Superdiffusion of a random walk driven by an ergodic Markov process with switching

Fedotov, Sergei; Milstein, Grigori N.; Tretyakov, Michael V.

doi:10.1088/1751-8113/40/22/001

Cited by 8 publications

(9 citation statements)

References 31 publications

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“…Finally, simulated densities of uni-directional flight lengths from this model show excellent agreement with truncated power-law distributions observed in experiments [10]. It is worth noting that there are a few examples where the power-law assumption has not been used as a starting point: superdiffusion of ultracold atoms [31] and a random walk driven by an ergodic Markov process with switching [32].…”

Section: Introductionsupporting

confidence: 66%

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

et al. 2021

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We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated Lévy walks observed in active intracellular transport by Chen et. al. [Nat. mat., 2015]. We derive the nonhomogeneous in space and time, hyperbolic PDE for the probability density function (PDF) of particle position. This PDF exhibits a bimodal density (aggregation phenomena) in the superdiffusive regime, which is not observed in classical linear hyperbolic and Lévy walk models. We find the exact solutions for the first and second moments and criteria for the transition to superdiffusion.

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Section: Introductionsupporting

confidence: 66%

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

et al. 2021

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“…Note that stochastic two-state models with nonexponential waiting time distributions occur in many areas of natural sciences. We mention the stochastic resonance theory [24], two-state model for anomalous diffusion [25], two-state gating process for ion channels [26], propagation of tumor cells [27], superdiffusion theory and random walk with memory [28].…”

Section: Two-state Reaction-transport Modelmentioning

confidence: 99%

Anomalous transport and nonlinear reactions in spiny dendrites

Fedotov

Al-Shamsi²,

Иванов³

et al. 2010

Phys. Rev. E

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We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov [Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle's position increases as t(μ) with μ<1 (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.

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“…To face these phenomena, which exhibit an anomalous diffusion, several approaches have been used. For instance, Langevin equations, [13][14][15][16] random walks, 17 Fokker-Planck equations, 18 and extensions by considering nonlinear terms 19 or fractional derivatives. [20][21][22][23] The formal aspects of these formalism has also been analyzed by considering several situations, such as presence of external forces, 24,25 reaction terms, [26][27][28] and variable boundary conditions, 29 in order to comprehend the formalisms and their potential applications.…”

Section: Introductionmentioning

confidence: 99%

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

Silva

Lenzi

Evangelista

et al. 2011

Journal of Mathematical Physics

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Response to "Comment on 'Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation' " [Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker-Planck equation We obtain an exact form for the propagator of the Fokker-Planck equationUsing the results found here, we also investigate the mean square displacement, survival probability, and first passage time distribution. In addition, we discuss the connection of these results with anomalous diffusion phenomena. C

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Superdiffusion of a random walk driven by an ergodic Markov process with switching

Cited by 8 publications

References 31 publications

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

Self-reinforcing directionality generates truncated Lévy walks without the power-law assumption

Anomalous transport and nonlinear reactions in spiny dendrites

Exact propagator for a Fokker-Planck equation, first passage time distribution, and anomalous diffusion

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