算子方法求解schlogl一级相变模型F─P方程的矩方程

本文采用转移算子和指数算子分解的方法求解一级相变模型Ｆ─Ｐ方程的矩方程，得出了一阶矩、二阶矩以及围绕平均值的涨落。

Fractal Studies on Dielectric Ageing

A stochastic model of conducting crack propagation is presented to provide a conceptual framework dedicated to the study of the formation of fractal structure of dielectric ageing patterns as a result of a competition between random fluctuation growth and applied electric strength enhanced deterministic growth. The necessary and sufficient conditions resulting in fractal behaviour in dielectric ageing are found.

Path prediction of flexible needles based on Fokker-Planck equation and disjunctive Kriging model

Path prediction of flexible needles based on the Fokker-Planck equation and disjunctive Kriging model is proposed to improve accuracy and consider the nonlinearity and anisotropy of soft tissues.The stochastic differential equation is developed into the Fokker-Planck equation with Gaussian noise,and the position and orientation probability density function of flexible needles are then optimized by the stochastic differential equation.The probability density function obtains the mean and covariance of flexible needle movement and helps plan puncture paths by combining with the probabilistic path algorithm.The weight coefficients of the ordinary Kriging are extended to nonlinear functions to optimize the planned puncture path,and the Hermite expansion is used to calculate nonlinear parameter values of the disjunctive Kriging optimization model.Finally,simulation experiments are performed.Detailed comparison results under different path planning maps show that the kinematics model can plan optimal puncture paths under clinical requirements with an error far less than 2 mm.It can effectively optimize the path prediction model and help improve the target rate of soft tissue puncture with flexible needles through data analysis and processing of the mean value and covariance parameters derived by the probability density and disjunctive Kriging algorithms.

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.

A Novel Approach for Numerical Computation of Fokker-Planck Equation

This paper present an implementation of＂modified cubic B-spline differential quadrature method （MCB-DQM）＂ proposed by Arora ＆ Singh （Applied Mathematics and Computation Vol. 224（1） （2013） 161-177） for numerical computation of Fokker-Planck equations. The modified cubic B-splines are used as set of basis functions in the differential quadrature to compute the weighting coefficients for the spatial derivatives, which reduces Fokker-Planck equation into system of first-order ordinary differential equations （ODEs）, in time. The well known SSP-RK43 scheme is then applied to solve the resulting system of ODEs. The efficiency of proposed method has been confirmed by three examples having their exact solutions. This shows that MCB-DQM results are capable of achieving high accuracy. Advantage of the scheme is that it can be applied very smoothly to solve the linear or nonlinear physical problems, and a very less storage space is required which causes less accumulation of numerical errors.

Retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential

The retainability of canonical distributions for a Brownian particle controlled by a time-dependent harmonic potential is investigated in the overdamped and underdamped situations, respectively. Because of different time scales, the overdamped and underdamped Langevin equations(as well as the corresponding Fokker-Planck equations) lead to distinctive restrictions on protocols maintaining canonical distributions. Two special cases are analyzed in details: First, a Brownian particle is controlled by a time-dependent harmonic potential and embedded in medium with constant temperature; Second, a Brownian particle is controlled by a timedependent harmonic potential and embedded in a medium whose temperature is tuned together with the potential stiffness to keep a constant effective temperature of the Brownian particle. We find that the canonical distributions are usually retainable for both the overdamped and underdamped situations in the former case. However, the canonical distributions are retainable merely for the overdamped situation in the latter case. We also investigate general time-dependent potentials beyond the harmonic form and find that the retainability of canonical distributions depends sensitively on the specific form of potentials.

Time-Delay Effects on Constitutive Gene Expression

The dynamics of constitutive gene expression with delayed m RNA degradation is investigated, where the intrinsic noise caused by the small number of reactant molecules is introduced. It is found that the oscillatory behavior claimed in previous investigations does not appear in the approximation of small time delay, and the steady state distribution still follows the Poisson law. Furthermore, we introduce the extrinsic noise induced by surrounding environment to explore the effects of this noise and time delay on the Fano factor. Based on a delay Langevin equation and the corresponding Fokker–Planck equation, the distribution of m RNA copy-number is achieved analytically. The time delay and extrinsic noise play similar roles in the gene expression system, that is, they are able to result in the deviation of the Fano factor from 1 evidently. The measured Fano factor for constitutive gene expression is slightly larger than 1, which is perhaps attributed to the time-delay effect.