Diffusing diffusivity: a new derivation and comparison with simulations

Jain, Rohit; Sebastian, K. L.

doi:10.1007/s12039-017-1308-0

Cited by 54 publications

(58 citation statements)

References 56 publications

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“…The DD concept was further studied by Jain and Sebastian [87,88] and Chechkin et al [67]. While Jain and Sebastian use a path integral approach, Chechkin et al invoke the concept of subordination and an explicit exact solution for the PDF in Fourier space.…”

Section: Introductionmentioning

confidence: 99%

“…In the following we generalise the ggBM model from [78][79][80][81][82] to incorporate the generalised Gamma function (4). We then demonstrate how to reformulate the Ornstein-Uhlenbeck picture of the DD minimal model [67] and the closely related DD models [83,87,88] to include the distribution (4). With this extension both models are considerably more flexible for the description of measured data.…”

Section: Introductionmentioning

confidence: 99%

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Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

et al. 2018

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A considerable number of systems have recently been reported in which Brownian yet non-Gaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly non-Gaussian, and often of exponential (Laplace) shape. This apparently ubiquitous behaviour observed in very different physical systems has been interpreted as resulting from diffusion in inhomogeneous environments and mathematically represented through a variable, stochastic diffusion coefficient. Indeed different models describing a fluctuating diffusivity have been studied. Here we present a new view of the stochastic basis describing time-dependent random diffusivities within a broad spectrum of distributions. Concretely, our study is based on the very generic class of the generalised Gamma distribution. Two models for the particle spreading in such random diffusivity settings are studied. The first belongs to the class of generalised grey Brownian motion while the second follows from the idea of diffusing diffusivities. The two processes exhibit significant characteristics which reproduce experimental results from different biological and physical systems. We promote these two physical models for the description of stochastic particle motion in complex environments. uncovered anomalous diffusion of the power-law formwith the anomalous diffusion exponent 0<α<1 and the generalised diffusion coefficient D α [11], for the motion of charge carriers in amorphous semiconductors [12]. With the advance of modern microscopy techniques, in particular, superresolution microscopy, as well as massive progress in supercomputing, anomalous diffusion of the type (3) has been reported in numerous complex and biological systems [13,14]. Thus, subdiffusion with 0<α<1 was observed for submicron tracers in the crowded cytoplasm of biological cells [15][16][17][18][19] as well as in artificially crowded environments [20][21][22][23]. Further reports of subdiffusion come from the motion of proteins embedded in the membranes of living cells [24][25][26]. Subdiffusion is also seen in extensive simulations studies, for instance, of lipid bilayer membranes [27][28][29][30] and relative diffusion in proteins [31]. Superdiffusion, due to active motion of molecular motors, was observed in various biological cell types for both introduced and endogenous tracers [16,17,32,33].Most of the anomalous diffusion phenomena mentioned here belong to two main classes of anomalous diffusion: (i) the class of continuous time random walk processes, in which scale-free power-law waiting times in between motion events give rise to the law (3) [12,34], along with a stretched Gaussian displacement probability density G(x, t) [11,12,34] as well as weak ergodicity breaking and ageing [35,36]. We note that similar effects of non-Gaussianity, weak non-ergodicity, and ageing also occur in spatially heterogeneous diffusion processes [37][38][39][40]. (ii) The secon...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

et al. 2018

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“…Recently, Brownian motion with fluctuating diffusivity has been intensively studied in the absence of the external force [10][11][12][13][14][15], but it would be also important to investigate the Brownian dynamics with some external forces, such as the forces by some confinements and external potentials. For example, the diffusion coefficient observed in single-particle-tracking experiments in bacterial cytoplasms is typically of the order of 10 −2 [µm 2 /sec] [8,16], whereas the size of the bacterial cell is of the order of 1µm.…”

Section: Introductionmentioning

confidence: 99%

Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation

2019

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We investigate Brownian motion with diffusivity alternately fluctuating between fast and slow states. We assume that sojourn-time distributions of these two states are given by exponential or power-law distributions. We develop a theory of alternating renewal processes to study a relaxation function which is expressed with an integral of the diffusivity over time. This relaxation function can be related to a position correlation function if the particle is in a harmonic potential, and to the self-intermediate scattering function if the potential force is absent. It is theoretically shown that, at short times, the exponential relaxation or the stretched-exponential relaxation are observed depending on the power law index of the sojourn-time distributions. In contrast, at long times, a power law decay with an exponential cutoff is observed. The dependencies on the initial ensembles (i.e., equilibrium or non-equilibrium initial ensembles) are also elucidated. These theoretical results are consistent with numerical simulations.

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“…It is thus natural to consider the diffusivity as a stochastic time-dependent process, D t , referred to as "annealed disorder". The concept of "diffusing diffusivity" was put forward by Chubynsky and Slater [38] and then was further developed by Jain and Sebastian [39,40] and Chechkin et al [41] (note that the impact of a stochastic volatility onto the distribution of asset returns was investigated much earlier by Drãgulescu and Yakovenko [42]). In [43], we proposed to model the stochastic diffusivity of a particle by a Feller process [44], also known as the square root process or the Cox-Ingersoll-Ross process [45]:…”

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confidence: 99%

Diffusion-limited reactions in dynamic heterogeneous media

Lanoiselée¹,

Moutal²,

Grebenkov³

2018

Nat Commun

153

129

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Most biochemical reactions in living cells rely on diffusive search for target molecules or regions in a heterogeneous overcrowded cytoplasmic medium. Rapid rearrangements of the medium constantly change the effective diffusivity felt locally by a diffusing particle and thus impact the distribution of the first-passage time to a reaction event. Here, we investigate the effect of these dynamic spatiotemporal heterogeneities onto diffusion-limited reactions. We describe a general mathematical framework to translate many results for ordinary homogeneous Brownian motion to heterogeneous diffusion. In particular, we derive the probability density of the first-passage time to a reaction event and show how the dynamic disorder broadens the distribution and increases the likelihood of both short and long trajectories to reactive targets. While the disorder slows down reaction kinetics on average, its dynamic character is beneficial for a faster search and realization of an individual reaction event triggered by a single molecule.

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Diffusing diffusivity: a new derivation and comparison with simulations

Cited by 54 publications

References 56 publications

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

Random diffusivity from stochastic equations: comparison of two models for Brownian yet non-Gaussian diffusion

Brownian motion with alternately fluctuating diffusivity: Stretched-exponential and power-law relaxation

Diffusion-limited reactions in dynamic heterogeneous media

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