Successive iteration and positive symmetric solution for a Sturm–Liouville-like four-point boundary value problem with a -Laplacian operator

In this paper, we consider the following Sturm–Liouville-like four-point p-Laplacian boundary value problem with the nonlinear term f depending on the first-order derivative subject to the boundary conditions By using a monotone iterative technique, the existence of symmetric positive solutions and corresponding iterative schemes are obtained.     

Unbounded positive solutions for m-point time-scale boundary value problems on infinite intervals

In this work, we consider the following second-order m-point boundary value problem on time scales $$\left\{\begin{array}{@{}l}(\phi_{p}(u^{\triangle}(t)))^{\nabla}+h(t)f(t,u(t),u^{\triangle }(t))=0,\quad t\in(0,+\infty)_{\mathbb{T}},\\[4pt]\displaystyle u(0)=\sum_{i=1}^{m-2}\alpha_{i}u(\eta_{i}),\qquad u^{\triangle}(+\infty)=\sum_{i=1}^{m-2}\beta_{i}u^{\triangle}(\eta_{i}).\end{array}\right.$$ We establish new criteria for the existence of at least three unbounded positive solutions. Our results are new even for the corresponding differential $({\mathbb{T}}={\mathbb{R}})$ , difference equation $({\mathbb{T}}={\mathbb{Z}})$ and for the general time-scale setting. An example is given to illustrate our results.     

Chaos in a modified van der Pol system and in its fractional order systems

Chaos in a modified van der Pol system and in its fractional order systems is studied in this paper. It is found that chaos exists both in the system and in the fractional order systems with order from 1.8 down to 0.8 much less than the number of states of the system, two. By phase portraits, Poincaré maps and bifurcation diagrams, the chaotic behaviors of fractional order modified van der Pol systems are presented.     

Multiple positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian

In this paper we consider the multiplicity of positive solutions for the one-dimensional p-Laplacian differential equation (?p^′(u^′))+q(t)f(t,u,u^′)=0, t∈(0,1), subject to some boundary conditions. By means of a fixed point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of multiple positive solutions to some multipoint boundary value problems.     

Model for spontaneous frequency sweeping of an Alfvén wave in a toroidal plasma

We study the frequency chirping signals arising from spontaneously excited toroidial Alfvén eigenmode (TAE) waves that are being driven by an inverted energetic particle distribution whose free energy is tapped from the generic particle/wave resonance interaction. Initially a wave is excited inside the Alfvén gap with a frequency determined from the linear tip model of Rosenbluth, Berk and Van dam (RBV) [1]. Hole/clumps structures are formed and are observed to chirp towards lower energy states. We find that the chirping signals from clump enter the Alfvén continuum which eventually produce more rapid chirping signals. The accuracy of the adiabatic approximation for the mode evolution is tested and verified by demonstrating that a WKB-like decomposition of the time response for the field phase and amplitude agree with the data. Plots of the phase space structure correlate well with the chirping dependent shape of the separatrix structure. A novel aspect of the simulation is that it performed close to the wave frame of the phase space structure, which enables the numerical time step to remain the same during the simulation, independent of the rest frame frequency.     

三种同轴双波纹周期慢波结构对比研究

利用Fourier级数展开法,给出了任意几何结构的表达式的求解方法.通过数值计算,对比分析了余弦、梯形和矩形波纹慢波结构(slow-wave structure,SWS)的色散特性.根据S参数理论,研究了这三种SWS纵向模式选择的特性,提出了在同轴慢波器件中加入同轴引出结构,可减少所需SWS周期数,不但使器件结构更为紧凑,还可避免纵模竞争从而提高器件效率、稳定产生微波频率.进一步通过KARAT 2.5维全电磁粒子模拟程序,探讨了分别采用三种SWS的相对论返波振荡器(backward-wave oscillator,BWO)的束-波作用的物理过程,设计了一种紧凑型、吉瓦级、同轴L波段BWO,分析了不同形状SWS的选取原则.在此基础上,开展了初步实验研究：在二极管电压为670 kV,电子束流为107 kA,引导磁场为075 T的条件下,输出微波峰值功率约为102 GW,微波波形半高宽为22 ns,功率转换效率约为142%,频率为161 GHz. 关键词： 同轴慢波结构 相对论返波振荡器 色散特性 高功率微波     

An integrated solution and analysis of bioluminescence tomography and diffuse optical tomography

While diffuse optical tomography (DOT) has been studied for years, bioluminescence tomography (BLT) is emerging as a promising optical molecular imaging tool. These two modalities have different goals. DOT is for reconstruction of optical parameters of a medium such as a breast from surface measurements induced by external sources. BLT is for reconstruction of a bioluminescent source distribution in a medium such as a mouse from surface measurements induced by internal bioluminescent sources. However, an important pre-requisite for BLT reconstruction is the knowledge on the distribution of optical parameters within the medium, which is the output of DOT. In this paper, we propose a mathematical model integrating BLT and DOT at the fundamental level; that is, performing the two types of reconstructions simultaneously instead of doing them sequentially. The model is introduced through minimizing the difference between predicted quantities and boundary measurements, as well as incorporating regularization terms. Then, we show the solution existence, introduce numerical schemes and prove convergence of the numerical solution. We also present numerical results to illustrate the utility of our approach.     

湍流的耗散及弥散相互作用理论

本文推导了表征耗散与弥散相互作用的新的湍流控制方程组,其特点是:用稳定性分析得到湍流动能产生项,再根据广义熵增原理推出并列存在的分别适用于强弱涡量的两个湍流动量方程。运用该理论已成功地计算了一些典型的湍流问题:湍流边界层中的马蹄涡拟序结构、钝体尾涡区的湍流能量逆转、湍流涡团散裂弛豫及各向异性分布,文中还给出了部分算例。     

The limits of hamiltonian structures in three-dimensional elasticity,shells, and rods

Summary This paper uses Hamiltonian structures to study the problem of the limit of three-dimensional (3D) elastic models to shell and rod models. In the case of shells, we show that the Hamiltonian structure for a three-dimensional elastic body converges, in a sense made precise, to that for a shell model described by a one-director Cosserat surface as the thickness goes to zero. We study limiting procedures that give rise to unconstrained as well as constrained Cosserat director models. The case of a rod is also considered and similar convergence results are established, with the limiting model being a geometrically exact director rod model (in the framework developed by Antman, Simo, and coworkers). The resulting model may or may not have constraints, depending on the nature of the constitutive relations and their behavior under the limiting procedure. The closeness of Hamiltonian structures is measured by the closeness of Poisson brackets on certain classes of functions, as well as the Hamiltonians. This provides one way of justifying the dynamic one-director model for shells. Another way of stating the convergence result is that there is an almost-Poisson embedding from the phase space of the shell to the phase space of the 3D elastic body, which implies that, in the sense of Hamiltonian structures, the dynamics of the elastic body is close to that of the shell. The constitutive equations of the 3D model and their behavior as the thickness tends to zero dictates whether the limiting 2D model is a constrained or an unconstrained director model. We apply our theory in the specific case of a 3D Saint Venant-Kirchhoff material andderive the corresponding limiting shell and rod theories. The limiting shell model is an interesting Kirchhoff-like shell model in which the stored energy function is explicitly derived in terms of the shell curvature. For rods, one gets (with an additional inextensibility constraint) a one-director Kirchhoff elastic rod model, which reduces to the well-known Euler elastica if one adds an additional single constraint that the director lines up with the Frenet frame. This paper is dedicated to the memory of Juan C. Simo This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan Simo.     

非参数逐步判别分析在脑中风分类诊断中的应用

本文采用不等带宽核密度估计的非参数逐步判别分析,使用SAS软件,对复旦大学附属中山医院78例脑中风样本病例,科学地进行了脑出血、脑缺血的分类诊断。经交叉证实法得判别正确率为:脑出血87 88%、脑缺血88 89%,总判别正确率88 46%,判别效果良好。应用78例训练样本建立的判别函数,在苏州大学附属医院2002年42例脑中风病人的分类诊断中,取得了成功的实际应用效果。