两斑块间具有非对称双向脉冲扩散的周期单种群模型

研究了两斑块间具有脉冲扩散的周期单种群模型。利用脉冲微分方程的比较原理和一些分析方法,得到了系统持久性的充分条件,然后利用Brouwer不动点理论和构造Lyapunov函数的方法,得到了系统正周期解全局渐近稳定的充分条件。     

几种不同周期性单元的PBG天线的设计与仿真

提出了几种不同周期性单元的PBG结构的贴片天线.采用有限元法对其进行仿真分析,通过相互对比,研究出这几种不同PBG结构对贴片天线性能的影响.结果表明,在贴片天线中增加PBG结构能减少天线的回波损耗,提高天线的增益和辐射效率.并得出周期性单元的形状和数目对其特性的影响.     

Asymptotic approximations for Bloch waves and topological mode steering in a planar array of Neumann scatterers

We study the canonical problem of wave scattering by periodic arrays, either of infinite or finite extent, of Neumann scatterers in the plane; the characteristic lengthscale of the scatterers is considered small relative to the lattice period. We utilise the method of matched asymptotic expansions, together with Fourier series representations, to create an efficient and accurate numerical approach for finding the dispersion curves associated with Floquet–Bloch waves through an infinite array of scatterers. The approach lends itself to direct scattering problems for finite arrays and we illustrate the flexibility of these asymptotic representations on topical examples from topological wave physics.     

Sound attenuation of a periodic array of micro-perforated tube mufflers

The wave propagation in a periodic array of micro-perforated tube mufflers is investigated theoretically, numerically and experimentally. Because of the high acoustic resistance and low mass reactance due to the sub-millimeter perforation, the micro-perforated muffler can provide considerable sound attenuation of duct noise. Multiple mufflers are often used to enhance attenuation performance. When mufflers are distributed periodically in a duct, the periodic structure produces special dispersion characteristics in the overall sound transmission loss. The Bloch wave theory and the transfer matrix method are used to study the wave propagation in periodic micro-perforated tube mufflers and the dispersion characteristics of periodic micro-perforated mufflers are examined. The results predicted by the theory are compared with finite element method simulation and experimental results. The results indicate that the periodic structure can influence the performance of micro-perforated mufflers. With different periodic distances, the combination of the periodic structure and the micro-perforated tube muffler can contribute to the control of lower frequency noise with a broader frequency range or improvement of the peak transmission loss around the resonant frequency.     

Instability of two-phase flows: A lower bound on the dimension of the global attractor of the Cahn-Hilliard-Navier-Stokes system

We consider a model for the flow of a mixture of two viscous and incompressible fluids in a two or three dimensional channel-like domain. The model consists of the Navier-Stokes equations governing the fluid velocity coupled with a convective Cahn-Hilliard equation for the relative density of atoms of one of the fluids. We prove the instability of certain stationary solutions for such a system endowed with periodic boundary conditions on elongated domains (0,2π/α₀)×(0,2π) or (0,2π/α₀)×(0,2π)×(0,2π/β₀) for a special class of periodic body forces, provided that α₀ and β₀ are small enough. As a consequence, we deduce a lower bound for the Hausdorff dimension of the global attractor.     

Almost global stability of nonlinear switched systems with mode-dependent and edge-dependent average dwell time

It has recently been shown that almost global stability of nonlinear switched systems can be characterized using multiple Lyapunov densities. This has been accomplished for switched systems subject to a minimum dwell time or an average dwell time constraint. In this paper, as an extension of the aforementioned results, we provide a sufficient condition on mode-dependent and edge-dependent average dwell time to ensure almost global stability of a nonlinear switched system. The relations between average dwell time, mode-dependent, and edge-dependent average dwell time have been discussed. The obtained results for nonlinear switched systems imply the existing results for linear switched systems.     

Stabilization of novel multi-layer networks with noise-based nonlinear superior couplings via aperiodically adaptive intermittent pinning control

In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.     

Effect of the Noise Correlation Time on the Stationary Current of Brownian Particle in a Spatially Symmetric Periodic Potential

We investigate the noise-induced transport of Brownian particle in a deterministic spatial symmetrical periodic potential driven by colored cross correlation between a multiplicative white noise and an additive white noise. We derive the general formula of the stationary current. Based on numerical computation, we found that directed motion of the Brownian particles can be induced by the correlation time τ of cross correlation between the multiplicative noise and the additive noise and the current reversal and the direction of the current is controlled by the τ.     

Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.