The mechanochemical stochastic processes of molecular motors

In this article, we develop a rigorous mathematical foundation of microscopic motors. The main characteristic is the combination of Brownian and Poisson noises.     

Effecfs of Cross-Correlation Between Real Noise in Transient Process of Single-Mode and Imaginary Parts of Colored Pump Laser

A two-dimensional single-mode laser model with cross-correlation between the real and imaginary parts of the colored quadric pump noise is investigated. A novel laser amplitude Langevin equation is obtained, in which the cross-correlation λp between the real and imaginary parts of the pump noise appears. The mean, variance, and skewness of first-passage-time are calculated. It is shown that the mean, variance, and skewness of first-passage-time are strongly affected by λp.     

The crossover from classical to quantum regime in the problem of the decay of the metastable state

The probability of the decay of the metastable state has been found as a function of viscosity and temperature. At low temperatures, a classical overbarrier transition changes to the quantum tunneling. At low viscosity in classical and transitive semiquantum region of temperatures a depopulation of the distribution function is significant. The distribution function is shown to satisfy the integral kinetic equation, the kernel of which equals the transition probability. The probability of transitions, induced by the red noise, with the frequency comparable to the transition frequency, is found.     

The quantum stochastic equation is unitarily equivalent to a symmetric boundary value problem for the Schrödinger equation

We prove that the solution of the Hudson-Parthasarathy quantum stochastic differential equation in the Fock space coincides with the solution of a symmetric boundary value problem for the Schrödinger equation in the interaction representation generated by the energy operator of the environment. The boundary conditions describe the jumps in the phase and the amplitude of the Fourier transforms of the Fock vector components as any of its arguments changes the sign. The corresponding Markov evolution equation (the Lindblad equation or the “master equation”) is derived from the boundary value problem for the Schrödinger equation.     

中国北方古建油饰彩画中绿色颜料的光谱分析

古建油饰彩画中颜料成分的分析鉴定是古建维修、保护的重要基础工作。文章利用X射线荧光分析、X射线衍射分析、扫描电镜-能谱分析技术,首次系统地分析检测了来自北京、山西、甘肃等中国北方地区的27个古建油饰彩画中的绿色颜料。结果表明,其中15个样品使用了巴黎绿这种含铜、砷的人工合成颜料,其余样品未检测出矿物颜料,显色成分应为人工合成的有机物。在所有分析样品中未检测到古代常用的绿色颜料石绿和氯铜矿的存在。该研究工作开辟了光谱分析技术应用于古建油饰彩画颜料鉴定的新领域,为该类文物分析鉴定、修复材料的选择提供了科学数据。     

Stochastic Fractional Anderson Models with Fractional Noises

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.     

雾玻璃上的彩色环

向一个冷玻璃上哈气,在玻璃表面会形成水雾.透过起雾的玻璃去观察白光光源,会看到有多层彩色环(内层蓝色,外层红色),并且在中央会出现白色亮斑.利用散射光干涉的模型解释了彩色圆环的成因.     

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 D M and the additive noise D A , 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 (λ = 0.0), the increase in D M and D A 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 D A 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.     

The protection zone for biological population in random environment

A biomathematical model is described by stochastic differential equations with Markovian switching. The long‐time dynamical properties are studied both theoretically and numerically. Results show that both the persistence and extinction have close relationship with environmental noises (white and color noises). These results are of important biological significance for biological conservation. Copyright © 2012 John Wiley & Sons, Ltd.