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

Directed transport of particles in coupled fractional-order systems excited by Lévy noise

This paper investigates the directed transport of particles in a coupled fractional-order system excited by Lévy noise. Numerical simulations reveal the effects of fractional order, Lévy noise and coupling coefficients on the directed transport. It is found that there exists an optimal fractional order, which maximizes the directed transport of particles. The optimal fractional order for the directed transport shifts to the left or right with different noise parameters, which means that the appropriate fractional order and noise parameters should be taken into account to maximize the directed transport. Meanwhile, the increase of the scale and symmetry parameters intensifies the directed transport of the particles, while the increase of the stability index suppresses the directed transport, so appropriate Lévy noise parameters will effectively amplify the directed transport. In addition, strong coupling can also effectively promote the directed transport of particles. These studies may provide a theoretical basis for the design of nanomachines, improving drug delivery across cell membranes and treating diseases of the nervous system.

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

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.

Characterizing stochastic resonance in a triple cavity

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)'.

Transport of coupled particles in rough ratchet driven by Lévy noise

This paper studies the transport of coupled particles in a tilted rough ratchet potential. The relationship between particles transport and roughness, noise intensity, external force, coupling strength, and free length is explored numerically by calculating the average velocity of coupled particles. Related investigations have found that rough potential can accelerate the process of crossing the barrier by increasing the particles velocity compared with smooth potential. It is based on the fact that the roughness on the potential surface is like a "ladder," which helps particles climb up and blocks them from sliding down. Moreover, superimposing an appropriate external force on the coupled particles or strengthening the Lévy noise leads to the particles velocity to increase. It is worth emphasizing that when the external force is selected properly, an optimal roughness can be found to maximize the particles velocity. For a given roughness, an optimal coupling coefficient is discovered to match the maximum velocity. And once the coupling coefficient is greater than the optimal value, the particles velocity drops sharply to zero. Furthermore, our results also indicate that choosing an appropriate free length between particles can also speed up transport.

Capturing multifractality of pressure fluctuations in thermoacoustic systems using fractional-order derivatives

The stable operation of a turbulent combustor is not completely silent; instead, there is a background of small amplitude aperiodic acoustic fluctuations known as combustion noise. Pressure fluctuations during this state of combustion noise are multifractal due to the presence of multiple temporal scales that contribute to its dynamics. However, existing models are unable to capture the multifractality in the pressure fluctuations. We conjecture an underlying fractional dynamics for the thermoacoustic system and obtain a fractional-order model for pressure fluctuations. The data from this model has remarkable visual similarity to the experimental data and also has a wide multifractal spectrum during the state of combustion noise. Quantitative similarity with the experimental data in terms of the Hurst exponent and the multifractal spectrum is observed during the state of combustion noise. This model is also able to produce pressure fluctuations that are qualitatively similar to the experimental data acquired during intermittency and thermoacoustic instability. Furthermore, we argue that the fractional dynamics vanish as we approach the state of thermoacoustic instability.

Heterogeneous diffusion processes and nonergodicity with Gaussian colored noise in layered diffusivity landscapes

Heterogeneous diffusion processes (HDPs) with space-dependent diffusion coefficients D(x) are found in a number of real-world systems, such as for diffusion of macromolecules or submicron tracers in biological cells. Here, we examine HDPs in quenched-disorder systems with Gaussian colored noise (GCN) characterized by a diffusion coefficient with a power-law dependence on the particle position and with a spatially random scaling exponent. Typically, D(x) is considered to be centerd at the origin and the entire x axis is characterized by a single scaling exponent α. In this work we consider a spatially random scenario: in periodic intervals ("layers") in space D(x) is centerd to the midpoint of each interval. In each interval the scaling exponent α is randomly chosen from a Gaussian distribution. The effects of the variation of the scaling exponents, the periodicity of the domains ("layer thickness") of the diffusion coefficient in this stratified system, and the correlation time of the GCN are analyzed numerically in detail. We discuss the regimes of superdiffusion, subdiffusion, and normal diffusion realisable in this system. We observe and quantify the domains where nonergodic and non-Gaussian behaviors emerge in this system. Our results provide new insights into the understanding of weak ergodicity breaking for HDPs driven by colored noise, with potential applications in quenched layered systems, typical model systems for diffusion in biological cells and tissues, as well as for diffusion in geophysical systems.