A multistep flux-corrected transport scheme

A multistep flux-corrected transport (MFCT) scheme is developed to achieve conservative and monotonic tracer transports for multistep dynamical cores. MFCT extends Zalesak two-time level scheme to any multistep time-differencing schemes by including multiple high-order fluxes in the antidiffusive flux, while computing the two-time level low-order monotone solution. The multistep time-differencing scheme used in this study is the third-order Adams–Bashforth (AB3) scheme implemented in a finite-volume icosahedral shallow-water model. The accuracy of AB3 MFCT is quantified by the shape-preserving advection experiments in non-divergent flow, as well as a cosine bell whose shape changes during advection in shear flow. AB3 MFCT has been shown to be insensitive to time step size. This make AB3 MFCT an attractive transport scheme for explicit high resolution model applications with small time step. MFCT is tested in shallow-water model simulations to demonstrate that the use of MFCT maintains positive-definite tracer transport, while at the same time conserving both fluid mass and tracer mass within round-off errors in the AB3 dynamic core.     

New existing results for a system of nonlinear third-order differential equation via fixed point index

By using fixed point index theory, we investigate a system of nonlinear third-order differential equation. We give some sufficient conditions for the existence of at least one or two positive solutions to the system of nonlinear third-order differential equation. As applications, we also present two examples to demonstrate the main results.     

2-(芘-1-基)-1,8-萘啶的合成、理论计算及超快三阶非线性光学响应

合成了一个供体-受体(D-A)型含芘萘啶衍生物2-(芘-1-基)-1,8-萘啶(PN)。 通过核磁共振波谱(NMR)、傅里叶变换红外光谱(FTIR)、液-质联用仪(LC-MS)表征了其结构。 通过电子光谱和Z-扫描技术方法分别研究了化合物PN的线性光学性质和三阶非线性光学吸收,采用综合热分析方法测定了它的热稳定性。 结果表明,在532 nm、180 fs条件下,PN的三阶非线性吸收行为为反饱和吸收,其吸收系数为β=9.0×10^-14 m/W,显示出超快三阶非线性光学响应。 运用密度泛函理论方法计算了分子轨道能量、极化率和超极化率,结果表明电子转移能够在分子内部进行。 2-(芘-1-基)-1,8-萘啶的紫外光谱在450 nm以上无吸收,在非线性光学吸收、激光防护、吸收型光开关或双稳器件等方面可作备选材料。     

A first-second order splitting method for a third-order partial differential equation

A splitting of a third order partial differential equation into a first-order and a second-order one is proposed as the basis for a mixed finite element method to approximate its solution. A time-continuous numerical method is described and error estimates for its solution are demonstrated. Finally, a full discretization is described based on backward Euler finite differences in time, and error estimates for the resulting approximation are established. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 89–96, 1998     

Synthesis of ladder polymers containing polydiacetylene backbones connected with methylene chains and their optical properties

The polymers consisting of polydiacetylene (PDA) backbones were obtained from the novel monomer derivatives, R CC CC R′ CC CC R [where R =  (CH₂)₄OCONHCH₂COOC₄H₉, R′ =  (CH₂)_n ; n = 2, 4, 8] [4BCMU4A(n)], in which linear methylene chain is sandwiched between two diacetylene moieties by solid-state 1,4-addition reaction. The polymerization process was investigated in detail by using spectroscopic techniques such as solid-state ¹³C-NMR, visible absorption, and IR absorption spectra. It was estimated that the polymerization of 4BCMU4A(8) and 4BCMU4A(4) takes place by two consecutive 1,4-addition reactions to form two PDA backbones, which constitute the two poles of the respective ladders. The bridging methylene chain length in the monomer was found to play a vital role as far as the polymerization process is concerned. Thus, the monomers with eight or four methylene units could form the ladder–PDAs by a two-step process, whereas the monomer containing two methylene units could only undergo one-step of 1,4-addition reaction. Further, it was found that the crystallinity of the polymers depends on the methylene chain length in the monomers, 4BCMU4A(8) being the most crystalline of all. These structural features strongly affect their absorption spectra. The third-order nonlinear optical susceptibilities (χ⁽³⁾) for these polymers were measured using third-harmonic generation method. The largest χ⁽³⁾ value obtained was 3.4 × 10⁻¹¹ esu for the poly[4BCMU4A(8)] thin film in resonant region. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3537–3548, 1999     

一类三阶非线性非自治系统解的有界性

本文利用一为三阶非线性自治系统的李雅夫函数,给出了一类三阶非线性非自治系统解有界的充分性准则,推广了文「１－２」的结果。     

Tracking problem under a time-varying topology

This paper studies the multi-agent tracking problem of a third-order maneuvering target under uncertain communication environments. Each tracking agent is assumed to be a third-order system and can only use its own and neighbors＇ position, velocity, and acceleration information to design its control input. In this work, the uncertain communication environments are modelled by a finite number of constant Laplacian matrices together with their corresponding scheduling functions. Sufficient conditions for the existence of a tracking strategy have been expressed in terms of the solvability of linear matrix inequalities. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed tracking strategy.     

极化子效应对ZnS/CdSe量子点三阶极化率的影响

在有效质量近似下,利用量子力学的密度矩阵理论,采用无限深势阱模型,从理论上计算了考虑极化子效应后在导带子带间跃迁时ZnS/CdSe柱型核壳结构量子点二次电光效应(QEOE)和电吸收过程(EA)的三阶极化率。通过数值计算,分析了电子-LO声子和电子-IO声子相互作用对ZnS/CdSe柱型核壳结构量子点二次电光效应和电吸收过程的三阶极化率的影响。结果表明,极化子效应对二次电光效应的三阶极化率χ⁽³⁾_QEDE和电吸收过程的三阶极化率χ⁽³⁾_EA都有很大影响,并且影响的大小与量子点的尺寸大小有关。     

Computation of the oscillator strength and absorption coefficients for the intersubband transitions of the spherical quantum dot

The electronic structure and optical properties of one-electron Quantum Dot (QD) with and without an on-center impurity were investigated by assuming a spherically symmetric confining potential of finite depth. The energy eigenvalues and the state functions of QD were calculated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock Roothan (HFR) method. We have calculated the binding energy for the states 1s,1p,1d,1f, oscillator strengths, the linear and third-order nonlinear optical absorption coefficients as a function of the incident photon energy and incident optical intensity for the 1s–1p, 1p–1d and 1d–1f transitions. The existence of the impurity has great influence on the optical absorption spectra and the oscillator strengths. Also we found that the magnitudes of the total absorption coefficients of the spherical QD increase for transitions between higher states.     

Conditional linearizability criteria for a system of third-order ordinary differential equations

We provide linearizability criteria for a class of systems of two third-order ordinary differential equations that is cubically nonlinear in the first derivative, by differentiating a system of second-order quadratically nonlinear ordinary differential equations and using the original system to replace the second derivatives. The procedure developed splits into two cases: those for which the coefficients are constant and those for which they are variables. Both cases are discussed and examples given.