General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the $su(2)$ algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.Comment: 8 pages, no figure. Presentation improve

Event-based H∞ consensus control of multi-agent systems with relative output feedback: The finite-horizon case

In this technical note, the H∞ consensus control problem is investigated over a finite horizon for general discrete time-varying multi-agent systems subject to energy-bounded external disturbances. A decentralized estimation-based output feedback control protocol is put forward via the relative output measurements. A novel event-based mechanism is proposed for each intelligent agent to utilize the available information in order to decide when to broadcast messages and update control input. The aim of the problem addressed is to co-design the time-varying controller and estimator parameters such that the controlled multi-agent systems achieve consensus with a disturbance attenuation level γ over a finite horizon [0,T]. A constrained recursive Riccati difference equation approach is developed to derive the sufficient conditions under which the H∞ consensus performance is guaranteed in the framework of event-based scheme. Furthermore, the desired controller and estimator parameters can be iteratively computed by resorting to the Moore-Penrose pseudo inverse. Finally, the effectiveness of the developed event-based H∞ consensus control strategy is demonstrated in the numerical simulation

Excitation of nonlinear ion acoustic waves in CH plasmas

Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $k\lambda_{De}$ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $T_i/T_e < 0.2$ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\lambda_{De}$ increasing. When $k\lambda_{De}$ is not large, such as $k\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\lambda_{De}$ is large, such as $k\lambda_{De}=0.7$, the linear frequency can not be applied to exciting the nonlinear IAW, while the frequency calculated by the dispersion relation with no damping can be applied to exciting the nonlinear IAW.Comment: 10 pages, 9 figures, Accepted by POP, Publication in August 1