Transient subdiffusion from an Ising environment

Muñoz-Gil, Gorka; Charalambous, Christos; García-March, Miguel Ángel; García‐Parajó, María F.; Manzo, Carlo; Lewenstein, Maciej; Celi, Alessio

doi:10.1103/physreve.96.052140

Cited by 7 publications

(7 citation statements)

References 40 publications

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“…where g(s) is defined in (44). Note that the expression ( 52) is the Laplace transform of the survival probability (28) and consistently matches with expression (65) found in [48] with θ = π.…”

Section: J Stat Mech (2022) 113205supporting

confidence: 78%

“…Interestingly, the presence of a trapping environment sometimes yields to a regime of anomalous diffusion where the mean-square displacement of a diffusive particle is no longer proportional to time. The anomalous diffusion can either be an asymptotic property of the system or a transient non-equilibrium state with a finite lifetime, in which case it is usually referred to as transient anomalous diffusion [44,45]. In the latter case, there exists a characteristic time at which the system switches over into a long term permanent dynamics.…”

Section: Introduction 1presentation Of the Problemmentioning

confidence: 99%

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Transport properties of diffusive particles conditioned to survive in trapping environments

Pozzoli¹,

Bruyne²

2022

J. Stat. Mech.

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We consider a one-dimensional Brownian motion with diffusion coefficient D in the presence of n partially absorbing traps with intensity β, separated by a distance L and evenly spaced around the initial position of the particle. We study the transport properties of the process conditioned to survive up to time t. We find that the surviving particle first diffuses normally, before it encounters the traps, then undergoes a period of transient anomalous diffusion, after which it reaches a final diffusive regime. The asymptotic regime is governed by an effective diffusion coefficient D eff, which is induced by the trapping environment and is typically different from the original one. We show that when the number of traps is finite, the environment enhances diffusion and induces an effective diffusion coefficient that is systematically equal to D eff = 2D, independently of the number of the traps, the trapping intensity β and the distance L. On the contrary, when the number of traps is infinite, we find that the environment inhibits diffusion with an effective diffusion coefficient that depends on the traps intensity β and the distance L through a non-trivial scaling function D eff = D F ( β L / D ) , for which we obtain a closed-form. Moreover, we provide a rejection-free algorithm to generate surviving trajectories by deriving an effective Langevin equation with an effective repulsive potential induced by the traps. Finally, we extend our results to other trapping environments.

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Section: J Stat Mech (2022) 113205supporting

confidence: 78%

Section: Introduction 1presentation Of the Problemmentioning

confidence: 99%

Transport properties of diffusive particles conditioned to survive in trapping environments

Pozzoli¹,

Bruyne²

2022

J. Stat. Mech.

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“…Recently, a number of diffusion models of continuous-time random walk type [62][63][64][65][66][67][68][69][70][71][72][73], viscoelastic diffusion [10,[74][75][76], fractional BM [5,[77][78][79][80], some combinations of continuoustime random walk and fractional BM [81][82][83], diffusion based on the fractional Langevin equation [10,84], heterogeneous diffusion processes with the space-dependent diffusivity [85][86][87][88][89][90][91][92][93][94]…”

Section: Anomalous Diffusion and Its Modelsmentioning

confidence: 99%

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

Cherstvy¹,

Safdari²,

Metzler³

2021

J. Phys. D: Appl. Phys.

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We investigate a diffusion process with a time-dependent diffusion coefficient, both exponentially increasing and decreasing in time, D ( t ) = D 0 e ± 2 α t . For this (hypothetical) nonstationary diffusion process we compute—both analytically and from extensive stochastic simulations—the behavior of the ensemble- and time-averaged mean-squared displacements (MSDs) of the particles, both in the over- and underdamped limits. Simple asymptotic relations derived for the short- and long-time behaviors are shown to be in excellent agreement with the results of simulations. The diffusive characteristics in the presence of ageing are also considered, with dramatic differences of the over- versus underdamped regime. Our results for D ( t ) = D 0 e ± 2 α t extend and generalize the class of diffusive systems obeying scaled Brownian motion featuring a power-law-like variation of the diffusivity with time, D ( t ) ∼ t α − 1 . We also examine the logarithmically increasing diffusivity, D ( t ) = D 0 log [ t / τ 0 ] , as another fundamental functional dependence (in addition to the power-law and exponential) and as an example of diffusivity slowly varying in time. One of the main conclusions is that the behavior of the massive particles is predominantly ergodic, while weak ergodicity breaking is repeatedly found for the time-dependent diffusion of the massless particles at short times. The latter manifests itself in the nonequivalence of the (both nonaged and aged) MSD and the mean time-averaged MSD. The current findings are potentially applicable to a class of physical systems out of thermal equilibrium where a rapid increase or decrease of the particles’ diffusivity is inherently realized. One biological system potentially featuring all three types of time-dependent diffusion (power-law-like, exponential, and logarithmic) is water diffusion in the brain tissues, as we thoroughly discuss in the end.

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“…A model which results from the motion of a Brownian particle whose diffusion coefficient varies in time is the annealed transient time motion (ATTM) model [5]. Other models are obtaining considering a variety of situations and geometries, like the bouncing of a particle in a set of regions with partially transmitting boundaries of stochastic heights [6], interactions between heterogeneous partners [7], the movement of a particle in an environment with critical behavior [8], etc. Another class of models can be defined from the Langevin equation: the stochastic differential equation governing the movement of a single particle with stochastic noise driving its movement (and modeling an environment interacting with the particle).…”

Section: Introductionmentioning

confidence: 99%

Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories

Garibo‐i‐Orts¹,

Baeza-Bosca²,

García-March³

et al. 2021

J. Phys. A: Math. Theor.

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Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the anomalous exponent associated to a given particle trajectory, thus determining whether the particle subdiffuses, superdiffuses or performs normal diffusion, is of key importance to understand the diffusion process. Also it is often important to trustingly identify the model behind the trajectory, as it this gives a large amount of information on the system dynamics. Both aspects are particularly difficult when the input data are short and noisy trajectories. It is even more difficult if one cannot guarantee that the trajectories output in experiments are homogeneous, hindering the statistical methods based on ensembles of trajectories. We present a data-driven method able to infer the anomalous exponent and to identify the type of anomalous diffusion process behind single, noisy and short trajectories, with good accuracy. This model was used in our participation in the anomalous diffusion (AnDi) challenge. A combination of convolutional and recurrent neural networks was used to achieve state-of-the-art results when compared to methods participating in the AnDi challenge, ranking top 4 in both classification and diffusion exponent regression.

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Transient subdiffusion from an Ising environment

Cited by 7 publications

References 40 publications

Transport properties of diffusive particles conditioned to survive in trapping environments

Transport properties of diffusive particles conditioned to survive in trapping environments

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

Efficient recurrent neural network methods for anomalously diffusing single particle short and noisy trajectories

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