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Generalized cell mapping, a global analysis method, is introduced to describe the global longterm behavior of the chaotic climate system, and to predict its global probability evolution.


A conceptually intuitive nonlinear technique, multidimensional probability evolution (MDPE), is introduced.


Then, both the state conditional probability evolution, and the associated Dynamic Programming Equation can be solved for off line, ahead of time, retaining the same truncation level as that of the process model.


Its neglect seriously distorts the probability evolution except at elevated temperatures where the Bose occupation factors considerably exceed 1.




 In this paper,onedimensional random walk process and its many propertiesunder the action of an applied field are investigated systematically and in detail.FirstMarkov chain type of equations for the probability evolution are established withstochastic variables being discrete and continuous,then their exact analytic solutions are obtained for the biased walk model with the nearestneighbor steps,andfinally many interesting transport and statistical properties of this process are discussed which are... In this paper,onedimensional random walk process and its many propertiesunder the action of an applied field are investigated systematically and in detail.FirstMarkov chain type of equations for the probability evolution are established withstochastic variables being discrete and continuous,then their exact analytic solutions are obtained for the biased walk model with the nearestneighbor steps,andfinally many interesting transport and statistical properties of this process are discussed which are characterized by the many results.A characteristic common tothese results but different from that of the symmetric(unbiased)walk without theaction of no applied field lies in the direct and explicit dependence of them onthe applied field hence on time,i.e.,is dispersive.In particular,the dispersiveeffect disappears with the field when it is switched off and then many corresponding results to the unbiased(sysmmetric)walk are obtained immediately,whichmakes the present discussion more general.  本文较系统地对外场作用下的一维无规行走过程及其若干性质进行了研究。在分立与连续随机变量两种情况下,首先建立了概率演化的Markov链方程,然后在最近邻偏向行走的模型下,求出了它们的严格的解析解,最后利用这些解析解讨论了这个过程的由一些结果所表征的输运性质与统计性质。  This paper reports researches on the property of laser traveling in a thick medium and photoionization of laser atom interaction. The equation of three step photoionization for describing the field and the density matrix as well as the atomic population was derived. The ionization probability evolution with laser parameters is calculated in different cases. It was found that the laser transfer in a long distance causes evolution of laser parameters. Laser power, laser pulse shape, pulse width and... This paper reports researches on the property of laser traveling in a thick medium and photoionization of laser atom interaction. The equation of three step photoionization for describing the field and the density matrix as well as the atomic population was derived. The ionization probability evolution with laser parameters is calculated in different cases. It was found that the laser transfer in a long distance causes evolution of laser parameters. Laser power, laser pulse shape, pulse width and time stepout of three laser bunches are the main factors of affecting the photoionization probability.  研究了激光在厚介质中的传输特性以及激光与原子相互作用的光电离。推导了三步光电离的场方程组和原子布居的密度矩阵方程组。计算了在不同情况下电离几率与激光参数的变化关系。深入研究了激光在厚介质中传输引起激光参数的变化，以及激光功率、脉冲形状、脉冲宽度、三束激光的时间不同步对电离几率的影响。  Stochastic mechanics has gradually drawn much attention in the area of physics and mechanics since it was established by Nelson in 1966. In stochastic mechanics, quantum fluctuational phenomena are described in terms of diffusion processes instead of wave functions. The importance of stochastic mechanics can be shown from the fact that stochastic mechanics and orthodox quantum mechanics make the same predictions for the same position measurements. Since all measurements ultimately consist of position ones,... Stochastic mechanics has gradually drawn much attention in the area of physics and mechanics since it was established by Nelson in 1966. In stochastic mechanics, quantum fluctuational phenomena are described in terms of diffusion processes instead of wave functions. The importance of stochastic mechanics can be shown from the fact that stochastic mechanics and orthodox quantum mechanics make the same predictions for the same position measurements. Since all measurements ultimately consist of position ones, the two descriptions are experimentally indistinguishable. That is, if the laws of the quantum mechanics apply both to the system being measured and to the measuring apparatus, then the predictions of quantum mechanics will be identical with those of stochastic mechanics, since positions of all constituents of the system plus apparatus are determined by the probability density ρ=ψ 2 , where ψ is the wave function of the system plus apparatus.For a given stochastic mechanical system, in addition to its kinematics can be approximated by smooth diffusion processes, the dynamical laws should be obeyed. Therefore, the actual motion of the given system should make stationary a certain action functional which may be described as “the mean stochastic action”. In fact, diffusions have no differentiable sample paths, so that diffusion motions of systems should be estimated by discretization or path wise stochastic calculus. In this paper, the mechanical systems with configurations defined by diffusion processes are considered. By using the path wise calculus of variations, the dynamical equations of the conservative systems and nonconservative systems are derived in terms of generalized coordinates. These equations, together with the continuity equation, describe actually the probability evolution of quantum fluctuations of the given systems. It is shown that there exists a class of n+1 dimensional vector potentials that is invariant under certain gauge transformation. This class of invariant vector potentials can determine a one to one correspondence between solutions (wave functions) of certain Schrdinger equations and diffusion processes satisfying appropriate regularity conditions. As an example, the quantum fluctuations of a particle pair in an one dimensional trap is finally given to illustrate the application of the results of this paper.  研究位形由扩散过程定义的力学系统．利用变分的路径计算给出系统广义坐标表示的动力学方程，该方程连同连续方程描述系统量子波动随时间演化的概率进程．文末的表示定理指出，在满足适当正规条件的扩散过程和Ｓｃｈｒｄｉｎｇｅｒ方程的解（波函数）之间存在一一对应关系   << 更多相关文摘 
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