摘要翻译：
我们指出了白矮星的极限质量（钱德拉塞卡极限）与广义Keller-Segel趋化模型中细菌种群的临界质量之间的显著类比[Chavanis&Sire,PRE，69，016116(2004)]。该模型是基于广义随机过程得出Tsallis统计量。平衡态对应于类似于天体物理中的气体多晶的多晶构型。对于临界指数n_3=d/(d-2)（其中d是空间维数），多项式理论导出了质量M_c的唯一值，我们将其解释为极限质量。在d=3的情况下，求出M_c=202.8956...在d=2时，我们恢复了著名的结果m_c=8pi（以适当的单位为单位）。对于m<m_c，系统蒸发（在无限域中）或趋于平衡态（对于箱形限制构型）。对于M>M_c，系统坍缩并形成一个Dirac峰，其质量为M_c，被晕包围。本文揭示了该模型，并通过简单的考虑说明了临界质量的起源。广义Keller-Segel模型的临界动力学的详细描述将在即将发表的论文中给出。
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英文标题：
《Critical mass of bacterial populations in a generalized Keller-Segel
  model. Analogy with the Chandrasekhar limiting mass of white dwarf stars》
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作者：
Pierre-Henri Chavanis and Clement Sire
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最新提交年份：
2008
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  We point out a remarkable analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in a generalized Keller-Segel model of chemotaxis [Chavanis & Sire, PRE, 69, 016116 (2004)]. This model is based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations similar to gaseous polytropes in astrophysics. For the critical index n_3=d/(d-2) (where d is the dimension of space), the theory of polytropes leads to a unique value of the mass M_c that we interpret as a limiting mass. In d=3, we find M_c=202.8956... and in d=2, we recover the well-known result M_c=8 pi (in suitable units). For M<M_c, the system evaporates (in an infinite domain) or tends to an equilibrium state (for box-confined configurations). For M>M_c, the system collapses and forms a Dirac peak containing a mass M_c surrounded by a halo. This paper exposes the model and shows, by simple considerations, the origin of the critical mass. A detailed description of the critical dynamics of the generalized Keller-Segel model will be given in a forthcoming paper.
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PDF链接：
https://arxiv.org/pdf/705.4366