Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter （including p, q, r, λ, τ） on the mean first-passage time （MFPT） is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that （1） the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, （2） suppression appears on the curve of the MFPT with small λ （e.g. λ 〈 0.5） but there is a peak on the curve of the MFPT when λ is big （e.g. λ 〉 0.5）, and （3） with different values of r （e.g. r = 0.1, 0.5, 1.5）, the effort of τ on the MFPT is diverse.

Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

FIRST-PASSAGE TIME OF QUASI-NON-INTEGRABLE-HAMILTONIAN SYSTEM

Studies on first-passage failure are extended to the multi-degree-of-freedom quasi-non-integrable-Hamiltonian systems under parametric excitations of Gaussian white noises in this paper. By the stochastic averaging method of energy envelope, the system's energy can be modeled as a one-dimensional approximate diffusion process by which the classical Pontryagin equation with suitable boundary conditions is applicable to analyzing the statistical moments of the first-passage time of an arbitrary order. An example is studied in detail and some numerical results are given to illustrate the above procedure.

MOMENTS OF PASSAGE TIMES AND ASYMPTOTIC BEHAVIOR OF INCREASING SELF-SIMILAR MARKOV PROCESSES

By using Lamperti＇s bijection between self-similar Markov processes and L@vy processes~ we prove finiteness of moments and asymptotic behavior of passage times for increasing self-similar Markov processes valued in （0, ~）. We Mso investigate the behavior of the process when it crosses a level. A limit theorem concerning the distribution of the process immediately before it crosses some level is proved. Some useful examples are given.

The mean first passage time of a three-level atomic optical bistable system subjected to noise

The transient properties of a three-level atomic optical bistable system in the presence of multiplicative and additive noises are investigated. The explicit expressions of the mean first-passage time （MFPT） of the transition from the high intracavity intensity state to the low one are obtained by numerical computations. The impacts of the intensities of the multiplicative noise DM and the additive noise DA, the intensity of correlation between two noises λ, and the intensity of the incident light y on the MFPT are discussed, respectively. Our results show： （i） for the case of no correlation between two noises （2, = 0.0）, the increase in DM and DA can lead to an increase in the probability of the transition to the low intracavity intensity state, while the increase in y can lead to a retardation of the transition; and （ii） for the case of correlation between two noises （λ≠ 0.0）, the increase in λ can cause an increase in the probability of the transition, and the increase in DA can cause a retardation of the transition firstly and then an increase in the probability of the transition, i.e., the noise-enhanced stability is observed for the case of correlation between two noises.

Mean First Passage Time for System with Fluctuating Potential Barrier and Coupled Noise

In this paper we study the mean first passage time （MFPT） over a fluctuation potential barrier driven by a coupled noise. It is shown that the MFPT over the fluctuation potential barrier displays resonant activations as the function of the flipping rate of the fluctuation potential barrier, and as the function of the dichotomous noise transition rate.

Exit Probability and First Passage Time of a Lazy Pearson Walker: Scaling Behaviour

The motion of a lazy Pearson walker is studied with different probability (p) of jump in two and three dimensions. The probability of exit ( ) from a zone of radius is studied as a function of with different values of jump probability p. The exit probability is found to scale as , which is obtained by method of data collapse. The first passage time ( ) i.e., the time required for first exit from a zone is studied. The probability distribution of first passage time was studied for different values of jump probability (p). The probability distribution of first passage time was found to scale as . Where, F and G are two scaling functions and a, b, g and d are some exponents. In both the dimensions, it is found that, , , and .

Distribution of First Passage Times for Lumped States in Markov Chains

First passage time in Markov chains is defined as the first time that a chain passes a specified state or lumped states. This state or lumped states may indicate first passage time of an interesting, rare and amazing event. In this study, obtaining distribution of the first passage time relating to lumped states which are constructed by gathering the states through lumping method for a irreducible Markov chain whose state space is finite was deliberated. Thanks to lumping method the chain＇s Markov property has been preserved. Another benefit of lumping method in the way of practice is reduction of the state space thanks to gathering states together. As the obtained first passage distributions are continuous, it may be used in many fields such as reliability and risk analysis

Functional Neuroanatomy of Time-To-Passage Perception

The time until an approaching object passes the observer is referred to as time-to-passage (TTP). Accurate judgment of TTP is critical for visually guided navigation, such as when walking, riding a bicycle, or driving a car. Previous research has shown that observers are able to make TTP judgments in the absence of information about local retinal object expansion. In this paper we combine psychophysics and functional MRI (fMRI) to investigate the neural substrate of TTP processing. In a previous psychophysical study, we demonstrated that when local retinal expansion cues are not available, observers take advantage of multiple sources of information to judge TTP, such as optic flow and object retinal velocities, and integrate these cues through a flexible and economic strategy. To induce strategy changes, we introduced trials with motion but without coherent optic flow (0% coherence of the background), and trials with coherent, but noisy, optic flow (75% coherence of the background). In a functional magnetic resonance imaging (fMRI) study we found that coherent optic flow cues resulted in better behavioral performance as well as higher and broader cortical activations across the visual motion processing pathway. Blood oxygen-level-dependent (BOLD) signal changes showed significant involvement of optic flow processing in the precentral sulcus (PreCS), postcentral sulcus (PostCS) and middle temporal gyrus (MTG) across all conditions. Not only highly activated during motion processing, bilateral hMT areas also showed a complex pattern in TTP judgment processing, which reflected a flexible TTP response strategy.

Feedback minimization of first-passage failure of quasi integrable Hamiltonian systems

Abstract A nonlinear stochastic optimal control strategy for minimizing the first-passage failure of quasi integrable Hamiltonian systems （multi-degree-of-freedom integrable Hamiltonian systems subject to light dampings and weakly random excitations） is proposed. The equations of motion for a controlled quasi integrable Hamiltonian system are reduced to a set of averaged It6 stochastic differential equations by using the stochastic averaging method. Then, the dynamical programming equations and their associated boundary and final time conditions for the control problems of maximization of reliability and mean first-passage time are formulated. The optimal control law is derived from the dynamical programming equations and the control constraints. The final dynamical programming equations for these control problems are determined and their relationships to the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the mean first-passage time are separately established. The conditional reliability function and the mean first-passage time of the controlled system are obtained by solving the final dynamical programming equations or their equivalent Kolmogorov and Pontryagin equations. An example is presented to illustrate the application and effectiveness of the proposed control strategy.

Development potential of the Northeast Passage based on a multinomial-logit-based stochastic user equilibrium model

We developed a multinomial-logit-based stochastic user equilibrium(MNL SUE)model incorporating time value of cargo to investigate future proportions of cargo flow through the Northeast Passage(NEP)and the Suez Canal Route between representative ports.We studied navigation during the ice-free and ice-covered seasons using sea ice projections for 2070 based on 1991–2021 NEP ice data.Sailing distance and time between selected ports are lower via the NEP than the Suez Canal Route.Under the scenario of year-round operation of the NEP,the proportion of cargo flow through the NEP is estimated to be 68.5%,which represents considerable commercial potential.Proportions are higher for the ice-free season and for ports at high latitudes.We also assessed flow under different scenarios.Under the scenario of fuel price increase,proportion of flow through the NEP in the ice-covered season is expected to increase.If time value is ignored,flow through the NEP is expected to increase all year round.If shippers become more cost-conscious,flow through the NEP is also expected to increase.

Seize the Day:Awareness of Time in You,Andrew Marvell

Based on the alternation of scenes,awareness of time is analyzed from three perspectives.The common one is to be aware of time flow in the change of scenes.The outstanding ones include the psychological and philosophical perception of time.Being aware of the temporality of life,the individual need to take an open and unforced attitude toward death -"carpe diem!".

Could one single dichotomous noise cause resonant activation for exit time over potential barrier?

This paper studies the mean first passage time （or exit time, or escape time） over the non-fluctuating potential harrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential harrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.

Analysis of Residence Time in the Measurement of Radon Activity by Passive Diffusion in an Open Volume: A Micro-Statistical Approach

Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion in an open volume (i.e. no flow cell or control volume), the concept of residence time was generalized to apply to measurement conditions with random, rather than directed, flow. The generalization, leading to a quantity Δtr, involved use of a) a phenomenological alpha-particle range function to calculate the effective detection volume, and b) a phenomenological description of diffusion by Fick’s law to determine the effective flow velocity. This paper examines the residence time in passive diffusion from the micro-statistical perspective of single-particle continuous Brownian motion. The statistical quantity “mean residence time” Tr is derived from the Green’s function for unbiased single-particle diffusion and is shown to be consistent with Δtr. The finite statistical lifetime of the randomly moving radioactive atom plays an essential part. For stable particles, Tr is of infinite duration, whereas for an unstable particle (such as 222Rn), with diffusivity D and decay rate λ, Tr is approximately the effective size of the detection region divided by the characteristic diffusion velocity . Comparison of the mean residence time with the time of first passage (or exit time) in the theory of stochastic processes shows the conditions under which the two measures of time are equivalent and helps elucidate the connection between the phenomenological and statistical descriptions of radon diffusion.

基于OpenFOAM地铁隧道防火门的活塞风作用时变特性研究

为了研究地铁隧道联络通道防火门表面的活塞风压特征,基于OpenFOAM开源软件,建立了地铁隧道三维非稳态流动模拟模型,并使用动网格方法模拟了地铁列车在隧道内的实时运动。通过与既有试验数据的对比,发现该方法能够准确地模拟地铁隧道内的风环境。在此基础上,建立了完整的足尺地铁隧道-联络通道复合模型,分析了不同行车速度、不同联络通道设计和不同测点距离下防火门的表面风压及其周边的流动特征。计算结果表明,联络通道防火门的表面压力对行车速度最为敏感,对联络通道的几何形态不敏感,隧道-列车间的剪切流动对联络通道内部的流动特征影响较小。

基于改进多稳态系统随机共振的轴承微弱故障诊断

针对传统随机共振方法在强噪声背景下对轴承微弱故障诊断中存在严重的边频干扰问题,提出了一种应用改进多稳态随机共振模型进行轴承微弱故障诊断的方法.在高斯白噪声和周期性激励作用下,推导得到了改进多稳态系统的平均首次穿越时间和功率谱放大因子的解析表达式.研究发现,存在一组最优的参数使得改进多稳态系统的随机共振效应最大化.将改进的多稳态随机共振模型应用于轴承内外圈的微弱故障诊断,并利用量子粒子群优化算法对系统参数和阻尼系数进行优化.研究结果表明,所提方法能够在强噪声背景下有效识别出微弱故障特征频率,且与传统多稳态随机共振方法相比,该方法解决了严重的边频干扰问题,输出信号特征频率处的频谱峰值更高,大大提高了轴承微弱故障诊断的性能.

First passage times for multidimensional denumerable state Markov processes

For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective arguments.Some numerical results are presented.

Mean and variance of first passage time of non-homogeneous random walk

The prime concern of this paper is the first passage time of a nonhomogeneous random walk, which is nearest neighbor but able to stay at its position. It is revealed that the branching structure of the walk corresponds to a 2-type non-homogeneous branching process and the first passage time of the walk can be expressed by that branching process. Therefore, one can calculate the mean and variance of the first passage time, though its exact distribution is unknown.

Logical stochastic resonance in a cross-bifurcation non-smooth system

This paper investigates logical stochastic resonance(LSR)in a cross-bifurcation non-smooth system driven by Gaussian colored noise.In this system,a bifurcation parameter triggers a transition between monostability,bistability and tristability.By using Novikov's theorem and the unified colored noise approximation method,the approximate Fokker-Planck equation is obtained.Then we derive the generalized potential function and the transition rates to analyze the LSR phenomenon using numerical simulations.We simulate the logic operation of the system in the bistable and tristable regions respectively.We assess the impact of Gaussian colored noise on the LSR and discover that the reliability of the logic response depends on the noise strength and the bifurcation parameter.Furthermore,it is found that the bistable region has a more extensive parameter range to produce reliable logic operation compared with the tristable region,since the tristable region is more sensitive to noise than the bistable one.

First passage times: Busy periods and waiting times

General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.