Analytical solution of the generalized Langevin equation with hydrodynamic interactions: Subdiffusion of heavy tracers

Grebenkov, Denis S.; Vahabi, M.

doi:10.1103/physreve.89.012130

Cited by 30 publications

(35 citation statements)

References 59 publications

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“…Here K β is the generalised diffusion coefficient with units cm sec Subdiffusion in the crowded cytoplasm of living cells was observed for fluorescent smaller proteins [13,14], labelled polymeric dextrane [15] and messenger RNA [1,16], chromosomal loci and telomeres [16,17], as well as submicron endogenous granules [18][19][20] and viruses [21]. Subdiffusion was also reported for the motion of tracer particles in artificially crowded environments [22][23][24][25][26][27][28][29][30]. We note that active transport processes in living cells may lead to superdiffusion with 1 2 b < < [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 82%

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

et al. 2016

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A topic of intense current investigation pursues the question of how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. Motivated by recent experiments we report results of extensive simulations of the motion of a finite sized tracer particle in a heterogeneously crowded environment made up of quenched distributions of monodisperse crowders of varying sizes in finite circular two-dimensional domains. For given spatial distributions of monodisperse crowders we demonstrate how anomalous diffusion with strongly non-Gaussian features arises in this model system. We investigate both biologically relevant situations of particles released either at the surface of an inner domain or at the outer boundary, exhibiting distinctly different features of the observed anomalous diffusion for heterogeneous distributions of crowders. Specifically we reveal an asymmetric spreading of tracers even at moderate crowding. In addition to the mean squared displacement (MSD) and local diffusion exponent we investigate the magnitude and the amplitude scatter of the time averaged MSD of individual tracer trajectories, the non-Gaussianity parameter, and the van Hove correlation function. We also quantify how the average tracer diffusivity varies with the position in the domain with a heterogeneous radial distribution of crowders and examine the behaviour of the survival probability and the dynamics of the tracer survival probability. Inter alia, the systems we investigate are related to the passive transport of lipid molecules and proteins in two-dimensional crowded membranes or the motion in colloidal solutions or emulsions in effectively two-dimensional geometries, as well as inside supercrowded, surface adhered cells.

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Section: Introductionmentioning

confidence: 82%

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

et al. 2016

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“…In this appendix, following [47] we derive an analytical expression of the VACF for all rational λ (with 0 < λ < 2) as a simple summatory of Mittag-Leffler functions. This provides an advantageous expression for it from a numerical perspective.…”

Section: Appendix B: Analytical Expression Of the Vacf For Rational λmentioning

confidence: 99%

Velocity autocorrelation of a free particle driven by a Mittag-Leffler noise: Fractional dynamics and temporal behaviors

Viñales

Paissan

2014

Phys. Rev. E

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We investigate the dynamical phase diagram of the generalized Langevin equation of the free particle driven by a Mittag-Leffler noise and show critical curves and a critical value of the exponent parameter of the MittagLeffler function that mark different dynamical regimes. By considering that the modeling of a Mittag-Leffer memory kernel corresponds to a power-law second-order memory kernel, we show that the generalized Langevin equation of the velocity autocorrelation function (VACF) is transformed in a fractional Langevin equation. In the superdiffusive case our results exhibit oscillations and negative correlations of the VACF that are not provided by the usual power-law noise model.

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“…In a more general hydrodynamic theory of the BM [2] the Stokes force is replaced by the Boussinesq force [13], derived from the linearized Navier-Stokes and continuity equations for incompressible fluids. This force describes hydrodynamic interactions of a spherical tracer with the surrounding fluid [14]. These interactions appear at short time scales and, as distinct from the more familiar Kubo's generalization of the LE [15], the memory integral contains the acceleration of the Brownian particle instead of its velocity.…”

Section: Time Correlations Of the Thermal Noisementioning

confidence: 99%

Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids

Tóthová

Lisý

2016

EPJ Web of Conferences

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Abstract. In several recent works high-resolution interferometric detection allowed to study the Brownian motion of optically trapped microparticles in air and fluids. The observed positional fluctuations of the particles are well described by the generalized Langevin equation with the Boussinesq-Basset "history force" instead of the Stokes friction, which is valid only for the steady motion. Recently, also the time correlation function of the thermal random force F th driving the Brownian particles through collisions with the surrounding molecules has been measured. In the present contribution we propose a method to describe the statistical properties of F th in incompressible fluids. Our calculations show that the time decay of the correlator F th (t)F th (0) is significantly slower than that found in the literature. It is also shown how the "color" of the thermal noise can be determined from the measured positions of the Brownian particles.

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Analytical solution of the generalized Langevin equation with hydrodynamic interactions: Subdiffusion of heavy tracers

Cited by 30 publications

References 59 publications

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

Anomalous, non-Gaussian tracer diffusion in crowded two-dimensional environments

Velocity autocorrelation of a free particle driven by a Mittag-Leffler noise: Fractional dynamics and temporal behaviors

Statistical Properties of Thermal Noise Driving the Brownian Particles in Fluids

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