Anomalous diffusion in viscosity landscapes

Burgis, M; Schaller, Volker; Glässl, Martin; Kaiser, Benjamin; Krekhov, A. P.; Zimmermann, Walter

doi:10.1088/1367-2630/13/4/043031

Cited by 11 publications

(14 citation statements)

References 48 publications

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“…Following experimental observations of deterministic gradients of the local diffusivity in both pro-and eukaryotic cells [71,72] and the existence of thermal gradient conditions [73], the model of heterogeneous diffusion processes (HDPs) with a power-law, exponential, and logarithmic form for D(x) was recently introduced by the authors [74][75][76]; see also Refs. [77][78][79][80]. These Markovian processes based on a Langevin description with multiplicative noise exhibit anomalous diffusion and weak er-godicity breaking [74][75][76].…”

Section: B Deterministic Variation Of the Diffusivity With Position O...mentioning

confidence: 99%

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

Cherstvy

Metzler

2016

Phys. Chem. Chem. Phys.

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We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical results. We explore the regimes of normal Brownian motion as well as anomalous diffusion in the sub- and superdiffusive regimes. We also consider effects of the inertial term on the particle motion. The investigation of the resulting diffusion is performed for unconfined and confined motion.

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Section: B Deterministic Variation Of the Diffusivity With Position O...mentioning

confidence: 99%

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

Cherstvy

Metzler

2016

Phys. Chem. Chem. Phys.

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“…one could interpret our SVFC as the diffusion in some effective viscosity landscape. In this context, it is particularly intriguing, whether the subdiffusive behavior predicted in [45] could emerge in our approach. Unfortunately, as our equations of motion are highly nonlinear and the dependence between K(r), F (r) and g(r) is strictly fixed (unlike in Ref.…”

Section: Scn In Molecular Systemsmentioning

confidence: 95%

“…The notion of SVFC itself is also not entirely new and it can be encountered in the research on the diffusion in viscosity landscapes, e.g. in [45]. Interestingly, in this context the authors intuitively conclude that the system must be driven by the multiplicative noise.…”

Section: Scn In Molecular Systemsmentioning

confidence: 99%

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise

Majka¹,

Góra²

2017

J. Phys. A: Math. Theor.

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The collectivity in the simultaneous diffusion of many particles, i.e. the interdependence of stochastic forces affecting different particles in the same solution, is a largely overlooked phenomenon with no well-established theory. Recently, we have proposed a novel type of thermodynamically consistent Langevin dynamics driven by the Spatially Correlated Noise (SCN) that can contribute to the understanding of this problem. This model draws a link between the theory of effective interactions in binary colloidal mixtures and the properties of SCN. In the current article we review this model from the perspective of collective diffusion and generalize it to the case of multiple (N > 2) particles. Since our theory of SCN-driven Langevin dynamics has certain issues that could not be resolved within its framework, in this article we also provide another approach to the problem of collectivity. We discuss the multi-particle Mori-Zwanzig model, which is fully microscopically consistent. Indeed, we show that this model supplies many information, complementary to the SCN-based approach, e.g. it predicts the deterministic dynamics of the relative distance between the particles, it provides the approximation for non-equilibrium effective interactions and predicts the collective subdiffusion of tracers in group. These results provide the short-range, inertial limit of the earlier model and agree with its predictions under some general conditions. In this article we also review the origin of SCN and its consequences for the variety of physical systems, with emphasis on the colloids.

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“…Recently, it has been shown that such a situation can lead to sub-or super-diffusive motion on intermediate time scales. 38 Although there is no intrinsic length scale in the power law decay of T(r), we can take a characteristic length of l ≈ 1 μm for the comparison of the various time scales. Almost 90% of the temperature change occurs within a sphere of this radius and also the major portion of the concentration bubble is confined within this sphere as long as excessive saturation of the concentration bleaching is avoided (Fig.…”

Section: E Time Scalesmentioning

confidence: 99%

Transient cage formation around hot gold colloids dispersed in polymer solutions

Schwaiger

Zimmermann

2011

The Journal of Chemical Physics

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Gold colloids dispersed in dilute to concentrated polymer solutions can efficiently be heated by laser irradiation and act as almost pointlike heat sources. In systems with positive Soret coefficients S(T) of the polymer, such as solutions of polystyrene in toluene, the polymer can almost entirely be removed from the particle surface. The colloid attracts the solvent and a transient cage of low viscosity and dramatically enhanced mobility is formed, which follows the motion of the particle with a certain retardation. Based on a complete parameterization of S(T)(M, c, T), we analyze in detail the stationary temperature, concentration, and viscosity profiles. Depending on the polymer molar mass and concentration on the distance to the glass transition temperature, the negative or positive feedback-loops are established that lead to either attenuation or self-amplification of the polymer depletion.

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Anomalous diffusion in viscosity landscapes

Cited by 11 publications

References 48 publications

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes

Collectivity in diffusion of colloidal particles: from effective interactions to spatially correlated noise

Transient cage formation around hot gold colloids dispersed in polymer solutions

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