) formalism, the numerous modifications permitted by its flexibility, its various applications, and the promising perspectives in the various fields of knowledge. A short review of significant achievements and possibilities is given. However, this review is still far from completeness. We focused on a pivotal role of CTRWs mainly in anomalous stochastic processes discovered in physics and beyond. This article plays the role of an extended announcement of the Eur. Phys. J. B Special Issue [http://epjb.epj.org/open-calls-for-papers/123-epj-b/1090-ctrw-50-years-on] containing articles which show incredible possibilities of the CTRWs.

  • the continuous time Random Walk still trendy fifty year history state of art and outlook
    arXiv: Statistical Mechanics, 2016
    Co-Authors: Ryszard Kutner, J. Masoliver
    Abstract:

    In this issue we demonstrate the very inspiring role of the Continuous-Time Random Walk (CTRW) formalism and its numerous modifications thanks to their flexibility and various applications as well its promising perspectives in different fields of knowledge. A short review of significant achievements and possibilities is given, however, still far from completeness.

  • The continuous time Random Walk formalism in financial markets
    Journal of Economic Behavior & Organization, 2006
    Co-Authors: J. Masoliver, Miquel Montero, Josep Perelló, George H. Weiss
    Abstract:

    We adapt continuous time Random Walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price distribution from high-frequency data, and (ii) the inverse problem, obtaining information on the market microstructure as reflected by high-frequency data knowing only the daily volatility. We apply the formalism to financial data to show that the CTRW offers alternative tools to deal with several complex issues of financial markets.

  • continuous time Random Walk model for financial distributions
    Physical Review E, 2003
    Co-Authors: J. Masoliver, Miquel Montero, George H. Weiss
    Abstract:

    We apply the formalism of the continuous time Random Walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the US dollar/Deutsche Mark future exchange, finding good agreement between theory and the observed data.