Sopik Julien, Sire Clément, Chavanis Pierre-Henri
Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, Route de Narbonne, 31062 Toulouse Cedex 4, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 2):026105. doi: 10.1103/PhysRevE.72.026105. Epub 2005 Aug 3.
We study the thermodynamical properties of a self-gravitating gas with two or more types of particles. Using the method of linear series of equilibria, we determine the structure and stability of statistical equilibrium states in both microcanonical and canonical ensembles. We show how the critical temperature (Jeans instability) and the critical energy (Antonov instability) depend on the relative mass of the particles and on the dimension of space. We then study the dynamical evolution of a multicomponent gas of self-gravitating Brownian particles in the canonical ensemble. Self-similar solutions describing the collapse below the critical temperature are obtained analytically. We find particle segregation, with the scaling profile of the slowest collapsing particles decaying with a nonuniversal exponent that we compute perturbatively in different limits. These results are compared with numerical simulations of the two-species Smoluchowski-Poisson system. Our model of self-attracting Brownian particles also describes the chemotactic aggregation of a multi-species system of bacteria in biology.
我们研究了具有两种或更多种粒子的自引力气体的热力学性质。使用平衡线性系列方法，我们确定了微正则系综和正则系综中统计平衡态的结构和稳定性。我们展示了临界温度（金斯不稳定性）和临界能量（安东诺夫不稳定性）如何依赖于粒子的相对质量和空间维度。然后我们研究了正则系综中自引力布朗粒子多组分气体的动力学演化。通过解析得到了描述低于临界温度下坍缩的自相似解。我们发现了粒子分离现象，最慢坍缩粒子的标度轮廓以一个我们在不同极限下微扰计算得到的非普适指数衰减。我们将这些结果与双物种斯莫卢霍夫斯基 - 泊松系统的数值模拟进行了比较。我们的自吸引布朗粒子模型还描述了生物学中多物种细菌系统的趋化聚集现象。
