From Household Size to the Life Course

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66696/2/10.1177_000276427702100207.pd

Dynamical stability of infinite homogeneous self-gravitating systems: application of the Nyquist method

We complete classical investigations concerning the dynamical stability of an infinite homogeneous gaseous medium described by the Euler-Poisson system or an infinite homogeneous stellar system described by the Vlasov-Poisson system (Jeans problem). To determine the stability of an infinite homogeneous stellar system with respect to a perturbation of wavenumber k, we apply the Nyquist method. We first consider the case of single-humped distributions and show that, for infinite homogeneous systems, the onset of instability is the same in a stellar system and in the corresponding barotropic gas, contrary to the case of inhomogeneous systems. We show that this result is true for any symmetric single-humped velocity distribution, not only for the Maxwellian. If we specialize on isothermal and polytropic distributions, analytical expressions for the growth rate, damping rate and pulsation period of the perturbation can be given. Then, we consider the Vlasov stability of symmetric and asymmetric double-humped distributions (two-stream stellar systems) and determine the stability diagrams depending on the degree of asymmetry. We compare these results with the Euler stability of two self-gravitating gaseous streams. Finally, we determine the corresponding stability diagrams in the case of plasmas and compare the results with self-gravitating systems

Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection

Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, including the situations when turbulent reconnection is self-driven, i.e. the turbulence in the system is generated by the reconnection process itself. We show how turbulent reconnection entails the violation of magnetic flux freezing, the conclusion that has really far reaching consequences for many realistically turbulent astrophysical environments. In addition, we consider observational testing of turbulent reconnection as well as numerous implications of the theory. The former includes the Sun and solar wind reconnection, while the latter include the process of reconnection diffusion induced by turbulent reconnection, the acceleration of energetic particles, bursts of turbulent reconnection related to black hole sources as well as gamma ray bursts. Finally, we explain why turbulent reconnection cannot be explained by turbulent resistivity or derived through the mean field approach.Comment: 66 pages, 24 figures, a chapter of the book "Magnetic Reconnection - Concepts and Applications", editors W. Gonzalez, E. N. Parke