Ricci流中运动快速发电机算子的谱
Spectrum of kinematic fast dynamo operator in Ricci flows
摘要：
研究了Einstein二维流形中Ricci可压缩流中运动学快速发电机算子的谱。对于快速发电机算子，给出了与Chicone，Latushkin和Montgomery-Smith（Comm Math Phys（1995））得到的表达式类似的表达式。在高导电介质中，根据Ricci标量的线性和非线性阶，得到了算子本征值。本征值谱表明，流的Ricci标量与流的展开有一定的关系。在理想等离子体的极限下，得到了Friedmann-Robertson-Walker（FRW）的空间3-Einstein流形截面。如果里奇曲率张量的迹是负的，宇宙的暴胀相就会发生收缩，发电机作用也会发生。当宇宙膨胀时，就会产生一个衰减的磁场或非发电机。正如Latushkin和Visik（Comm Math Phys（2003））中所述，还研究了运动发电机中的李雅普诺夫指数。由于正曲率标量在Ricci流下保持不变，证明了快速发电机在同一流下也保持不变。
英文摘要：
Spectrum of kinematic fast dynamo operators in Ricci compressible flows in Einstein 2-manifolds is investigated. A similar expression, to the one obtained by Chicone, Latushkin and Montgomery-Smith (Comm Math Phys (1995)) is given, for the fast dynamo operator. The operator eigenvalue is obtained in a highly conducting media, in terms of linear and nonlinear orders of Ricci scalar. Eigenvalue spectra shows that there is a relation between the Ricci scalar and expansion of the flow. Spatial 3-Einstein manifold section of Friedmann-Robertson-Walker (FRW) is obtained in the limit of ideal plasma. If the trace of the Ricci curvature tensor is negative, a contraction of the inflationary phase of the universe takes place, and the dynamo action takes place. When the universe expands a decaying magnetic field or non-dynamo is obtained. As in Latushkin and Vishik (Comm Math Phys (2003)) the Lyapunov exponents in kinematic dynamos is also investigated. Since positive curvature scalar are preserved under Ricci flow, it is shown that fast dynamos are preserved under this same flow.
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。
