Anomalous diffusion and random search in <i>xyz</i>-comb: exact results

Lenzi, E. K.; Sandev, Trifce; Ribeiro, Haroldo V.; Jovanovski, Petar; Iomin, Alexander; Kocarev, Ljupčo

doi:10.1088/1742-5468/ab7af4

Cited by 10 publications

(10 citation statements)

References 48 publications

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“…(36a) and (36b) is multiplicative, however in Refs. [46,48] the authors verified that the value ε has no influence in the diffusive process, as long as ε and the noise amplitudes β 1 , β 2 , β 3 are of the same order of magnitude. In our simulations, we have set ε = β x = β y = β z = 0.1.…”

Section: Langevin Equation Approach Numerical Simulationsmentioning

confidence: 93%

Stochastic resetting on comblike structures

Domazetoski

Masó-Puigdellosas

Sandev

et al. 2020

Phys. Rev. Research

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We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the corresponding backbone and resetting from secondary fingers to the main fingers. The transient dynamics along the backbone in all three cases is different due to the different resetting mechanisms, finding a wide range of dynamics for the mean squared displacement. For the particular geometry studied herein, we compute the stationary solution and the mean square displacement and find that the global resetting breaks the transport in the three directions. Regarding the resetting to the backbone, the transport is broken in two directions but it is enhanced in the main axis. Finally, the resetting to the fingers enhances the transport in the backbone and the main fingers but reaches a steady value for the mean squared displacement in the secondary fingers.

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Section: Langevin Equation Approach Numerical Simulationsmentioning

confidence: 93%

Stochastic resetting on comblike structures

Domazetoski

Masó-Puigdellosas

Sandev

et al. 2020

Phys. Rev. Research

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“…Then, in the backbone's transport equation, the Lévy-Smirnov distribution P y (y 0 , t) plays a role of a strength of a δ sourcesink term at x = x 0 . This situation differs from both scenarios considered above and has been discussed for anomalous diffusion and random search in two and three dimensional combs [30,31].…”

Section: Appendix a Imaginary Optical Potential Vs Optical Theoremmentioning

confidence: 81%

Quantum dynamics and relaxation in comb turbulent diffusion

Iomin

2020

Preprint

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Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. The interplay between the backbone inhomogeneous advection δ(y)x∂ x along the x axis, which takes place only at the y = 0, and normal diffusion inside fingers ∂ 2 y along the y axis leads to turbulent diffusion. This geometrical constraint of transport coefficients due to comb geometry and properties of a dilatation operator lead to consideration of two possible scenarios of quantum mechanics. These two variants of continuous time quantum walks are described by non-Hermitian operators of the form Ĥ = Â + i B. Operator Â is responsible for the unitary transformation, while operator i B is responsible for quantum/classical relaxation. At the first quantum scenario, the initial wave packet can move against the classical streaming. This quantum swimming upstream is due to the dilatation operator, which is responsible for the quantum (not unitary) dynamics along the backbone, while the classical relaxation takes place in fingers. In the second scenario, the dilatation operator is responsible for the quantum relaxation in the form of an imaginary optical potential, while the quantum unitary dynamics takes place in fingers. Rigorous analytical analysis is performed for both wave and Green's functions.

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“…Over forty years after its inception, anomalous diffusion continues to be a vibrant multidisciplinary scientific field. Examples of recent anomalous-diffusion research include: anomalous diffusion in complex media [54]; anomalous diffusion in the evolution of inhomogeneous systems [55]; anomalous diffusion in random dynamical systems [56]; anomalous diffusion and recurrent neural networks [57]; heterogeneous diffusion processes [58]; anomalous diffusion in heterogeneous binary media [59]; anomalous diffusion and time-dependent diffusivity [60]; anomalous diffusion in the noisy voter model [61,62]; anomalous diffusion under stochastic resetting [63,64]; anomalous diffusion in comb structures [64][65][66][67]; and random diffusivity [26,[68][69][70].…”

Section: Regular and Anomalous Diffusionmentioning

confidence: 99%

Anomalous diffusion: fractional Brownian motion vs fractional Ito motion

Eliazar¹,

Kachman²

2022

J. Phys. A: Math. Theor.

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Generalizing Brownian motion (BM), fractional Brownian motion (FBM) is a paradigmatic selfsimilar model for anomalous diﬀusion. Speciﬁcally, varying its Hurst exponent, FBM spans: sub-diﬀusion, regular diﬀusion, and super-diﬀusion. As BM, also FBM is a symmetric and Gaussian process, with a continuous trajectory, and with a stationary velocity. In contrast to BM, FBM is neither a Markov process nor a martingale, and its velocity is correlated. Based on a recent study of selfsimilar Ito diﬀusions, we explore an alternative selfsimilar model for anomalous diﬀusion: fractional Ito motion (FIM). The FIM model exhibits the same Hurstexponent behavior as FBM, and it is also a symmetric process with a continuous trajectory. In sharp contrast to FBM, we show that FIM: is not a Gaussian process; is a Markov process; is a martingale; and its velocity is not stationary and is not correlated. On the one hand, FBM is hard to simulate, its analytic tractability is limited, and it generates only a Gaussian dissipation pattern. On the other hand, FIM is easy to simulate, it is analytically tractable, and it generates non-Gaussian dissipation patterns. Moreover, we show that FIM has an intimate linkage to diﬀusion in a logarithmic potential. With its compelling properties, FIM oﬀers researchers and practitioners a highly workable analytic model for anomalous diﬀusion.

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Anomalous diffusion and random search in xyz-comb: exact results

Cited by 10 publications

References 48 publications

Stochastic resetting on comblike structures

Stochastic resetting on comblike structures

Quantum dynamics and relaxation in comb turbulent diffusion

Anomalous diffusion: fractional Brownian motion vs fractional Ito motion

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