Various Extensions of Original Born-Kramers-Slater Model for Reactions Kinetics Based on Brownian Motion and Fokker-Plank Equation Including 1D, 2D, 3D, and Multi-dimensional Approaches

Different extensions, such as Transition State theory of Eyring-Polanyi-Evans model of the original Born-Kramers-Slater Model for the Velocity of Chemical Reactions are discussed based on Smoluchowski and Fokker-Plank equations with various properties of Brownian motion and including 1-, 2-, 3-, and multi- dimensional models with applications in Neuroscience.

Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

外噪声下相变模型福克-普朗克方程的含时精确解

采用微分方程的李群方法 ,研究了外噪声影响下的非平衡相变模型对应的Fokker Planck(FP)方程 ,得出了含时间概率密度P(x ,t)的严格表达式 ;讨论了最可几值x随时间的变化 .在时间t→∞时 ,由严格解给出了概率密度的定态解Pst(x) ,并讨论了此时的最可几值x与确定性描述的区别 .

基于AR模型的载频测量

从现代谱估计出发,利用Yule_Walker方程构造信号的AR模型,从中提取信号的调制载波频率信息。信号的功率谱表示了信号能量的分布。用谱估计法估计出载波频率后,依据频谱对所测频率进行修正,可有效提高载波频率的测量精度。

湍流粒子的速度及其F-P方程的定态解

建立了湍流粒子的速度，并由此得到相应的Fokker－Planck方程（FPE），得到了其定态解．讨论了各方向上的方差．

外噪声下马尔萨斯系统随时间的演化

采用微分方程的李群方法 ,研究了外噪声影响下的马尔萨斯系统对应的福克—普朗克方程 ,得出了含时间概率密度P(x ,t)的严格表达式 ;讨论了最可几值x随时间的变化。

外噪声下二级相变模型Stratonovich—F—P方程的含时精确解

本文采用微分方程的李群方法,求解了外噪声影响下的非平衡二级相变模型对应的F—P方程,得出含时概率密度P（x.t）的严格表达式,讨论了最概然值x随时间的变化。在时间t→∞时,给出概率的定态解Pst(x)以及此时的最概然值;得出了它与确定性描述的差别。

Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises

The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system.

双噪声系统的定态几率密度

对于双噪声源的随机郎之万方程,在噪声均为OU噪声的情况下,从三维的FPE出发,利用类WKB方法,详细分析了双噪声源在其噪声强度均很小时对非平衡相变行为的影响,得到了定态几率密度的表达式。并从数值上分析了单模染料激光模型中的自发辐射噪声与泵浦噪声对非平衡相变的影响。

A Closed-Form Formulation for the Build-Up Factor and Absorbed Energy for Photons and Electrons in the Compton Energy Range in Cartesian Geometry

In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two di- mensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTSN method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTSN nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature.

Statistical Transform of Signal Field with ASE Noise through a Fiber Amplifier

While the signal field + ASE noise pass through a span of transmission fiber, a dispersion compensation grating and a fiber amplifier(with the generation of ASE noise), the nonlinear Fokker-Plank equations, describing the probability transforms of the field, are established and solved. Based on these statistical theories, the probability distributions of the signal + ASE noise field through 50km NZDSF, a dispersion compensation grating and a fiber amplifier link, are obtained. The dispersion and nonlinear effects in transmission fiber induce frequency offsets in the probability distribution of field and they cannot be dissipated by dispersion compensation. The generation of ASE noise in the amplifier will accelerate this frequency offset.

Molecular Chaperone-Dependent Polymer Translocation through Nanopores: The Effects of Chaperone Concentration and Chaperone-Polymer Interaction

The polymer translocation through a nanopore from a donor space(or named cis side) to a receiver space(trans side) in the chaperone-induced crowded environment has attracted increasing attention in recent years due to its significance in biological systems and technological applications. In this work, we mainly focus on the effects of chaperone concentration and chaperone-polymer interaction on the polymer translocation. By assuming the polymer translocation to be a quasi-equilibrium process, the free energy F of the polymer can be estimated by Rosenbluth-Rosenbluth method and then the translocation time τ can be calculated by Fokker-Plank equation based on the obtained free energy landscape. Our calculation results show that the translocation time can be controlled by independently tuning the chaperone concentration and chaperone-polymer interaction at the cis side or the trans side. There exists a critical chaperone-polymer attraction ε~*=-0.2 at which the volume exclusion and interaction effects of the chaperone can balance each other. Additionally, we also find that at large chaperone-polymer attraction, the translocation time is mainly governed by the diffusion coefficient of the polymer.

Approximation of the Mean Escape Time for a Tilted Periodic Potential

We present a formula approximating the mean escape time(MST)of a particle from a tilted multi-periodic potential well.The potential function consists of a weighted sum of a finite number of component functions,each of which is periodic.For this particular case,the least period of the potential function is a common period amongst all of its component functions.An approximation of the MST for the potential function is derived,and this approximation takes the form of a product of the MSTs for each of the individual periodic component functions.Our first example illustrates the computational advantages of using the approximation for model validation and parameter tuning in the context of the biological application of DNA transcription.We also use this formula to approximate the MST for an arbitrary tilted periodic potential by the product of MSTs of a finite number of its Fourier modes.Two examples using truncated Fourier series are presented and analyzed.