在白噪声分析中的广义维里拉普拉斯

一类广义维里拉普拉斯，把在白噪声分析构架中通常定义的维里拉普拉斯作为特殊情形而包含。     

关于“信息熵”分析及其应用的研究

本文用Ｓｈａｎｎｏｎ熵函数的观点及最大离散熵原理，探讨了对随机试验项目的优选问题：即压缩某种“不确定性”试验项目的实施与探索．并通过应用实例的计算，获得了满意的聚类效果．这种方法对于信息资料的数据处理及压缩“不确定性“验项目具有普遍意义．     

单模光纤中皮秒啁啾脉冲压缩

对单模光纤正群速色散区秒啁啾脉冲的非线性传进行了近似的解析分析和定量的数值计算。结果表明，负啁啾脉冲在传输过程中能得到有效压缩。压缩比与脉冲初始峰值功率和初始啁啾程度有关。初始峰值功率一定的脉冲，其压缩比随初始啁啾程度的增大面大，初始啁啾程度一定的脉冲，压缩比随初始峰值功率的增大而减小，表明自相位调制效应导致脉冲压缩效果变差。计算结果还表明，在脉冲时域宽度得到压缩的同时，光谱宽度也能得到同步压缩。     

Looking at Fokker-Planck dynamics with a noisy instrument

We consider the class of experiments which can be characterized by a Fokker-PIanck dynamics corresponding to the overdamped motion of a state point in a suitable stochastic potential. We assume that the general form of the potential is known (or can be guessed with reasonable accuracy), but that its parameters are to be determined experimentally by measurements made with a noisy instrument. This possible method for determining the potential parameters, which exploits the system's own internal stochastic motion in order to explore rapidly its available parameter space, is substantially more efficient than traditional methods involving time averages of single point measurements, and yet does not appear to have been previously considered. The method could be important when, for example, the experiment must be completed in a limited time owing either to the expense of the experimental materials or to the temporary stationarity of the preparation, situations which are commonly encountered in experimental biochemistry and biology.     

Sparse-grid finite-volume multigrid for 3D-problems

We introduce a multigrid algorithm for the solution of a second order elliptic equation in three dimensions. For the approximation of the solution we use a partially ordered hierarchy of finite-volume discretisations. We show that there is a relation with semicoarsening and approximation by more-dimensional Haar wavelets. By taking a proper subset of all possible meshes in the hierarchy, a sparse grid finite-volume discretisation can be constructed.The multigrid algorithm consists of a simple damped point-Jacobi relaxation as the smoothing procedure, while the coarse grid correction is made by interpolation from several coarser grid levels.The combination of sparse grids and multigrid with semi-coarsening leads to a relatively small number of degrees of freedom,N, to obtain an accurate approximation, together with anO(N) method for the solution. The algorithm is symmetric with respect to the three coordinate directions and it is fit for combination with adaptive techniques.To analyse the convergence of the multigrid algorithm we develop the necessary Fourier analysis tools. All techniques, designed for 3D-problems, can also be applied for the 2D case, and — for simplicity — we apply the tools to study the convergence behaviour for the anisotropic Poisson equation for this 2D case.     

On the phase space approach to complexity

We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang.     

Model-dependent nature of blowtorch effect on the escape and equilibration rates

We analyze the relaxation behavior of a bistable system when the background temperature profile is inhomogeneous due to the presence of a localized hot region (blowtorch) on one side of the potential barrier. Since the diffusion equation for inhomogeneous medium is model-dependent, we consider two physical models to study the kinetics of such system. Using a conventional stochastic method, we obtain the escape and equilibration rates of the system for the two physical models. For both models, we find that the hot region enhances the escape rate from the well where it is placed while it retards the escape rate from the other well. However, the value of the escape rate from the well where the hot region is placed differs for the two models while that of the escape rate from the other well is identical for both. This work, for the first time, gives a detailed report of the similarities and differences of the escape rates and, hence, exposes the common and distinct features of the two known physical models in determining the way the bistable system relaxes. Received 25 September 2001     

电子直线加速器磁控管频率稳定的自适应线性神经元方法

 电子直线加速器电子束能量的稳定与否取决于功率源工作频率的稳定性,磁控管在短时间内的散谱和轻微跳谱造成稳频系统的控制精度下降,最后电子束的扫描均匀度下降。引入自适应线性神经元方法(ADALINE)和噪声对消技术以消除对工作频率长期稳定性的影响,从而保证了电子束的扫描均匀度。     

Quasipotentials for simple noisy maps with complicated dynamics

The theory of nonequilibrium potentials or quasipotentials is a physically motivated approach to small random perturbations of dynamical systems, leading to exponential estimates of invariant probabilities and mean first exit times. In the present article we develop the mathematical foundation of this theory for discrete-time systems, following and extending the work of Freidlin and Wentzell, and Kifer. We discuss strategies for calculating and estimating quasipotentials and show their application to one-dimensionalS-unimodal maps. The method proves to be especially suited for describing the noise scaling behavior of invariant probabilities, e.g., for the map occurring as the limit of the Feigenbaum period-doubling sequence. We show that the method allows statements about the scaling behavior in the case of localized noise, too, which does not originally lie within the scope of the quasipotential formalism.     

既不离散也不连续的随机变量

讨论了既不离散也不连续的随机变量 ,并纠正了有关文献中关于连续型随机变量定义中的错误 .