一个非线性扩散方程的PAINLEVE-BACKLUND变换及其精确解

选择Painlevé-Backlund方程组的不同解,给出一类非线性扩散方程的某些精确孤立波解.这个方法也可以用来寻找其他非线性偏微分方程的精确孤立波解.     

一个非线性扩散方程的PAINLEV-BCKLUND变换及其精确解(英文)

选择Painlev啨 -B cklund方程组的不同解 ,给出一类非线性扩散方程的某些精确孤立波解 .这个方法也可以用来寻找其他非线性偏微分方程的精确孤立波解 .     

修正的非稳非线性Schrodinger方程的显式精确解

首先利用一个标准变换将修正的非稳非线性Schrodinger方程化成一个非线性偏微分方程组,接着通过选取不同参数得到一些非线性代数方程和非线性常微分方程.然后通过直接方法和假设方法的结合求得约化得到的非线性常微分方程的精确解,从而得到修正的非稳非线性Schrodinger方程的显式精确解,包括精确平面波解、钟状孤立波解、扭状孤立波解、奇异行波解和三角函数状周期波解.     

长短波共振方程的显式精确解

通过扩展的双曲函数方法获得了描述长短波相互作用的非线性发展方程的显式精确解.这些解包括S和L的钟状孤立波解,S的扭状及L的钟状孤立波解,S和L的钟状与扭状复合的孤立波解,4种奇异行波解,6种三角函数状周期波解,有理函数型行波解.展示了长短波方程精确解的结构的多样性.该方法也可以用于求多维非线性波方程的精确解.     

广义色散Camassa-Holm方程的精确解

为了研究非线性色散对Compacton和孤立波形成的作用,对非线性Camassa-Holm方程增加一色散项(ul)3x后得到广义色散Camassa-Holm方程.拟设该方程具有4种形式解,得到了丰富的精确解.讨论了在各种不同的非线性参数条件下,得到单峰、双峰Compacton解、斑图解、孤立波解、周期波解以及Kink Compacton解.研究了高维广义色散Camassa-Holm方程的精确解.结果表明,非线性和色散的相互作用是形成孤立波的关键.     

修正的非稳非线性Schrdinger方程的显式精确解

首先利用一个标准变换将修正的非稳非线性 Schro¨ dinger方程化成一个非线性偏微分方程组 ,接着通过选取不同参数得到一些非线性代数方程和非线性常微分方程。然后通过直接方法和假设方法的结合求得约化得到的非线性常微分方程的精确解 ,从而得到修正的非稳非线性 Schro¨ dinger方程的显式精确解 ,包括精确平面波解、钟状孤立波解、扭状孤立波解、奇异行波解和三角函数状周期波解     

一类非线性演化方程的新的精确波类解

通过Fan-辅助方程展开法,得到了一类非线性演化方程的一系列显式精确解,包括孤立波解、类孤立波解、奇异类孤立波解,以及纽结波解、奇异纽结波解和三角函数周期解.     

三阶非线性Schrödinger方程行波解的分支

用动力系统分支理论研究了三阶非线性Schr(o)dinger方程.证明了该方程存在光滑孤立波解、扭结和反扭结波解和光滑周期波解.在不同的参数条件下,给出了上述解存在的各类充分条件.求出了该方程的显式精确行波解.     

一类非线性波动方程新的精确孤立波解

利用双曲函数方法求解一类非线性波动方程的精确行波解，得到了若干其它方法不曾给出的新的精确解.这种方法的基本原理是利用非线性波方程孤立波解的局部特点，将方程的孤立波解表示为双曲函数的多项式，从而将非线性波动方程的求解问题转化为非线性代数方程组的求解问题.     

具波动算子的非线性Schrdinger方程的显式精确解

借助于一个规范变换和组合的假设方法,求出了具波动算子的非线性Schr dinger方程的一些显式精确行波解,包括精确的平面波解、扭状孤立波解、包络孤立波解、钟状扭状组合的孤立波解、奇异行波解和三角函数周期波解.展示了该方程解的结构的丰富多样性.     

盾构机密封舱渣土非线性本构模型参数识别

根据密封舱改性渣土的三轴压缩实验数据,建立了基于优化方法的Duncan-Chang双曲线本构模型参数反演方法。为了解决参数识别反问题解的不稳定性问题,在Gauss-Newton优化迭代算法的基础上,提出了正则化参数反演方法。实际应用结果表明,所提出的反演方法具有较快的收敛速度和较强的鲁棒性,预测的实验模型变形与实验值吻合较好。     

Electrochemical properties of LiNi<Subscript>0.5</Subscript>Mn<Subscript>1.3</Subscript>Ti<Subscript>0.2</Subscript>O<Subscript>4</Subscript>/Li<Subscript>4</Subscript>Ti<Subscript>5</Subscript>O<Subscript>12</Subscript> cells

Spinel compounds LiNi_0.5Mn_1.3Ti_0.2O₄ (LNMTO) and Li₄Ti₅O₁₂ (LTO) were synthesized by different methods. The particle sizes of LNMTO and LTO are 0.5–2 and 0.5–0.8 μm, respectively. The LNMTO/LTO cell exhibits better electrochemical properties at both a low current rate of 0.2C and a high current rate of 1C. When the specific capacity was determined based on the mass of the LNMTO cathode, the LNMTO/LTO cell delivered 137 mA·h·g⁻¹ at 0.2C and 118.2 mA·h·g⁻¹ at 1C, and the corresponding capacity retentions after 30 cycles are 88.5% and 92.4%, respectively.     

Kinetic parameters of oscillating reaction of amino acid- BrO3^——Mn^2＋-H2SO4-acetone system

In the previous papers[1—3], the oscillating reactionusing amino acids as organic substrates was studied. Inorder to obtain information about the kinetic parameters ofoscillating reaction of amino acids in amino acid- BrO3 - ?Mn2 -H2SO4-acetone sy…     

Preparation of Al<Subscript>72</Subscript>Ni<Subscript>8</Subscript>Ti<Subscript>8</Subscript>Zr<Subscript>6</Subscript>Nb<Subscript>3</Subscript>Y<Subscript>3</Subscript> amorphous powders and bulk materials

Amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were successfully fabricated by mechanical alloying. The microstructure, glass-forming ability, and crystallization behavior of amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were investigated by X-ray diffraction (XRD), transmission electron microscopy (TEM), and differential scanning calorimetry (DSC). The isothermal crystallization kinetics was analyzed by the Johnson–Mehl–Avrami equation. In the results, the supercooled liquid region of the amorphous alloy is as high as 81 K, as determined by non-isothermal DSC curves. The activation energy for crystallization is as high as 312.6 kJ·mol?1 obtained by Kissinger and Ozawa analyses. The values of Avrami exponent (n) imply that the crystallization is dominated by interface-controlled three-dimensional growth in the early stage and the end stage and by diffusion-controlled two- or three-dimensional growth in the middle stage. In addition, the amorphous Al₇₂Ni₈Ti₈Zr₆Nb₃Y₃ powders were sintered under 2 GPa at temperatures of 673 K and 723 K. The results show that the Vickers hardness of the compacted powders is as high as Hv 1215.     

Acid etching process for fabrication of Bi2Sr2CaCu2O8＋x stack

We adopted a new method, acid etching process, to fabricate the intrinsic Josephson junctions based on the Bi2Sr2CaCu2O8 x single crystals. By soaking the crystals into the dilute hydrochloric acid, we fabricated a junction stack successfully, and meantime made the surrounding area insulated. A certain concentration of hydrochloric acid was used to maintain the roughness of the modified layer. The cur-rent-voltage characteristic was achieved through the four terminal measurement. We could control the junctions' number by changing the concentration and the soaking time. We also found that the thick-ness of the stack was equal to the average height of the insulation layer. Such a simple, convenient and controllable fabrication method with a high yield might widen the applications of the intrinsic Joseph-son junctions.     

Investigation on high magnetoresistance Ni0.81Fe0.19 films grown on （Ni0.81Fe0.19）1-xCrx underlayers

We have fabricated Ni0.18Fe0.19 films with (Ni0.18Fe0.19)1-xCrx films as underlayers by dc magnetron sputtering, the results show that larger anisotropic magnetoresistance (△R/R) values of Ni0.18Fe0.19 films are observed using the underlayers with Cr concentration of -36 at.% at an optimum underlayer thickness of -4.4 nm, the maximum AMR value is 3.35%. The results of atomic force microscope (AFM) and X-ray diffraction (XRD) show that the △R/R enhancement is attributed to the formation of large average grain size and the strong(111)texture in the Ni0.18Fe0.19 films.     

基于遗传算法的带附加气室空气悬架多目标优化

以带附加气室的空气弹簧悬架为研究对象,按照物理模型建立带附加气室空气弹簧的数学模型,考虑到空气弹簧刚度的非线性,将该模型以空气弹簧非线性力的形式直接引入到1/4车辆模型。以提高车辆平顺性、行驶安全性及操纵稳定性的综合性能为目标,以附加气室容积为优化变量,设计带附加气室空气悬架的多目标优化模型;考虑到悬架性能各指标量在量纲与量级上的差异,对各指标量进行统一化处理,并采用线性加权和法将多目标函数转化为单目标评价函数。在MAT-LAB/Simulink中搭建系统仿真模型,采用遗传优化算法对典型工况下的最优附加气室容积进行寻优。优化结果表明,优化附加气室容积能有效提高悬架的综合性能,降低车身加速度、悬架动行程,但轮胎动载荷有所增加。     

Rolling-induced microstructure change in Zr_（65）Al_（7.5）Ni_（10）Cu_（12.5）Ag_5 bulk metallic glass

The microstructures and free-volume evolutions of as-cast and pre-annealed Zr65Al7.5Ni10Cu12.5Ag5 bulk metallic glasses during rolling deformation have been investigated. No phase transformation is detected in the as-cast/rolled specimen. However,the structural stability of the glass against plastic deformation is worse after pre-annealing,indicated by nanocrystallization in preannealed/rolled specimens with large deformation degrees. Moreover,with increasing deformation degree,the free-volume content in a pre-annealed/rolled specimen increases at a lower average rate than that in an as-cast/rolled specimen.     

Synthesis, Characterization and Calorimetry of Ni（C4H8N2O3）2Cl2

A coordination complex was synthesized from NiCl2 and dipeptide glycylglycine（GG）. It was characterized by element analysis, NMR and TG methods, and then was determined to be Ni（C4HsN2O3）2Cl2. Using an isoperibolic reaction calorimeter, the standard molar enthalpy of formation of Ni（GG）2Cl2（solid） has been determined to be -（1 674.66±2.02） kJ · mol^-1 at 298.15 K.     

Work toughening effect in Zr_（41）Ti_（14）Cu_（12.5）Ni_（10）Be_（22.5） bulk metallic glass

Work hardening is a well-known phenomenon occurring in crystalline metals during deformation,which has been widely used to increase the strength of metals although their ductility is usually reduced simultaneously. Here we report that the plastic strain of Zr41Ti14Cu12.5Ni10Be22.5 (at.%) bulk metallic glasses has been increased from 0.3% for the as-cast sample to 2.5%-8.0% for samples that have experienced pre-deformation under constrained conditions. The pre-deformed glassy alloys possess more free volume and abundant introduced shear bands,which are believed to promote the activation of shear bands in post-deformation and result in an increase in plasticity. The orientation of the pre-introduced shear bands relative to the loading direction will affect the deformation behavior of pre-deformed samples. The present results show that pre-deformation of this glassy alloy will result in work toughening. This work toughening effect can be removed by isothermal annealing at a sub-Tg (glass transition) temperature,which causes annihilation of free volume and healing of shear bands.