EFFECT OF EMPIRICAL COEFFICIENTS ON SIMULATION IN TWO-SCALE SECOND-ORDER MOMENT PARTICLE-PHASE TURBULENCE MODEL

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concept of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision. The proposed model is used to simulate gas-particle downer reactor flows. The computational results of both particle volume fraction and mean velocity are in agreement with the experimental results. After analyzing effects of empirical coefficient on prediction results, we can come to a conclusion that, inside the limit range of empirical coefficient, the predictions do not reveal a large sensitivity to the empirical coefficient in the downer reactor, but a relatively great change of the constants has important effect on the prediction.

Second-order two-scale analysis and numerical algorithms for the hyperbolic–parabolic equations with rapidly oscillating coefficients

We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.

DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

Extensions of An Approach to Generalized Fibonacci and Lucas Numbers with Binomial Coefficients

The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.

Theoretical Calculations on the Second-order Nonlinear Optical Property of Chiral Bis-corroles

The second-order nonlinear optical （NLO） properties of 5,10,15-triphenylcorrole （TPC）, 5,10,15,20-tetraphenylporphyrin （TPP） and L-amino acid bridged bis-corroles 1,2,3 and 4 have been calculated by using TDHF/PM3 method based on the RHF/6-31G （TPC and TPP） or semiempirical PM3 （1, 2, 3, 4） optimized geometries. Calculation results showed TPC and TPP have C1 and D2h symmetry, respectively when N-H protons are localized on the nitrogen atoms. TPC is the second-order NLO active chromophore due to the cancellation of centrosymmetrical structure and its first hyperpolarizability β increases to 11.524×10^-30 esu. Under electrical dipole approximation, βvalues of bis-corroles 1, 2, 3 and 4 vary from 9.831×10^-30 to 14.221×10^-30 esu, and no much improvement in the first hyperpolarizability was observed as compared to TPC monomer.However, β values of bis-corroles 1, 2, 3 and 4 are improved by about 4 times as compared to their bis-porphyrin counterparts. The analysis of β components indicates that β of this kind of bis-corroles is mainly contributed from its radial component βr. With the variation of amino acid side chains, βHRS, β,βxyz, βr and βa of bis-corroles change remarkably. Chiral L-amino acid bridged bis-corroles 2, 3 and 4 have a right-handed helix structure, and their chiral component βxyz matches βxyz ∝ r^2 ζ/L^4 （helix parameters）, showing the second-order chiral NLO response of these bis-corroles could be described by one-electron helical model theory. It was found that the radial component βr of chiral helix bis-corroles also matches βr ∝ r^2 ζ/L^4.

ANALYTICAL SOLUTION OF FLOW OF SECOND-ORDER NON-NEWTONIAN FLUIDS THROUGH ANNULAR PIPES

This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.

咪唑氧自由基分子NLO性质的密度泛函理论研究

采用密度泛函理论(DFT)UB3LYP方法,在6-31g(d)水平上对2,2'-(1,2-乙炔基-4,1-亚苯基)双[4,4',5,5'-四氢]咪唑氧自由基分子及其异构体的自旋耦合性质进行分析,并结合有限场(FF)方法计算它们的非线性光学(NLO)系数,以探讨咪唑氧环在共轭链不同位置时体系的自旋耦合规律和NLO系数.结果表明,所有体系基态自旋符合自旋极化规则,它们的极化率随自旋多重度的增加而减小;一阶超极化率因受分子对称性影响,对称性不同其一阶超极化率的变化也不同;二阶超极化率呈现随着自旋多重度的增加而增加的趋势.从理论上探讨这些自由基分子自旋耦合规律与NLO活性的关系,为有机自由基NLO材料的分子设计与实验研究提供一定的理论依据。

联吖叮氮氧自由基体系及其衍生物NLO性质的密度泛函理论研究

以实验合成的联吖叮氮氧自由基分子为母体,设计了7个自由基分子.采用密度泛函理论(DFT)UB3LYP/6-31g(d,p)方法对这些自由基分子不同自旋态的稳定性和非线性光学(NLO)系数进行计算.结果表明,联吖叮氮氧自由基分子及其衍生物三重态为稳定基态,符合自旋极化规则.引入给吸电子取代基使自由基体系的极化率αs与二阶超极化率γs值有所增大,且基团的给吸电子能力越强,αs和γs值增加越明显;对于一阶超极化率βtot,自由基体系处于单重态时,取代基的影响较大.所有自由基分子三重态的NLO系数都小于单重态,表明可以通过控制体系的自旋多重度来调节体系的NLO性质.

Analytical estimation of mixing coefficient induced by surface wave-generated turbulence based on the equilibrium solution of the second-order turbulence closure model

Based on the equations of motion and the assumption that ocean turbulence is of isotropy or quasi-isotropy, we derived the closure equations of the second-order moments and the variation equations for characteristic quantities, which describe the mechanisms of advection transport and shear instability by the sum of wave-like and eddy-like motions and circulation. Given that ocean turbulence generated by wave breaking is dominant at the ocean surface, we presented the boundary conditions of the turbulence kinetic energy and its dissipation rate, which are determined by energy loss from wave breaking and entrainment depth respectively. According to the equilibrium solution of the variation equations and available data of the dissipation rate, we obtained an analytical estimation of the characteristic quantities of surface-wave-generated turbulence in the upper ocean and its related mixing coefficient. The derived kinetic dissipation rate was validated by field measurements qualitatively and quantitatively, and the mixing coefficient had fairly good consistency with previous results based on the Prandtl mixing length theory.

Solvothermal Synthesis, Structure and the Secondorder NLO Properties of a Novel Non-metal 3-D Borophosphate:（NH4）2[B2P2O8（OH）2]

A new non-metal 3-D borophosphate compound formulated as(NH4)2[B2P2O8(OH)2](1)has been synthesized by a solvothermal method and characterized by elemental analysis,energy-dispersive X-ray spectroscopy(EDS),IR spectrum and single-crystal X-ray diffraction.The borophosphate(NH4)2[B2P2O8(OH)2]crystallizes in the cubic system,space group P213 with Z=2,a=b=c=7.586(4)?,V=436.6(4)?3,Mr=281.64,Dc=2.127 g/cm^3,λ=0.71073?,μ=0.551 mm^-1,F(000)=284,R=0.0277 and wR=0.0758 for 262 observed reflections with I>2σ(I)and S=1.082.Its structure is constructed by the connection of PO4 and BO3(OH)tetrahedra to form a 3-D anionic framework containing 4-and 8-membered rings(MRs),with two NH4+cations located in the channels of the 8-membered rings.The N–H…O hydrogen bonds are observed in its packing structure and enhanced the stability of crystal structure.In addition,its thermal stability,UV spectrum and second-order NLO properties have been also investigated.

Synthesis and characterization of multifunctional copolyimide incorporating triarylamine and NLO chromophore in backbone

Presents the synthesis of Copolyimide containing triarylamine and NLO chromophore in backbone by azo coupling of 4 nitrobenzenediazonium tetrafloroborate to copoly(amic acid) in organic solvent and characterized by IR and UV Vis spectra, which had high glass transition temperatrue and big second order nonlinear optical coefficient  x (2) .

非视距环境下基于改进卡尔曼滤波器的LLOP-Taylor定位方法

在无线通信定位中,无线信号中引入的非视距(Non-Line of Sight,NLOS)误差会严重降低系统的定位精度。针对上述问题,首先引入信息阈值和缩放因子,细分非视距误差的影响程度,对卡尔曼迭代过程中的增益进行更为精准的实时调整,利用改进后的卡尔曼滤波算法更大程度上消除了NLOS误差和系统测量误差;其次引入基于测距残差的加权系数对线性位置线(Linear Line of Position,LLOP)和Taylor定位方法的计算结果进行综合处理,进一步提高定位精度和稳健性。实验结果表明,在NLOS环境下,所提算法优于经典的LLOP算法、Chan算法、LLOP-Taylor算法和基于卡尔曼滤波的LLOP算法。

中心对称吡嗪衍生物电子光谱和三阶非线性光学性质的理论计算研究

采用量子化学 ab initio HF和半经验 ZINDO-SOS方法计算了吡嗪及其衍生物的电子光谱和三阶非线性光学系数 .结果表明 ,中心对称的吡嗪衍生物随着体系共轭链的增长 ,最大吸收谱线波长增大 ,前线轨道能级差减小 ,体系的三阶非线性光学系数增大 ;引入取代基后可改变其三阶非线性光学性质 .在相同骨架中引入吸电子基团— NO2 形成 A-π-A共轭结构 ,其三阶非线性光学系数比引入供电子基— NH2

H_3PAuR型单核Au(Ⅰ)配合物的结构和非线性光学系数的量子化学计算比较

采用量子化学ab initio和DFT中的不同方法和基组对H3PAuR型单核Au(Ⅰ)配合物结构和二阶NLO系数进行计算,探讨不同计算方法和Au基组对计算结果产生的影响.对计算结果分析表明,不同计算方法对Au(Ⅰ)配合物结构和二阶NLO系数影响较大,其中用考虑电子相关效应的DFT-B3LYP和MP2方法优化得到的Au—P配键长比用HF方法的短,相应的二阶NLO系数比HF方法的大2倍左右;同一计算方法下,Au基组中d轨道个数增加优化得到的Au—P配键键长减小;随着Au基组的增大,前线分子轨道能级差减小,其中SDD和CEP-121G基组之间的变化更明显.基组变化对分子二阶NLO系数的影响较小,多数分子Au取不同基组计算的βμ值相差在10%以内.

分散红掺杂高T_g聚合物母体的非线性光学性质的研究

利用具有非线性光学（ＮＬＯ）活性的分散红（ＤＲＩ）掺杂高玻璃化转变温度的酚酞聚羟基醚（ＰＨＰ）和酚酞－联苯二酚－二氯二苯酮三元共聚物（ＰＰＨＢＰ－ＤＣＢＰｃｏｐｌｙｍｅｒ），得到了两种掺杂型非线性光学材料．升温电晕极化（ＣＯＰＥＴ）表明有较高的取向和较慢松驰，并推算了极化场强度Ｅｐ和二阶非线性系数ｄ３３。

大气散射衰减定标系统设计

观测高能宇宙射线可通过大气荧光探测技术对次级粒子的研究间接实现,而次级粒子在大气传输中受到大气吸收、散射等影响,会影响探测的准确性。为定性定量地确定上述影响,设计了大气散射衰减定标系统,利用已知脉冲能量的激光器向指定方向发射激光脉冲,通过在地面上另外一点测量散射激光的能量,就可以对大气散射的参数进行标定,从而对次级粒子的能量及方向进行修正。此外通过散射通信中常用的非视距单次散射模型研究了大气传输过程中的散射衰减作用,得到不同角度下的计算仿真结果,为大气散射衰减定标提供了理论依据。

晶体二阶有效非线性系数在全卦限中的对称性

从分析二阶有效非线性系数公式入手，针对各类单轴、双轴晶体，讨论了其二阶有效非线性系数在其折射率主轴坐标系八个卦限中的变化情况，给出了相应的对称性结果．为寻求晶体中的最佳相位匹配方向提供了理论依据．

新型有机/无机复合非线性光学材料制备及特性

用溶胶 -凝胶 (Sol_Gel)法制备了含对硝基偶氮苯酚 (NHA)和分散橙 3(DO3)生色团的两种掺杂型有机 /无机复合非线性光学 (NLO)材料 ,并通过FTIR、1H_NMR、UV_VIS、DSC和二次谐波信号 (SHG)测量等方法对它们的制备过程和NLO性能进行了考察 .实验结果表明 :两种掺杂型聚合物膜的最高掺杂量分别为w =7.2 %和w =11.3% ;二阶非线性光学系数 (d33)值分别为 2 .91× 10 - 8esu和 6.14× 10 - 8esu ;两种聚合物膜的常温稳定性都较好 ,90d后d33 值都能保持其初值的 85%以上 ,373K下 10h后d33值也能保持其初值的 50 %左右 .

SYNTHESIS AND CHARACTERIZATION OF NOVEL SOL-GEL DOPED ORGANIC/INORGANIC HYBRID NONLINEAR OPTICAL MATERIALS

hydroxy-4-nitro azobenzene (NHA) and 4-amino-4-nitro azobenzene (DO3) were prepared respectively from p-nitrophenylamine as a precursor compound. Two kinds of doped organic/inorganic hybrid nonlinear optical (NLO) materials containing NHA and DO3 were synthesized by Sol-Gel process. The preparation and properties of two NLO materials were studied and characterized by FTIR, 1H-NMR, UV-VIS, SEM, DSC and SHG measurements. The results show that the maximum doping amounts of NHA and DO3 in two doped hybrid NLO materials are 7.2(wt)% and 11.3(wt)% respectively, and the corresponding second-order NLO coefficients (d33 values) are 2.91×10 8esu and 6.14×10 8esu. Two doped NLO materials have relatively good RT stability, after 90 days at RT the d33 values can maintain about 85% of their initial values, but after 10h at 100℃ can only maintain about 50% of their initial values. In this report, the reasons for high-temperature instability of doped materials were discussed, and the possible improvements were also suggested.

取代肉桂酸异构体的稳定性和二阶非线性光学性质的DFT研究

采用量子化学B3LYP/6-31G 方法对6种取代肉桂酸异构体分子的几何构型进行优化,通过计算比较了其稳定性、前线分子轨道和二阶非线性光学(NLO)系数.结果表明:肉桂酸异构体分子Ⅰ—Ⅵ中,—NH2和—NO2与甲氧基处于间位的异构体最稳定;前线分子轨道能级差顺序为ΔEg(Ⅰ)>ΔEg(Ⅱ)>ΔEg(Ⅲ)和ΔEg(Ⅳ)<ΔEg(Ⅴ)<ΔEg(Ⅵ);6个肉桂酸异构体分子的|βμ|值与典型共轭有机分子相似,表现出良好的二阶NLO活性.由于甲氧基与引入基团的给、吸电子性质相互作用,—NH2和甲氧基处于邻位的异构体二阶NLO系数最大,而—NO2和甲氧基处于对位的异构体二阶NLO系数最大.