Subdiffusion in an external force field

Chen, Yao; Wang, Xudong; Deng, Weihua

doi:10.1103/physreve.99.042125

Cited by 32 publications

(36 citation statements)

References 67 publications

(200 reference statements)

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“…It seems that the Langevin equation ( 3) is ergodic due to the equivalence between the EAMSD and the ensemble-averaged TAMSD as (25) shows. However, the TAMSD is usually a random variable for anomalous diffusion processes.…”

Section: Fixed and Random Initial Velocity Vmentioning

confidence: 94%

“…The most typical model of describing particle's motion is continuous-time random walk (CTRW) [6,21,22,23], which is characterized by waiting time and jump length. By assuming the specific distributions of waiting time and jump length, together with the possible correlation between them, the CTRW can yield many kinds of diffusion processes, which present anomalous diffusion phenomena with different anomalous exponents [24,25,26,27,28]. However, more and more new classes of diffusive dynamics have been observed, especially in the field of soft matter, biological, and other complex systems.…”

Section: Introductionmentioning

confidence: 99%

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Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

Chen,

Wang

2021

Preprint

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The diffusion behavior of particles moving in complex heterogeneous environment is a very topical issue. We characterize particle's trajectory via an underdamped Langevin system driven by a Gaussian white noise with a time dependent diffusivity of velocity, together with a random relaxation timescale τ to parameterize the effect of complex medium. We mainly concern how the random parameter τ influences the diffusion behavior and ergodic property of this Langevin system. Besides, the comparison between the fixed and random initial velocity v 0 is conducted to show the effect of different initial ensembles. The heavy-tailed distribution of τ with finite mean is found to suppress the decay rate of the velocity correlation function and promote the diffusion behavior, playing a competition role to the time dependent diffusivity. More interestingly, a random v 0 with a specific distribution depending on random τ also enhances the diffusion. Both the random parameters τ and v 0 influence the dynamics of the Langevin system in an non-obvious way, which cannot be ignored even they has finite moments.

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Section: Fixed and Random Initial Velocity Vmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

Chen,

Wang

2021

Preprint

Self Cite

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“…Were the walk taking place on a static domain, the particle would remain at the same physical position between two consecutive jumps; on a growing or shrinking domain, this is no longer true, since the particle is drifted in physical space because of the displacement of the (expanding/contracting) "volume element" in which it dwells. From the point of view of the walker's motion, this kind of drift can be viewed as arising from a physical force; in fact, the effect of an exponential contraction on the diffusing particle turns out to be equivalent to the action of the harmonic force in the OU process [46].…”

Section: Ctrw Model and Ffpe For Diffusion On A Growing Domainmentioning

confidence: 99%

“…Ref. [46]). As a result of this equivalence, it is clear that the OU process on an exponentially growing domain may give rise to an interesting competition depending on the values chosen for κ/ξ = t r and for H.…”

Section: B Exponential Growthmentioning

confidence: 99%

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Standard and fractional Ornstein-Uhlenbeck process on a growing domain

2019

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We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing/contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive Continuous-Time Random Walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the ageing of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing/contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

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Anomalous Colloidal Motion under Strong Confinement

Abelenda-Núñez

Ortega

Rubio

et al. 2023

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Diffusion of biological macromolecules in the cytoplasm is a paradigm of colloidal diffusion in an environment characterized by a strong restriction of the accessible volume. This makes of the understanding of the physical rules governing colloidal diffusion under conditions mimicking the reduction in accessible volume occurring in the cell cytoplasm, a problem of a paramount importance. This work aims to study how the thermal motion of spherical colloidal beads in the inner cavity of giant unilamellar vesicles (GUVs) is modified by strong confinement conditions, and the viscoelastic character of the medium. Using single particle tracking, it is found that both the confinement and the environmental viscoelasticity lead to the emergence of anomalous motion pathways for colloidal microbeads encapsulated in the aqueous inner cavity of GUVs. This anomalous diffusion is strongly dependent on the ratio between the volume of the colloidal particle and that of the GUV under consideration as well as on the viscosity of the particle's liquid environment. Therefore, the results evidence that the reduction of the free volume accessible to colloidal motion pushes the diffusion far from a standard Brownian pathway as a result of the change in the hydrodynamic boundary conditions driving the particle motion.

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Subdiffusion in an external force field

Cited by 32 publications

References 67 publications

Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

Standard and fractional Ornstein-Uhlenbeck process on a growing domain

Anomalous Colloidal Motion under Strong Confinement

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