论文标题
在封闭系统经典振荡器 +随机环境中进行自组织过程的理论和数值研究
Theoretical and Numerical Study of Self-Organizing Processes In a Closed System Classical Oscillator + Random Environment
论文作者
论文摘要
在满足langevin型随机微分方程的复杂概率过程的框架内，考虑了一个自组织的关节系统经典振荡器 +随机环境。考虑了环境产生的各种随机性。在统计平衡（SEQ）的限制中，二阶部分微分方程（PDE）得出了描述经典环境场的分布。振荡器轨迹的数学期望是以功能综合表示的形式构造的，该功能综合表示在SEQ限制下，将其压缩为二维积分代表，并与intemperand-二阶复杂PDE的解决方案。事实证明，在一般情况下，复杂的PDE将减少为二阶的两个独立PDE，并具有空间偏差的参数。详细研究了这些方程式的二维子空间的几何和拓扑特征。已经开发了用于并行建模的算法。
A self-organizing joint system classical oscillator + random environment is considered within the framework of a complex probabilistic process that satisfies a Langevin-type stochastic differential equation. Various types of randomness generated by the environment are considered. In the limit of statistical equilibrium (SEq), second-order partial differential equations (PDE) are derived that describe the distribution of classical environmental fields. The mathematical expectation of the oscillator trajectory is constructed in the form of a functional-integral representation, which, in the SEq limit, is compactified into a two-dimensional integral representation with an integrand - the solution of the second-order complex PDE. It is proved that the complex PDE in the general case is reduced to two independent PDEs of the second-order with spatially deviating arguments. The geometric and topological features of the two-dimensional subspace on which these equations arise are studied in detail. An algorithm for parallel modeling of the problem has been developed.
