@misc{deCarvalhoMetzlerCherstvy2016,
  author    = {de Carvalho, Sidney J. and Metzler, Ralf and Cherstvy, Andrey G.},
  title     = {Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-100295},
  pages     = {17},
  year      = {2016},
  abstract  = {We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition—demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces—are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye-H{\"u}ckel approximation is often not feasible and the nonlinear Poisson-Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson-Boltzmann equation is smaller than the Debye-H{\"u}ckel result, such that the required critical surface charge density for polyelectrolyte adsorption σc increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical-chemical and biophysical systems.},
  language  = {en}
}
@article{LiuCherstvyMetzler2017,
  author    = {Liu, Lin and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Facilitated Diffusion of Transcription Factor Proteins with Anomalous Bulk Diffusion},
  series = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  volume    = {121},
  journal   = {The journal of physical chemistry : B, Condensed matter, materials, surfaces, interfaces \& biophysical chemistry},
  publisher = {American Chemical Society},
  address   = {Washington},
  issn      = {1520-6106},
  doi       = {10.1021/acs.jpcb.6b12413},
  pages     = {1284 -- 1289},
  year      = {2017},
  abstract  = {What are the physical laws of the diffusive search of proteins for their specific binding sites on DNA in the presence of the macromolecular crowding in cells? We performed extensive computer simulations to elucidate the protein target search on DNA. The novel feature is the viscoelastic non-Brownian protein bulk diffusion recently observed experimentally. We examine the influence of the protein-DNA binding affinity and the anomalous diffusion exponent on the target search time. In all cases an optimal search time is found. The relative contribution of intermittent three-dimensional bulk diffusion and one-dimensional sliding of proteins along the DNA is quantified. Our results are discussed in the light of recent single molecule tracking experiments, aiming at a better understanding of the influence of anomalous kinetics of proteins on the facilitated diffusion mechanism.},
  language  = {en}
}
@article{AkimotoCherstvyMetzler2018,
  author    = {Akimoto, Takuma and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Ergodicity, rejuvenation, enhancement, and slow relaxation of diffusion in biased continuous-time random walks},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {98},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.98.022105},
  pages     = {6},
  year      = {2018},
  abstract  = {Bias plays an important role in the enhancement of diffusion in periodic potentials. Using the continuous-time random walk in the presence of a bias, we report on an interesting phenomenon for the enhancement of diffusion by the start of the measurement in a random energy landscape. When the variance of the waiting time diverges, in contrast to the bias-free case, the dynamics with bias becomes superdiffusive. In the superdiffusive regime, we find a distinct initial ensemble dependence of the diffusivity. Moreover, the diffusivity can be increased by the aging time when the initial ensemble is not in equilibrium. We show that the time-averaged variance converges to the corresponding ensemble-averaged variance; i.e., ergodicity is preserved. However, trajectory-to-trajectory fluctuations of the time-averaged variance decay unexpectedly slowly. Our findings provide a rejuvenation phenomenon in the superdiffusive regime, that is, the diffusivity for a nonequilibrium initial ensemble gradually increases to that for an equilibrium ensemble when the start of the measurement is delayed.},
  language  = {en}
}
@article{AydinerCherstvyMetzler2019,
  author    = {Aydiner, Ekrem and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Money distribution in agent-based models with position-exchange dynamics},
  series = {The European physical journal : B, Condensed matter and complex systems},
  volume    = {92},
  journal   = {The European physical journal : B, Condensed matter and complex systems},
  number    = {5},
  publisher = {Springer},
  address   = {New York},
  issn      = {1434-6028},
  doi       = {10.1140/epjb/e2019-90674-0},
  pages     = {4},
  year      = {2019},
  abstract  = {Wealth and income distributions are known to feature country-specific Pareto exponents for their long power-law tails. To propose a rationale for this, we introduce an agent-based dynamic model and use Monte Carlo simulations to unveil the wealth distributions in closed and open economical systems. The standard money-exchange scenario is supplemented with the position-exchange agent dynamics that vitally affects the Pareto law. Specifically, in closed systems with position-exchange dynamics the power law changes to an exponential shape, while for open systems with traps the Pareto law remains valid.},
  language  = {en}
}
@article{CherstvyThapaWagneretal.2019,
  author    = {Cherstvy, Andrey G. and Thapa, Samudrajit and Wagner, Caroline E. and Metzler, Ralf},
  title     = {Non-Gaussian, non-ergodic, and non-Fickian diffusion of tracers in mucin hydrogels},
  series = {Soft matter},
  volume    = {15},
  journal   = {Soft matter},
  number    = {12},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1744-683X},
  doi       = {10.1039/c8sm02096e},
  pages     = {2526 -- 2551},
  year      = {2019},
  abstract  = {Native mucus is polymer-based soft-matter material of paramount biological importance. How non-Gaussian and non-ergodic is the diffusive spreading of pathogens in mucus? We study the passive, thermally driven motion of micron-sized tracers in hydrogels of mucins, the main polymeric component of mucus. We report the results of the Bayesian analysis for ranking several diffusion models for a set of tracer trajectories [C. E. Wagner et al., Biomacromolecules, 2017, 18, 3654]. The models with "diffusing diffusivity', fractional and standard Brownian motion are used. The likelihood functions and evidences of each model are computed, ranking the significance of each model for individual traces. We find that viscoelastic anomalous diffusion is often most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Our analysis also clarifies the distribution of time-averaged displacements, correlations of scaling exponents and diffusion coefficients, and the degree of non-Gaussianity of displacements at varying pH levels. Weak ergodicity breaking is also quantified. We conclude that-consistent with the original study-diffusion of tracers in the mucin gels is most non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. Using the Bayesian approach with the nested-sampling algorithm, together with the quantitative analysis of multiple statistical measures, we report new insights into possible physical mechanisms of diffusion in mucin gels.},
  language  = {en}
}
@article{ThapaLukatSelhuberUnkeletal.2019,
  author    = {Thapa, Samudrajit and Lukat, Nils and Selhuber-Unkel, Christine and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Transient superdiffusion of polydisperse vacuoles in highly motile amoeboid cells},
  series = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  volume    = {150},
  journal   = {The journal of chemical physics : bridges a gap between journals of physics and journals of chemistr},
  number    = {14},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {0021-9606},
  doi       = {10.1063/1.5086269},
  pages     = {18},
  year      = {2019},
  abstract  = {We perform a detailed statistical analysis of diffusive trajectories of membrane-enclosed vesicles (vacuoles) in the supercrowded cytoplasm of living Acanthamoeba castellanii cells. From the vacuole traces recorded in the center-of-area frame of moving amoebae, we examine the statistics of the time-averaged mean-squared displacements of vacuoles, their generalized diffusion coefficients and anomalous scaling exponents, the ergodicity breaking parameter, the non-Gaussian features of displacement distributions of vacuoles, the displacement autocorrelation function, as well as the distributions of speeds and positions of vacuoles inside the amoeba cells. Our findings deliver novel insights into the internal dynamics of cellular structures in these infectious pathogens. Published under license by AIP Publishing.},
  language  = {en}
}
@article{FernandezCharcharCherstvyetal.2020,
  author    = {Fernandez, Amanda Diez and Charchar, Patrick and Cherstvy, Andrey G. and Metzler, Ralf and Finnis, Michael W.},
  title     = {The diffusion of doxorubicin drug molecules in silica nanoslits is non-Gaussian, intermittent and anticorrelated},
  series = {Physical chemistry, chemical physics},
  volume    = {22},
  journal   = {Physical chemistry, chemical physics},
  number    = {48},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/d0cp03849k},
  pages     = {27955 -- 27965},
  year      = {2020},
  abstract  = {In this study we investigate, using all-atom molecular-dynamics computer simulations, the in-plane diffusion of a doxorubicin drug molecule in a thin film of water confined between two silica surfaces. We find that the molecule diffuses along the channel in the manner of a Gaussian diffusion process, but with parameters that vary according to its varying transversal position. Our analysis identifies that four Gaussians, each describing particle motion in a given transversal region, are needed to adequately describe the data. Each of these processes by itself evolves with time at a rate slower than that associated with classical Brownian motion due to a predominance of anticorrelated displacements. Long adsorption events lead to ageing, a property observed when the diffusion is intermittently hindered for periods of time with an average duration which is theoretically infinite. This study presents a simple system in which many interesting features of anomalous diffusion can be explored. It exposes the complexity of diffusion in nanoconfinement and highlights the need to develop new understanding.},
  language  = {en}
}
@article{WangCherstvyChechkinetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Chechkin, Aleksei V. and Thapa, Samudrajit and Seno, Flavio and Liu, Xianbin and Metzler, Ralf},
  title     = {Fractional Brownian motion with random diffusivity},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {53},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {47},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/aba467},
  pages     = {34},
  year      = {2020},
  abstract  = {Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time tau characterising the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on tau and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion, absent in the continuous-time formulation. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.},
  language  = {en}
}
@misc{KindlerPulkkinenCherstvyetal.2019,
  author    = {Kindler, Oliver and Pulkkinen, Otto and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Burst Statistics in an Early Biofilm Quorum Sensing Mode},
  series = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam Mathematisch-Naturwissenschaftliche Reihe},
  number    = {777},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-43909},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-439099},
  pages     = {21},
  year      = {2019},
  abstract  = {Quorum-sensing bacteria in a growing colony of cells send out signalling molecules (so-called "autoinducers") and themselves sense the autoinducer concentration in their vicinity. Once—due to increased local cell density inside a "cluster" of the growing colony—the concentration of autoinducers exceeds a threshold value, cells in this clusters get "induced" into a communal, multi-cell biofilm-forming mode in a cluster-wide burst event. We analyse quantitatively the influence of spatial disorder, the local heterogeneity of the spatial distribution of cells in the colony, and additional physical parameters such as the autoinducer signal range on the induction dynamics of the cell colony. Spatial inhomogeneity with higher local cell concentrations in clusters leads to earlier but more localised induction events, while homogeneous distributions lead to comparatively delayed but more concerted induction of the cell colony, and, thus, a behaviour close to the mean-field dynamics. We quantify the induction dynamics with quantifiers such as the time series of induction events and burst sizes, the grouping into induction families, and the mean autoinducer concentration levels. Consequences for different scenarios of biofilm growth are discussed, providing possible cues for biofilm control in both health care and biotechnology.},
  language  = {en}
}
@article{WangCherstvyLiuetal.2020,
  author    = {Wang, Wei and Cherstvy, Andrey G. and Liu, Xianbin and Metzler, Ralf},
  title     = {Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.012146},
  pages     = {012146-1 -- 012146-16},
  year      = {2020},
  abstract  = {Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x) = D-0|x|(alpha). Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble-and time-averaged mean-squared displacements couple the scaling exponents alpha of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y similar to |x|(1/(2/(2-alpha)))/t(H) coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), PHDP-FBM(y) = e(-y2)/root pi. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.},
  language  = {en}
}