考虑时滞效应与均值-方差效用的非零和投资与再保险博弈

在考虑时滞效应的影响下研究了非零和随机微分投资与再保险博弈问题.以最大化终端绝对财富和相对财富的均值-方差效用为目标,构建了两个相互竞争的保险公司之间的非零和投资与再保险博弈模型,分别在经典风险模型和近似扩散风险模型下探讨了博弈的Nash均衡策略.借助随机控制理论以及相应的广义Hamilton-Jacobi-Bellm...     

Construction of a Chemical Kinetic Model of Five-Component Gasoline Surrogates under Lean Conditions

The requirements for improving the efficiency of internal combustion engines and reducing emissions have promoted the development of new combustion technologies under extreme operating conditions (e.g., lean combustion), and the ignition and combustion characteristics of fuels are increasingly becoming important. A chemical kinetic reduced mechanism consisting of 115 species and 414 elementary reactions is developed for the prediction of ignition and combustion behaviors of gasoline surrogate fuels composed of five components, namely, isooctane, n-heptane, toluene, diisobutylene, and cyclohexane (CHX). The CHX sub-mechanism is obtained by simplifying the JetSurF2.0 mechanism using direct relationship graph error propagating, rate of production analysis, and temperature sensitivity analysis and CHX is mainly consumed through ring-opening reactions, continuous dehydrogenation, and oxygenation reactions. In addition, kinetic parameter corrections were made for key reactions R14 and R391 based on the accuracy of the ignition delay time and laminar flame velocity predictions. Under a wide range of conditions, the mechanism’s ignition delay time, laminar flame speed, and the experimental and calculated results of multi-component gasoline surrogate fuel and real gasoline are compared. The proposed mechanism can accurately reproduce the combustion and oxidation of each component of the gasoline-surrogate fuel mixture and real gasoline.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化,研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板,采用层合板表面连续变化的速度环量来模拟空气对其的作用,速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性,分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明,通过纤维的变角度铺设,可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

Singularities and spectral asymptotics of a random nonlinear wave in a nondispersive system

In this paper, we study the propagation of high-intensity acoustic noise in free space and in waveguide systems. A mathematical model generalizing the Burgers equation is used. It describes the nonlinear wave evolution inside tubes of variable cross-section, as well as in ray tubes, if the geometric approximation for heterogeneous media is used. The generalized equation transforms to the common Burgers equation with a dissipative parameter, known as the “Reynolds–Goldberg number”. In our model, this number depends on the distance travelled by the wave. With a zero “viscous” dissipative term, the model reduces to the Riemann (or Hopf) equation. Its solution presents the field by an implicit function. The spectral form of this solution makes it possible to derive explicit expressions for both dynamic and statistical characteristics of intense waves. The use of a spectral approach allowed us to describe the high-intensity noise in media with zero and finite viscosity. Applicability conditions of these solutions are defined. Since the phase matching is fulfilled for any triplet of interacting spectral components, there is an avalanche-like increase in the number of harmonics and the formation of shocks. The relationship between these discontinuities and other singularities and the high-frequency asymptotic of intense noise is studied. The possibility is shown to enhance nonlinear effects in waveguide systems during the evolution of noise.     

Vertex correction and conductivity in 2D Dirac-like systems with non-conserving spin disorder

We determine the classical diffusion of two dimensional Dirac-like quasiparticles, in the presence of conserving spin disorder (scattering off electric impurities) and non-conserving spin disorder (scattering off magnetic impurities). We use the Kubo formula for the conductivity tensor and employ diagrammatic perturbation theory to calculate the vertex correction and the renormalisation of the current operator for both electric and magnetic scattering. Scattering off electric impurities is isotropic and the current operator renormalised to two times the bare current operator irrespective of the direction of the dynamics, as usual for Dirac-like fermions. For magnetic scattering the renormalisation of the current operator depends on the direction of the dynamics and on the polarisation of the magnetic impurities, making the system anisotropic. We calculate the anisotropic magnetoresistance (AMR) and analyse it as a function of the ratio of the strength of the electric to the magnetic scattering potentials, for short range Gaussian correlation.     

The effect of two ferromagnetic metal stripes on valley polarization of electrons in a graphene

As the key factor for designing the valleytronic devices is to well understand the valley-dependent transport mechanism in graphene, we investigate, in this work, the effect of two ferromagnetic (FM) metal stripes on the valley polarization in a graphene nanostructure with a strain. The nearly 100% valley polarization is observed at certain energy windows and it can be easily controlled through changing the width and the position of the FM stripe as well as the strength of the magnetic field induced by the FM stripe. Our interesting findings reveal the valley-dependent transport mechanism of electrons and promote the realization of the new types of valleytronic devices modulated by the FM stripe and the strain.     

Stationary optical solitons with Sasa–Satsuma equation having nonlinear chromatic dispersion

This paper retrieves stationary optical solitons to Sasa–Satsuma equation that carries nonlinear chromatic dispersion. The solutions are in terms of Gauss' hypergeometric functions and consequently the convergence criteria are also listed.     

A new approach to solve the one-dimensional Schrödinger equation using a wavefunction potential

A new approach to find exact solutions to one–dimensional quantum mechanical systems is devised. The scheme is based on the introduction of a potential function for the wavefunction, and the equation it satisfies. We recover known solutions as well as to get new ones for both free and interacting particles with wavefunctions having vanishing and non–vanishing Bohm potentials. For most of the potentials, no solutions to the Schrödinger equation produce a vanishing Bohm potential. A (large but) restricted family of potentials allows the existence of particular solutions for which the Bohm potential vanishes. This family of potentials is determined, and several examples are presented. It is shown that some quantum, such as accelerated Airy wavefunctions, are due to the presence of non–vanishing Bohm potentials. New examples of this kind are found and discussed.     

Solitons and conservation laws in magneto–optic waveguides having parabolic–nonlocal law of refractive index

This paper reveals soliton solutions to magneto–optic waveguides that maintain parabolic–nonlocal law of refractive index. The unified Riccati equation expansion together with extended auxiliary equation approach together reveal bright, dark, singular as well as straddled optical solitons. These soliton solutions are obtained through a limiting process when the modulus of ellipticity approaches unity. Finally, the conservation laws are also listed.     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.