# Viscoelastic subdiffusion in a random Gaussian environment.

@article{Goychuk2018ViscoelasticSI, title={Viscoelastic subdiffusion in a random Gaussian environment.}, author={Igor Goychuk}, journal={Physical chemistry chemical physics : PCCP}, year={2018}, volume={20 37}, pages={ 24140-24155 } }

Viscoelastic subdiffusion governed by a fractional Langevin equation is studied numerically in a random Gaussian environment modeled by stationary Gaussian potentials with decaying spatial correlations. This anomalous diffusion is archetypal for living cells, where cytoplasm is known to be viscoelastic and a spatial disorder also naturally emerges. We obtain some first important insights into it within a model one-dimensional study. Two basic types of potential correlations are studied: short…

## 16 Citations

### Finite-range viscoelastic subdiffusion in disordered systems with inclusion of inertial effects

- Biology
- 2020

This work justifies further paradigmatic importance of the model of viscoelastic subdiffusion in random environments for the observed subdiffusion in cellular biological systems. Recently, we showed…

### Fractional Brownian motion with random diffusivity: emerging residual nonergodicity below the correlation time

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

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…

### Unexpected crossovers in correlated random-diffusivity processes

- PhysicsNew Journal of Physics
- 2020

The passive and active motion of micron-sized tracer particles in crowded liquids and inside living biological cells is ubiquitously characterised by ‘viscoelastic’ anomalous diffusion, in which the…

### The generalized Langevin equation with power-law memory in a nonlinear potential well

- MathematicsNonlinearity
- 2020

The generalized Langevin equation (GLE) is a stochastic integro-differential equation that has been used to describe the velocity of microparticles in viscoelastic fluids. In this work, we consider…

### Anomalous diffusion, nonergodicity, and ageing for exponentially and logarithmically time-dependent diffusivity: striking differences for massive versus massless particles

- PhysicsJournal of Physics D: Applied Physics
- 2021

We investigate a diffusion process with a time-dependent diffusion coefficient, both exponentially increasing and decreasing in time, D(t)=D0e±2αt . For this (hypothetical) nonstationary diffusion…

### Fractional electron transfer kinetics and a quantum breaking of ergodicity.

- PhysicsPhysical review. E
- 2019

The results question the applicability of all the existing and widely accepted ensemble theories of electron transfer in fractional, sub-Ohmic environments, on the level of single molecules, and provide a real challenge to face, both for theorists and experimentalists.

### From sub- to superdiffusion: fractional Brownian motion of membraneless organelles in early C. elegans embryos

- Physics
- 2021

Fractional Brownian motion (FBM) is a prevalent Gaussian stochastic process that has frequently been linked to subdiffusive motion in complex fluids, e.g. inside living cells. In contrast, examples…

### Diffusion of DNA-binding species in the nucleus: A transient anomalous subdiffusion model

- BiologybioRxiv
- 2019

The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP and has several implications for cell biophysics.

### Single-Particle Tracking Reveals Anti-Persistent Subdiffusion in Cell Extracts

- BiologyEntropy
- 2021

It is shown that these beads feature an anti-persistent subdiffusion that is consistent with fractional Brownian motion, suggesting that the high degree of macromolecular crowding in Xenopus extracts equips the fluid with a viscoelastic modulus, hence enforcing particles to perform random walks with a significant anti-Persistent memory kernel.

### Long-time persistence of hydrodynamic memory boosts microparticle transport

- PhysicsPhysical Review Research
- 2019

In a viscous fluid, the past motion of an accelerating particle is retained as an imprint on the vorticity field, which decays slowly as t−3/2. At low Reynolds number, the Basset-Boussinesq-Oseen…

## References

SHOWING 1-10 OF 181 REFERENCES

### Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlations.

- PhysicsPhysical review. E
- 2017

It is shown here that extremely persistent, macroscopic logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems.

### Viscoelastic subdiffusion: from anomalous to normal.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2009

The results justify the (ultra)slow fluctuating rate view of the corresponding bistable non-Markovian dynamics which displays bursting and anticorrelation of the residence times in two potential wells.

### Flashing subdiffusive ratchets in viscoelastic media

- Physics
- 2012

We study subdiffusive ratchet transport in periodically and randomly flashing potentials. A central Brownian particle is elastically coupled to the surrounding auxiliary Brownian quasi-particles,…

### Anomalous features of diffusion in corrugated potentials with spatial correlations: faster than normal, and other surprises.

- BiologyPhysical review letters
- 2014

It is shown that unbiased diffusion remains asymptotically normal also in the presence of spatial correlations decaying to zero, and predicted that such diffusion should be anomalous, but much faster than earlier expected on a typical length of genes for a realistic energy disorder of several room kBT.

### Markovian embedding of fractional superdiffusion

- Mathematics
- 2011

The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity…

### Anomalous fluctuations of currents in Sinai-type random chains with strongly correlated disorder.

- MathematicsPhysical review letters
- 2013

It is proved that moments of arbitrary order k of the steady-state current J(L) through a finite segment of length L of such a chain decay as L(-(1-H)), independently of k, which suggests that despite a logarithmic confinement the average current is much higher than its Fickian counterpart in homogeneous systems.

### Brownian particles on rough substrates: relation between intermediate subdiffusion and asymptotic long-time diffusion.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

It is shown that the asymptotic long-time diffusion coefficient can be related to the behavior at intermediate times, namely, the minimum of the exponent that characterizes subdiffusive dynamics and hence corresponds to the maximum degree of subdiffusion.

### Subdiffusive rocking ratchets in viscoelastic media: transport optimization and thermodynamic efficiency in overdamped regime.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2013

We study subdiffusive overdamped Brownian ratchets periodically rocked by an external zero-mean force in viscoelastic media within the framework of a non-Markovian generalized Langevin equation…