Research and application of tristable stochastic resonance based on harmonic and pinning potential model

In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

Monte Carlo study of transport in low-dimensional quantum disorder systems at finite temperature

Using the quantum generalized Langevin equation and the path integral Monte Carlo approach, we study the transport dynamics of low-dimensional quantum disorder systems at finite temperature. Motivated by the nature of the classical-to-quantum transformation in fluctuations in the time domain, we extend the treatment to the spatial domain and propose a quantum random-correlated potential, describing specifically quantum disorder. For understanding the Anderson localization from the particle transport perspective, we present an intuitive treatment using a classical analogy in which the particle moves through a flat periodic crystal lattice corrugated by classical or quantum disorder. We emphasize an effective classical disorder potential in studying the quantum effects on the transport dynamics. Compared with the classical case, we find that the quantum escape rate from a disordered metastable potential is larger. Moreover, the diffusion enhancement of a quantum system moving in a weak, biased, periodic disorder potential is more significant compared with the classical case; for an effective rock-ratcheted disorder potential, quantum effects increase the directed current with decreasing temperature. For the classical case, we explore surface diffusion on a two-dimensional biased disorder potential at finite temperature; surprisingly, the optimal angle of the external bias force is found to enhance diffusion in the biased disorder surface. Furthermore, to explain the quantum transport dynamics in a disorder potential, we adopt the barrier-crossing mechanism and the mean first passage time theory to establish the probability distribution function.

Scaling of average receiving time on double-weighted polygon networks

In this paper, we introduce a class of double-weighted polygon networks with two different meanings of weighted factors [Formula: see text] and [Formula: see text], which represent path-difficulty and path-length, respectively, based on actual traffic networks. Picking an arbitrary node from the hub nodes set as the trap node, and the double-weighted polygon networks are divided into [Formula: see text] blocks by combining with the iterative method. According to biased random walks, the calculation expression of average receiving time (ART) of any polygon networks is given by using the intermediate quantity the mean first-passage time (MFPT), which is applicable to any [Formula: see text] ([Formula: see text]) polygon networks. What is more, we display the specific calculation process and results of ART of the double-weighted quadrilateral networks, indicating that ART grows exponentially with respect to the networks order and the exponent is [Formula: see text] which grows with the product of [Formula: see text]. When [Formula: see text] increases, ART increases linearly ([Formula: see text]) or sublinearly ([Formula: see text]) with the size of networks, and the smaller value of [Formula: see text], the higher transportation efficiency.

Research and application of Stochastic Resonance in Quad-stable Potential System

To solve the problem of low weak signal enhancement performance in the quad-stable system, a new Quad-stable potential Stochastic Resonance (QSR) is proposed. Firstly, under the condition of adiabatic approximation theory, the Stationary Probability Distribution (SPD), the Mean First Passage Time (MFPT), the Work (W) and the power Spectrum Amplification Factor (SAF) are derived, and the impacts of system parameters on them are also deeply analyzed. Secondly, numerical simulations are performed to compare QSR with the Classical Tri-stable Stochastic Resonance (CTSR) by using the Genetic Algorithm (GA) and the fourth-order Runge-Kutta algorithm. It shows that the Signal-to-Noise Ratio (SNR) and Mean Signal-to-Noise Increase (MSNRI) of QSR are higher than CTSR, which indicates that QSR has superior noise immunity than CTSR. Finally, the two systems are applied in the detection on real bearing faults. The experimental results show that QSR is superior to CTSR, which provides a better theoretical significance and reference value for practical engineering application.

An encounter-based approach for restricted diffusion with a gradient drift

We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis to derive a spectral decomposition for the full propagator, i.e., the joint probability density function for the particle position and its boundary local time. This is the central quantity that determines various characteristics of diffusion-influenced reactions such as conventional propagators, survival probability, first-passage time distribution, boundary local time distribution, and reaction rate. As an illustration, we investigate the impact of a constant drift onto the boundary local time for restricted diffusion on an interval. More generally, this approach accesses how external forces may influence the statistics of encounters of a diffusing particle with the reactive boundary.

Mapping and characterizing animals’ places of interest in forest environment

Fauna impacts its environment as well as spatial environment influences fauna space use. Forest management implies taking into account pressure from animals in fragile-balanced patches. Our goal is to propose maps that would benefit forest planning by reflecting individual movement and space use depending on the animal species and local spatiotemporal environment. The study case focuses on two species, roe deer and red deer, and on a forested site in the northeast of France. Movements of several individuals were analysed from collected GPS locations. Foraging places likely to correspond to intense research behaviour were computed using the First-Passage Time method. These places were assumed as being of interest and were characterized with landscape features and temporal information. Maps were produced to synthetize information about foraging places by defining adapted symbolizations. Then maps about functional space were proposed based on extrapolation of favourable or avoided areas from the characterized observed foraging places and space use. Landscape patches were mapped according to a gradient of potential interest by animals’ species, in order to highlight needs of specific planning actions in the forestry context. Map displays were driven by forestry end-use and designed so that to be compliant to a numeric geographical portal, giving access to different available on-line layers and computed created ones.

Levy walk dynamics in non-static media

Almost all the media the particles move in are non-static, one of which is the most common expanding or contracting (by a scale factor) non-static medium discussed in this paper. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement caused by the non-static media, sometimes the non-static behaviors of the media can not be ignored. In this paper, we build the model describing L\'evy walks in one-dimension uniformly non-static media, where the physical and comoving coordinates are connected by scale factor. We derive the equation governing the probability density function of the position of the particles in comoving coordinate. Using the Hermite orthogonal polynomial expansions, some statistical properties are obtained, such as mean squared displacements (MSDs) in both coordinates and kurtosis. For some representative non-static media and L\'{e}vy walks, the asymptotic behaviors of MSDs in both coordinates are analyzed in detail. The stationary distributions and mean first passage time for some cases are also discussed through numerical simulations.