Particle Transport in a Confined Ratchet Driven by the Colored Noise

Xu, Yong; Mei, Ruoxing; Li, Yongge; Kurths, Jürgen

doi:10.1007/978-3-030-15096-9_15

Cited by 4 publications

(5 citation statements)

References 37 publications

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“…By solving the given FJ equation (7), one can derive the steady-state probability current J (x, t). As known, in a ratchet potential, the mean velocity can be obtained by J = v L. Thus, we get an explicit expression for D x, y = D 0 , which has proved to be accurate for small external forces in [23]…”

Section: Transport Propertiesmentioning

confidence: 66%

“…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%

“…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].…”

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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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Section: Transport Propertiesmentioning

confidence: 66%

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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“…Noise is ubiquitous in practical systems, and it is believed that noise plays a constructive role in nonlinear dynamical systems [5][6][7][8][9][10][11]. For example, it can change the dynamical behaviors and induce many interesting phenomena, which can hardly happen in deterministic systems, such as coherence [12][13][14] and stochastic resonance [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Coherence-resonance chimeras in coupled HR neurons with alpha-stable Lévy noise

Wang¹,

Li²,

Xu³

et al. 2022

J. Stat. Mech.

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In this paper, we have investigated the collective dynamical behaviors of a network of identical Hindmarsh–Rose neurons that are coupled under small-world schemes upon the addition of α-stable Lévy noise. According to the firing patterns of each neuron, we distinguish the neuronal network into spike state, burst state and spike-burst state coexistence of the neuron with both a spike firing pattern and a burst firing pattern. Moreover, the strength of the burst is proposed to identify the firing states of the system. Furthermore, an interesting phenomenon is observed that the system presents coherence resonance in time and chimera states in space, namely coherence-resonance chimeras (CRC). In addition, we show the influences of α-stable Lévy noise (noise intensity and stable parameter) and the small-world network (the rewiring probability) on the spike-burst state and CRC. We find that the stable parameter and noise intensity of the α-stable noise play a crucial role in determining the CRC and spike-burst state of the system.

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“…In soft condensed matter and biological systems, there exist confinements which limit the available space of a system and further influence the transport of particles inside the system [28–30]. Usually, these confinements can be modelled by channels with one unit, two units, or further periodic units.…”

Section: Introductionmentioning

confidence: 99%

Characterizing stochastic resonance in a triple cavity

Mei

et al. 2021

Phil. Trans. R. Soc. A.

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Many biological systems possess confined structures, which produce novel influences on the dynamics. Here, stochastic resonance (SR) in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically. Meanwhile, SR in the given triple cavity and differences from other structures are explored. First, it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum. Second, compared to a double cavity with similar maximum/minimum widths and distances between two maximum widths as the triple cavity, η in the triple one shows a larger maximum. Next, the conversion of the natural boundary in the pure potential to the reflection boundary in the triple cavity will create the necessity of a vertical force to induce SR and lead to a decrease in the maximum of η . In addition, η monotonically decreases with the increase of the vertical force and frequency of the periodic force, while it presents several trends when increasing the periodic force’s amplitude for different noise intensities. Finally, our studies are extended to the impact of fractional Gaussian noise excitations. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 2)’.

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Particle Transport in a Confined Ratchet Driven by the Colored Noise

Cited by 4 publications

References 37 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

Coherence-resonance chimeras in coupled HR neurons with alpha-stable Lévy noise

Characterizing stochastic resonance in a triple cavity

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