论文标题
重力在随机同质介质中的统计特性
Statistical properties of the gravitational force in a random homogeneous medium
论文作者
论文摘要
我们讨论了在无关颗粒的无限随机和同质气体中施加在测试粒子上的引力（牛顿）力的统计分布。精确的解决方案称为无限系统极限的HOLTSMARK分布，与体积内的粒子n数量和无穷大的体积相对应。可以通过组合n-最近的邻居粒子对总重力的贡献的组合来分析与距离差异粒子相当的尺度引力力的统计行为，这可以从一组N粒子的位置的关节概率密度得出。我们研究了两种独立的方法，以使用积分形式和顺序统计数据来得出一组n个邻居的关节概率密度，以使这种概率分布的一般表达具有广义的空间维度。我们发现，HOLTSMARK分布的非线分散剂是由于总重力中第一个最近的邻居的唯一贡献所致。
We discuss the statistical distribution of the gravitational (Newtonian) force exerted on a test particle in a infinite random and homogeneous gas of non-correlated particles. The exact solution is known as the Holtsmark distribution at the limit of infinite system corresponding to the number of particle N within the volume and the volume going to infinity. The statistical behaviour of the gravitational force for scale comparable to the inter-distance particle can be analyzed through the combination of the n-th nearest neighbor particle contribution to the total gravitational force, which can be derived from the joint probability density of location for a set of N particles. We investigate two independent approaches to derive the joint probability density of location for a set of N neighbors using integral forms and order statistics to give a general expression of such probability distribution with generalised dimension of space. We found that the non-finite dispersion of the Holtsmark distribution is due to the single contribution of the first nearest neighbor in the total gravitational force.
