Transport and escape in a deformable channel driven by fractional Gaussian noise

Mei, Ruoxing; Xu, Yong; Kurths, Jürgen

doi:10.1103/physreve.100.022114

Cited by 20 publications

(9 citation statements)

References 49 publications

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“…In the calculation, we add an alternative noise-induced term corresponding to the Itô and isothermal integral form respectively. The detailed algorithm applied here reads [15,26]:…”

Section: Model Descriptionmentioning

confidence: 99%

“…In the y direction, due to the confined channel, it can be regarded to be homogenous, which means in the steady state ∂ 2 ∂y 2 P x, y = 0. Based on this assumption, the FJ equation is developed, starting from the FPE, to describe the PDF in confined channels, which under the condition of D x, y = D 0 takes the form [19,20,[23][24][25][26]…”

Section: Steady State Probability Density Function (Pdf)mentioning

confidence: 99%

“…For asymmetric channels, it was found that the shape of the confinement contributes to the moving direction and mean displacement [20,23], which can be applied to fine separation of mixtures and also the design of many devices [24,25]. Time-dependent and deformable boundaries were discussed to explore the activity in living cells [26,27]. In addition, the interaction of hydrodynamics and entropic effect on colloidal diffusion were studied in corrugated channels [28,29].…”

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confidence: 99%

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Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Mei

et al. 2020

New J. Phys.

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This work focuses on the dynamics of particles in a confined geometry with position-dependent diffusivity, where the confinement is modelled by a periodic channel consisting of unit cells connected by narrow passage ways. We consider three functional forms for the diffusivity, corresponding to the scenarios of a constant (D 0 ), as well as a low (D m ) and a high (D d ) mobility diffusion in cell centre of the longitudinally symmetric cells. Due to the interaction among the diffusivity, channel shape and external force, the system exhibits complex and interesting phenomena. By calculating the probability density function, mean velocity and mean first exit time with the Itô calculus form, we find that in the absence of external forces the diffusivity D d will redistribute particles near the channel wall, while the diffusivity D m will trap them near the cell centre. The superposition of external forces will break their static distributions. Besides, our results demonstrate that for the diffusivity D d , a high dependence on the x coordinate (parallel with the central channel line) will improve the mean velocity of the particles. In contrast, for the diffusivity D m , a weak dependence on the x coordinate will dramatically accelerate the moving speed. In addition, it shows that a large external force can weaken the influences of different diffusivities; inversely, for a small external force, the types of diffusivity affect significantly the particle dynamics. In practice, one can apply these results to achieve a prominent enhancement of the particle transport in two-or three-dimensional channels by modulating the local tracer diffusivity via an engineered gel of varying porosity or by adding a cold tube to cool down the diffusivity along the central line, which may be a relevant effect in engineering applications. Effects of different stochastic calculi in the evaluation of the underlying multiplicative stochastic equation for different physical scenarios are discussed.New J. Phys. 22 (2020) 053016 Y Li et al confined spaces, transport of particles in nanopores, zeolites and gel networks [8-10], or protein diffusion in the mammalian cell cytoplasm [11]. In many cases, such structured environments can be viewed as confined channels with different boundaries and properties [12][13][14]. The behaviours of systems in these confined channels have been studied by virtue of the analytical Fick-Jacobs (FJ) equation and numerical simulations of the dynamic equations [15][16][17][18][19][20]. Results for symmetric periodic channels indicate that the mean transport velocity may be proportional to large external forces in the confined environment [19][20][21][22]. For asymmetric channels, it was found that the shape of the confinement contributes to the moving direction and mean displacement [20,23], which can be applied to fine separation of mixtures and also the design of many devices [24,25]. Time-dependent and deformable boundaries were discussed to explore the activity in living cells [26,27]. In addition, the interaction...

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“…In the calculation, we add an alternative noise-induced term corresponding to the Itô and isothermal integral form respectively. The detailed algorithm applied here reads [15,26]:…”

Section: Model Descriptionmentioning

confidence: 99%

Section: Steady State Probability Density Function (Pdf)mentioning

confidence: 99%

mentioning

confidence: 99%

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Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Mei

et al. 2020

New J. Phys.

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“…On the other hand, stochastic differential equations (SDEs) are considered an effective tool in the description of many processes and systems in different fields. Several authors [5][6][7][8] have dealt with different research interests for classical SDEs. Then, they extended their studies to the fractional case (FSDEs with constant order α) and investigated many results like existence, uniqueness, and stability for various classes of FSDEs (see [9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

Moualkia

2021

Mathematics

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Fractional stochastic differential equations are still in their infancy. Based on some existing results, the main difficulties here are how to deal with those equations if the fractional order is varying with time and how to confirm the existence of their solutions in this case. This paper is about the existence and uniqueness of solutions to the fractional stochastic differential equations with variable order. We prove the existence by using the Picard iterations and propose new sufficient conditions for the uniqueness.

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“…Random disturbances are ubiquitous and play an important role in the evolution of dynamical systems in the macro world. Throughout the various strands of research, the influences of random disturbances on dynamical systems have become a frontier topic and developed a wide-ranging corpus of results [19,20,21,22]. Any systems are inevitably disturbed by uncertainties, and thermoacoustic systems are no exception.…”

Section: Introductionmentioning

confidence: 99%

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

Zhang,

Xu,

Liu

et al. 2020

Preprint

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Tipping is a phenomenon in multistable systems where small changes in inputs cause huge changes in outputs. When the parameter varies within a certain time scale, the rate will affect the tipping behaviors. These behaviors are undesirable in thermoacoustic systems, which are widely used in aviation, power generation and other industries. Thus, this paper aims at considering the tipping behaviors of the thermoacoustic system with the time-varying parameters and the combined excitations of additive and multiplicative colored noises. Transient dynamical behaviors for the proposed thermoacoustic model are implemented through the reduced Fokker-Planck-Kolmogorov equation derived by a standard stochastic averaging method. Then, the tipping problems of the rate-dependent thermoacoustic systems with random fluctuations are studied by virtue of the obtained probability density functions. Our results show that the rate delays the value of the tipping parameter compared to the one with the quasi-steady assumption, which is called as a rate-dependent tipping-delay phenomenon.Besides, the influences of the initial values, the rate, the changing time of the parameters, and the correlation time of the noises on the rate-dependent tipping-delay phenomenon are analyzed in detail. These results are of great significance for research in related fields such as aviation and land gas turbines.

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Transport and escape in a deformable channel driven by fractional Gaussian noise

Cited by 20 publications

References 49 publications

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

Particle dynamics and transport enhancement in a confined channel with position-dependent diffusivity

On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order

Rate-dependent tipping-delay phenomenon in a thermoacoustic system with colored noise

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