Diffusive random process approximation in certain nonstationary statistical problems of physics
Diffusive random process approximation in certain nonstationary statistical problems of physics
复制标题
某些非平稳物理统计问题中的扩散随机过程近似
DOI：
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
V. I. Tatarskii
中科院分区：
文献类型：
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作者：
V. Klyatskin;V. I. Tatarskii
该综述在统一方法的基础上考虑了非线性动态系统中的布朗运动问题，包括受随机力作用的线性振荡器、具有随机参数的振荡系统中的参数共振、随机速度场中粒子的湍流扩散以及折射率随机不均匀介质中的射线扩散。同样的方法还可以用来考虑更复杂的问题，例如理想气体中的平衡流体动力涨落、用随机力方法描述流体动力湍流以及光在具有随机不均匀性的介质中的传播。用于处理这些问题的方法包括构造系统的概率密度或其统计矩的方程，使用随机行为的特征时间与系统的时间常数的比率作为小参数（在许多问题中，时间的作用是由空间坐标之一发挥的）。该方法的一阶近似相当于将动作的真实相关函数替换为δ函数；这产生了封闭形式的特征方程。该方法使得还可以根据前述一阶小参数确定更高的近似值。
The review considers, on the basis of a unified approach, the problem of Brownian motion in nonlinear dynamic systems, including a linear oscillator acted upon by random forces, parametric resonance in an oscillating system with random parameters, turbulent diffusion of particles in a random-velocity field, and diffusion of rays in a medium with random inhomogeneities of the refractive index. The same method is used to consider also more complicated problems such as equilibrium hydrodynamic fluctuations in an ideal gas, description of hydrodynamic turbulence by the method of random forces, and propagation of light in a medium with random inhomogeneities. The method used to treat these problems consists of constructing equations for the probability density of the system or for its statistical moments, using as the small parameter the ratio of the characteristic time of the random actions to the time constant of the system (in many problems, the role of the time is played by one of the spatial coordinates). The first-order approximation of the method is equivalent to replacement of the real correlation function of the action by a δ function; this yields equations for the characteristics in closed form. The method makes it possible to determine also higher approximations in terms of the aforementioned first-order small parameter.