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

Effect of signal and noise mutual coupling on MIMO channel capacity

In this paper we analyze the impact of mutual coupling on MIMO channel capacity, considering its effect on both signal and thermal noise. We calculate noise correlation matrix in the multi-antenna system with closely spaced antenna by applying Nyquist’s thermal noise theorem. Then, we employ the noise correlation matrix in the channel capacity formula, which enables the identification of thermal noise correlation contribution on the MIMO channel capacity. In addition, we examine the variations in the mean branch signal-to-noise ratios (SNR) due to the noise correlation. Our simulation results corroborate the theoretical analysis that mean and outage MIMO channel capacity is underestimated if noise correlation due to mutual coupling effect is not accounted fo