A sharp stability criterion for the Vlasov-Maxwell system

We consider the linear stability problem for a 3D cylindrically symmetric equilibrium of the relativistic Vlasov-Maxwell system that describes a collisionless plasma. For an equilibrium whose distribution function decreases monotonically with the particle energy, we obtained a linear stability criterion in our previous paper. Here we prove that this criterion is sharp; that is, there would otherwise be an exponentially growing solution to the linearized system. Therefore for the class of symmetric Vlasov-Maxwell equilibria, we establish an energy principle for linear stability. We also treat the considerably simpler periodic 1.5D case. The new formulation introduced here is applicable as well to the nonrelativistic case, to other symmetries, and to general equilibria

A game theory approach to mixed H2/H∞ control for a class of stochastic time-varying systems with randomly occurring nonlinearities

Copyright @ 2011 Elsevier B.V. This is the author’s version of a work that was accepted for publication in Systems and Control Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published and may be accessed at the link below.This paper is concerned with the mixed H2/H∞ control problem for a class of stochastic time-varying systems with nonlinearities. The nonlinearities are described by statistical means and could cover several kinds of well-studied nonlinearities as special cases. The occurrence of the addressed nonlinearities is governed by two sequences of Bernoulli distributed white sequences with known probabilities. Such nonlinearities are named as randomly occurring nonlinearities (RONs) as they appear in a probabilistic way. The purpose of the problem under investigation is to design a controller such that the closed-loop system achieves the expected H2 performance requirements with a guaranteed H∞ disturbance attenuation level. A sufficient condition is given for the existence of the desired controller by means of solvability of certain coupled matrix equations. By resorting to the game theory approach, an algorithm is developed to obtain the controller gain at each sampling instant. A numerical example is presented to show the effectiveness and applicability of the proposed method

Robust H∞ control of time-varying systems with stochastic non-linearities: the finite-horizon case

The official published version can be obtained from the link below.This paper is concerned with the robust H∞ control problem for the class of uncertain non-linear discrete time-varying stochastic systems with a covariance constraint. All the system parameters are time-varying and the uncertainties enter into the state matrix. The non-linearities under consideration are described by statistical means and they cover several classes of well-studied non-linearities. The purpose of the addressed problem is to design a dynamic output-feedback controller such that, the H∞ disturbance rejection attenuation level is achieved in the finite-horizon case while the state covariance is not more than an individual upper bound at each time point. An algorithm is developed to deal with the addressed problem by means of recursive linear matrix inequalities (RLMIs). It is shown that the robust H∞ control problem is solvable if the series of RLMIs is feasible. An illustrative simulation example is given to show the applicability and effectiveness of the proposed algorithm.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Robust H-infinity sliding mode control for nonlinear stochastic systems with multiple data packet losses

This is the post-print version of this Article. The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & SonsIn this paper, an ∞ sliding mode control (SMC) problem is studied for a class of discrete-time nonlinear stochastic systems with multiple data packet losses. The phenomenon of data packet losses, which is assumed to occur in a random way, is taken into consideration in the process of data transmission through both the state-feedback loop and the measurement output. The probability for the data packet loss for each individual state variable is governed by a corresponding individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time system considered is also subject to norm-bounded parameter uncertainties and external nonlinear disturbances, which enter the system state equation in both matched and unmatched ways. A novel stochastic discrete-time switching function is proposed to facilitate the sliding mode controller design. Sufficient conditions are derived by means of the linear matrix inequality (LMI) approach. It is shown that the system dynamics in the specified sliding surface is exponentially stable in the mean square with a prescribed ∞ noise attenuation level if an LMI with an equality constraint is feasible. A discrete-time SMC controller is designed capable of guaranteeing the discrete-time sliding mode reaching condition of the specified sliding surface with probability 1. Finally, a simulation example is given to show the effectiveness of the proposed method.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the National Natural Science Foundation of China under Grant 61028008 and the Alexander von Humboldt Foundation of German

Transmission of Water Waves under Multiple Vertical Thin Plates

The transmission of water waves under vertical thin plates, e.g., offshore floating breakwaters, oscillating water column wave energy converters, and so on, is a crucial feature that dominates the hydrodynamic performance of marine devices. In this paper, the analytical solution to the transmission of water waves under multiple 2D vertical thin plates is firstly derived based on the linear potential theory. The influences of relevant parameters on the wave transmission are discussed, which include the number of plates, the draft of plates, the distance between plates and the water depth. The analytical results suggest that the transmission of progressive waves gradually weakens with the growth of the number and draft of plates, and under the conditions of given number and draft of plates, the distribution of plates has significant influence on the transmission of progressive waves. The results of this paper contribute to the understanding of the transmission of water waves under multiple vertical thin plates, as well as the suggestion on optimal design of complex marine devices, such as a floating breakwater with multiple plates

Measurement-induced nonlocality over two-sided projective measurements

Measurement-induced nonlocality (MiN), introduced by Luo and Fu [Phys. Rev. Lett. 106(2011)120401], is a kind of quantum correlation that beyond entanglement and even beyond quantum discord. Recently, we extended MiN to infinite-dimensional bipartite system [arXiv:1107.0355]. MiN is defined over one-sided projective measurements. In this letter we introduce a measurement-induced nonlocality over two-sided projective measurements. The nullity of this two-sided MiN is characterized, a formula for calculating two-sided MiN for pure states is proposed, and a lower bound of (two-sided) MiN for maximally entangled mixed states is given. In addition, we find that (two-sided) MiN is not continuous. The two-sided geometric measure of quantum discord (GMQD) is introduced in [Phys. Lett. A 376(2012)320--324]. We extend it to infinite-dimensional system and then compare it with the two-sided MiN. Both finite- and infinite-dimensional cases are considered.Comment: 12 page

Nuclear β+\beta^+/EC decays in covariant density functional theory and the impact of isoscalar proton-neutron pairing

Self-consistent proton-neutron quasiparticle random phase approximation based on the spherical nonlinear point-coupling relativistic Hartree-Bogoliubov theory is established and used to investigate the $\beta^+$/EC-decay half-lives of neutron-deficient Ar, Ca, Ti, Fe, Ni, Zn, Cd, and Sn isotopes. The isoscalar proton-neutron pairing is found to play an important role in reducing the decay half-lives, which is consistent with the same mechanism in the $\beta$ decays of neutron-rich nuclei. The experimental $\beta^+$/EC-decay half-lives can be well reproduced by a universal isoscalar proton-neutron pairing strength.Comment: 12 pages, 4 figure

Is the f0(600)f_0(600) meson a dynamically generated resonance? -- a lesson learned from the O(N) model and beyond

O(N) linear $\sigma$ model is solvable in the large $N$ limit and hence provides a useful theoretical laboratory to test various unitarization approximations. We find that the large $N_c$ limit and the $m_\sigma\to \infty$ limit do not commute. In order to get the correct large $N_c$ spectrum one has to firstly take the large $N_c$ limit. We argue that the $f_0(600)$ meson may not be described as generated dynamically. On the contrary, it is most appropriately described at the same level as the pions, i.e, both appear explicitly in the effective lagrangian. Actually it is very likely the $\sigma$ meson responsible for the spontaneous chiral symmetry breaking in a lagrangian with linearly realized chiral symmetry.Comment: 15 pages, 3 figurs; references added; discussions slightly modified; revised version accepted by IJMP