Anomalous transport in the soft-sphere Lorentz model

Petersen, Charlotte F.; Franosch, Thomas

doi:10.1039/c9sm00442d

Cited by 11 publications

(10 citation statements)

References 86 publications

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“…4(c) and 4(d) that, at low p 0 , plots of r 2 (t ) /T only collapse in the ballistic regime, while conversely at high-p 0 they also collapse in the subdiffusive one. The emerging scenario resembles the diffusion of a particle in a random media as described by the Lorentz gas models [25][26][27]50,51], where a particle is free until it hits randomly placed obstacles, and subdiffusion occurs below the correlation length of the fractal cluster of free space.…”

Section: B T1 Transitionsmentioning

confidence: 99%

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Wei

Paoluzzi

et al. 2021

Phys. Rev. E

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Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

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Section: B T1 Transitionsmentioning

confidence: 99%

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Wei

Paoluzzi

et al. 2021

Phys. Rev. E

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“…Different modelling strategies have been advised to account for such situations 23 : spatio-temporal master equations exploit metastability of diffusion between compartments 24 , and crowding has been incorporated into the reactiondiffusion master equation on a mesoscale level 25 . In particle-based Brownian dynamics simulations, crowding is implemented frequently as explicit excluded volume via hard or short-range repulsions [26][27][28][29][30][31] , which can give rise to complex-shaped structures on a cascade of scales [32][33][34][35] .…”

Section: Introductionmentioning

confidence: 99%

Diffusion-influenced reaction rates in the presence of pair interactions

Dibak

Fröhner

Noé

et al. 2019

The Journal of Chemical Physics

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The kinetics of bimolecular reactions in solution depends, among other factors, on intermolecular forces such as steric repulsion or electrostatic interaction. Microscopically, a pair of molecules first has to meet by diffusion before the reaction can take place. In this work, we establish an extension of Doi's volume reaction model to molecules interacting via pair potentials, which is a key ingredient for interacting-particle-based reaction-diffusion (iPRD) simulations. As a central result, we relate model parameters and macroscopic reaction rate constants in this situation. We solve the corresponding reaction-diffusion equation in the steady state and derive semi-analytical expressions for the reaction rate constant and the local concentration profiles. Our results apply to the full spectrum from well-mixed to diffusion-limited kinetics. For limiting cases, we give explicit formulas, and we provide a computationally inexpensive numerical scheme for the general case, including the intermediate, diffusion-influenced regime. The obtained rate constants decompose uniquely into encounter and formation rates, and we discuss the effect of the potential on both subprocesses, exemplified for a soft harmonic repulsion and a Lennard-Jones potential. The analysis is complemented by extensive stochastic iPRD simulations, and we find excellent agreement with the theoretical predictions. arXiv:1908.07764v1 [cond-mat.soft]

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“…Note that a nonmonotonic variation of the TAMSD scaling exponent with lag time was also detected, e.g., for anomalous diffusion of proteins and lipids on/in lipid membranes130,131 and in the model of tracer diffusion in driven lattice Lorentz gases of immobile obstacles154,155 . * * We do not quantify here the spread of individual TAMSDs and the respective dispersion determining the value of the ergodicity breaking parameter24,25,93 .…”

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confidence: 92%

Non-Gaussian, transiently anomalous and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: coupled translational and rotational motions

Klett

Cherstvy

Shin

et al. 2021

Preprint

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We employ Langevin-dynamics simulations to unveil non-Brownian and non-Gaussian center-of-mass self-diffusion of massive flexible dumbbell-shaped particles in crowded two-dimensional solutions. We also study the intra-dumbbell dynamics due to the relative motion of the two constituent elastically-coupled disks. Our main focus is on effects of the crowding fraction φ and the particle structure on the diffusion characteristics. We evaluate the time-averaged mean-squared displacement (TAMSD), the displacement probability-density function (PDF) and the displacement autocorrelation function (ACF) of the dimers. For the TAMSD at highly crowded conditions of dumbbells, e.g., we observe a transition from the short-time ballistic behavior, via an intermediate subdiffusive regime, to long-time Brownian-like spreading dynamics. The crowded system of dimers exhibits two distinct diffusion regimes distinguished by the scaling exponent of the TAMSD, the dependence of the diffusivity on φ, and the features of the displacement-ACF. We attribute these regimes to a crowding-induced transition from a viscous to a viscoelastic diffusion medium upon growing φ. We also analyze the relative motion in the dimers, finding that larger φ suppress their vibrations and yield strongly non-Gaussian PDFs of rotational displacements. For the diffusion coefficients D(φ) of translational and rotational motion of the dumbbells an exponential decay with φ for weak and a power-law D(φ) ∝ (φ - φ*)2.4 for strong crowding is found. A comparison of simulation results with theoretical predictions for D(φ) is discussed and some relevant experimental systems are overviewed.

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Anomalous transport in the soft-sphere Lorentz model

Cited by 11 publications

References 86 publications

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Diffusion-influenced reaction rates in the presence of pair interactions

Non-Gaussian, transiently anomalous and ergodic self-diffusion of flexible dumbbells in crowded two-dimensional environments: coupled translational and rotational motions

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