引力作用下理想气体统计分形结构的动力学模型

摘要

通过引力作用下理想气体流体力学方程组的无量纲化,以空间尺度因子代换时间参数,根据量纲理论Ⅱ定理,在方程中用与尺度因子对应的统计量物理为度量单位,从理论上推导出流体力学微分方程组的分离变量形式,获得一组具有分形结构特征一阶微分方程组.引力作用下理想气体统计特征参量相对于空间尺度因子的一般函数形式具有广义分形的结构特征,这个结果表明局域性流体力学微分方程能够作为统计分形结构的动力学基础.%Differential equations of ideal gas under gravity are made dimensionless by choosing statistical quantities ρ(R), p(R), u(R) as the unit with respect to scale factor R(t) and substituting time t with spatial scale factor R(t). The equations that have separable variables are obtained based on Ⅱtheory, then a serial of differential equations having fractal structure characteristics are obtained. Statistical quantities of ideal gas under gravity Y(R) have generalized fractal characteristics. This result shows that the local differential equations of fluid can be the fundamental equations of the dynamics of statistical fractal structures.