Stability Analysis of Integral Delay Systems with Multiple Delays

This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting matrix for each term, which can be optimized to reduce the conservatism. With the help of the multiple Jensen inequalities and by developing a novel linearizing technique, two novel Lyapunov functional based approaches are established to obtain sufficient stability conditions expressed by linear matrix inequalities (LMIs). It is shown that these new conditions are always less conservative than the existing ones. Moreover, by the positive operator theory, a single LMI based condition and a spectral radius based condition are obtained based on an existing sufficient stability condition expressed by coupled LMIs. A numerical example illustrates the effectiveness of the proposed approaches.Comment: 14 page

Quark production, Bose-Einstein condensates and thermalization of the quark-gluon plasma

In this paper, we study the thermalization of gluons and N_f flavors of massless quarks and antiquarks in a spatially homogeneous system. First, two coupled transport equations for gluons and quarks (and antiquarks) are derived within the diffusion approximation of the Boltzmann equation, with only 2 2 processes included in the collision term. Then, these transport equations are solved numerically in order to study the thermalization of the quark-gluon plasma. At initial time, we assume that no quarks or antiquarks are present and we choose the gluon distribution in the form f = f_0 theta (1-p/Q_s) with Q_s the saturation momentum and f_0 a constant. The subsequent evolution of systems may, or may not, lead to the formation of a (transient) Bose condensate, depending on the value of f_0. In fact, we observe, depending on the value of f_0, three different patterns: (a) thermalization without gluon Bose-Einstein condensate (BEC) for f_0 < f_{0t}, (b) thermalization with transient BEC for f_{0t} < f_0 < f_{0c}, and (c) thermalization with BEC for f_{0c} < f_0. The values of f_{0t} and f_{0c} depend on N_f. When f_0> 1 > f_{0c}, the onset of BEC occurs at a finite time t_c ~ 1/((alpha_s f_0)^2 Q_s). We also find that quark production slows down the thermalization process: the equilibration time for N_f = 3 is typically about 5 to 6 times longer than that for N_f = 0 at the same Q_s.Comment: 32 pages, 25 figures, minor modifications, Final version published in NP

Experiment-simulation Study on Noise Reduction of Cylinder Shell with Horn Helmholtz Resonator

This paper focuses on the noise reduction of the cylindrical structure at low frequency (130 Hz-180 Hz). The low-frequency noise response spectrum in the cylindrical cavity is obtained by using the Helmholtz resonator (HR) to reduce the noise peak amplitude. The acoustic simulation software Virtual.Lab is used to establish the finite element model of the cylindrical shell with HR, and to obtain the low-frequency acoustic response in the cylindrical cavity. The simulation model is validated by the experimental results. Then, the influence of installation position, the number of installed resonators and the resonators with different resonance frequencies in the cylindrical cavity are discussed. The results indicate that both the noise reduction band and peak amplitude are increased by installing the HR\u27s on the cylinder shell. The noise reduction of the cylinder shell with HR installed on the upper position is larger than other situations. As the number of resonators increased, the frequency range of the noise reduction in the cylindrical cavity gradually increases, and the noise reduction of the cylinder cavity increases first and then decreases