二维自引力布朗粒子的临界质量和临界温度
Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions
摘要：
我们证明了二维细菌群体趋化问题的临界质量M_c=8π与二维自引力布朗粒子的临界温度T_c=GMm/4k_B是对应的。我们利用维里定理或考虑Keller-Segel模型和Smoluchowski-Poisson系统的定态解得到这些临界值。我们还考虑一维系统的情况下，并开发与Burgers方程的连接。最后，我们讨论了系统作为M或T的函数在有界和无界域的D=1，2和3维的发展，并显示每个维度的特殊性。本文旨在指出细菌种群，自引力布朗粒子和偶尔的二维涡旋之间的许多相似之处。
英文摘要：
We show that the critical mass M_c=8πof bacterial populations in two dimensions in the chemotactic problem is the counterpart of the critical temperature T_c=GMm/4k_B of self-gravitating Brownian particles in two-dimensional gravity. We obtain these critical values by using the Virial theorem or by considering stationary solutions of the Keller-Segel model and Smoluchowski-Poisson system. We also consider the case of one dimensional systems and develop the connection with the Burgers equation. Finally, we discuss the evolution of the system as a function of M or T in bounded and unbounded domains in dimensions d=1, 2 and 3 and show the specificities of each dimension. This paper aims to point out the numerous analogies between bacterial populations, self-gravitating Brownian particles and, occasionally, two-dimensional vortices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
