Critical dynamics of self-gravitating Langevin particles and bacterial populations.
Critical dynamics of self-gravitating Langevin particles and bacterial populations.
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自引力朗之万颗粒和细菌群体的临界动力学。
DOI：
10.1103/physreve.78.061111
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
P. Chavanis
中科院分区：
文献类型：
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作者：
C. Sire;P. Chavanis
本文研究了广义Smoluchowski-Poisson系统（自引力Langevin粒子）和广义Keller-Segel模型（细菌群体的趋化性）的临界动力学。这些模型[P. H. Chavanis和C. Sire，Phys. Rev. E 69，016116（2004）]基于导致Tsallis统计的广义随机过程。平衡态对应于指数为n的多方构型，类似于天体物理学中的多方星。当临界指数n_{3}= d（d-2）（其中d ≥ 2是空间维数）时，存在一个临界温度θ_{c}（对于给定的质量）或临界质量M_{c}（对于给定的温度）。当Theta> Theta_{c}或MM_{c}时，系统在有限时间内坍缩并形成一个Dirac峰，该峰包含总质量的有限部分M_{c}，并被一个晕所包围。我们研究这些制度的数值，并在可能的情况下，分析寻找自相似或伪自相似的解决方案。本文将d = 2的Smoluchowski-Poisson系统和Keller-Segel模型的临界动力学推广到n_{3}-->+无穷大的等温构型。我们还强调白色矮星的极限质量（Ehrasekhar极限）和细菌种群的临界质量之间的类比在广义凯勒-西格尔模型的趋化性。
We study the critical dynamics of the generalized Smoluchowski-Poisson system (for self-gravitating Langevin particles) or generalized Keller-Segel model (for the chemotaxis of bacterial populations). These models [P. H. Chavanis and C. Sire, Phys. Rev. E 69, 016116 (2004)] are based on generalized stochastic processes leading to the Tsallis statistics. The equilibrium states correspond to polytropic configurations with index n similar to polytropic stars in astrophysics. At the critical index n_{3}=d(d-2) (where d>or=2 is the dimension of space), there exists a critical temperature Theta_{c} (for a given mass) or a critical mass M_{c} (for a given temperature). For Theta>Theta_{c} or MM_{c} the system collapses and forms, in a finite time, a Dirac peak containing a finite fraction M_{c} of the total mass surrounded by a halo. We study these regimes numerically and, when possible, analytically by looking for self-similar or pseudo-self-similar solutions. This study extends the critical dynamics of the ordinary Smoluchowski-Poisson system and Keller-Segel model in d=2 corresponding to isothermal configurations with n_{3}-->+infinity . We also stress the analogy between the limiting mass of white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial populations in the generalized Keller-Segel model of chemotaxis.