An efficient numerical scheme for precise time integration of a diffusion-dissolution/precipitation chemical system

A numerical scheme based on an operator splitting method and a dense output event location algorithm is proposed to integrate a diffusion-dissolution/precipitation chemical initial-boundary value problem with jumping nonlinearities. The numerical analysis of the scheme is carried out and it is proved to be of order 2 in time. This global order estimate is illustrated numerically on a test case.

     

聚芳香杂环甲烯的三阶非线性光学效应与时间分辨光克尔效应

合成了一系列聚芳香杂环甲烯,包括聚吡咯甲烯和聚噻吩甲烯.采用四波混频法研究材料的共振三阶非线性光学效应(λ＝532nm),其共振二阶超分子极化率γ三阶非线性光学系数分别达到10^-30esu和10^-8esu.选择具有良好溶解性、成膜性的聚吡咯对二甲氨基苯甲烯(PPDMAB),采用飞秒时间分辨光克尔效应方法研究材料的非共振三阶非线性光学效应(λ=790nm).实验表明,翠绿亚胺碱溶液的光克尔信号仅表现一超快响应的成分,归功于π电子云扭转产生的非共振激发.PPDMAB的非共振二阶超分子极化率γ三阶非线性光学系数分别达到γ=5.78×10^-32esu和χ⁽³⁾=1.26×10^-10esu.     

Hille and Nehari type criteria for third-order dynamic equations

In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results.     

Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel

The effect of a third-order fluid on the peristaltic transport in an asymmetric channel is studied. The wavelength of the peristaltic waves is assumed to be large compared to the varying channel width, whereas the wave amplitudes need not be small compared to the varying channel width. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effects of Deborah number, phase difference, varying channel width and wave amplitudes on the pumping characteristics, streamline pattern and trapping phenomena are investigated. It is observed that the trapping regions increase as the channel becomes more and more symmetric and the trapped bolus volume decreases for increasing Deborah number, phase difference and varying channel width whereas it increases for increasing flow rate and wave amplitudes. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.     

聚酰胺酸及其接枝衍生物的三阶非线性光学性能研究

设计合成了苯代三聚氰胺与均苯四酸二酐缩聚物, 及不同侧链的p-π共轭缩聚物, 并以量子化学PM3/CIS方法为基础, 利用完全态求和(SOS)公式, 对不同侧链取代的聚酰胺酸的分子进行了几何构型优化, 并计算了其三阶非线性光学系数γ. 研究了不同侧链对聚合物三阶非线性性能的影响. 这些结果对合成具有优良加工性能的三阶非线性光学材料是有一定的指导作用.     

Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

Both the homometal cluster [P(ph₄)]₂[Mo₂O₂(μ-S)₂(S₂)₂] (1) and [Mo₂O₂(μ-S)₂(Et₂dtc)₂] (2) (Et₂dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145×10⁻³⁰ esu for (1) and 5.428×10⁻³⁰ esu for (2).     

含有陡峭势阱和凹凸非线性项的Kirchhoff型问题的多重正解*

在这篇文章中, 作者研究涉及凹凸非线性项的Kirchhoff型问题-(a + b ∫R3|▽u|²dx) Δu + λV (x)u = μf(x)|u|^q?2u + |u|^p?2u, x ∈ R³,u ∈ H¹(R³),其中a,b > 0 是常数, λ, μ > 0 是参数, 1 < q < 2, 4 < p < 6 且 V 是一个非负连续位势. 在f(x) 和 V 的合适条件下,此问题正解的存在性和集中性能够通过Nehari 流形和Ekeland 变分原理得到.     

Design of robust differential microphone arrays with the Jacobi–Anger expansion

Due to their small size, differential microphone arrays (DMAs) are very attractive. Moreover, they have been effective in combating noise and reverberation. Recently, a new class of DMAs of different orders have been developed with the MacLaurin’s series and the frequency-independent patterns. However, the MacLaurin’s series does not approximate well the exponential function, which appears in the general definition of the beampattern, when the intersensor spacing is not small enough. To circumvent this problem, we propose in this paper to approximate the exponential function with the Jacobi–Anger expansion. Based on this approximation and the frequency-independent Chebyshev patterns, we derive first-, second-, and third-order DMAs. Furthermore, in order to improve the robustness of DMAs against white noise amplification, we propose to use more microphones combined with minimum-norm filters. It is also shown that the Jacobi–Anger expansion is optimal from a mean-squared error perspective. Simulations are carried out to evaluate the performance of the proposed DMAs.     

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.     

Chaotic flows with a single nonquadratic term

This paper addresses a previously unexplored regime of three-dimensional dissipative chaotic flows in which all but one of the nonlinearities are quadratic. The simplest such systems are determined, and their equilibria and stability are described. These systems often have one or more infinite lines of equilibrium points and sometimes have stable equilibria that coexist with the strange attractors, which are sometimes hidden. Furthermore, the coefficient of the single nonquadratic term provides a simple means for scaling the amplitude and frequency of the system.