The Elimination of Grains and Grain Boundaries in Grain Growth

The topological changes that occur during coarsening of 2D and 3Dcellular structures, such as polycrystals, areinvestigated. Particular attention is given to the elimination ofgrain boundaries and grains with more than the minimum number oftopological elements. A thermodynamic criterion is introduced tofind out which topological transformations are favoured, based on theevaluation of the Gibbs free energy of the initial and finalconfigurations. In general, elimination of grains is possible only ifthe number of their neighbours is below a critical value, which maybe affected by geometry.     

Study on the dispersion characteristic of the plasma-loaded relativistic BWO

The dispersion characteristic of the plasma-loaded relativistic backward wave oscillator has been analyzed. The theoretical model has been established and the numerical calculations accord with the experimental results, which provides some useful suggestions on the designing of slow-wave structure of BWO.     

具有新光学性质的Zn-Zn2SiO4纳米同轴线阵列

采用气相沉积技术在Si衬底上生长了Zn-Zn₂SiO₄芯-壳结构纳米同轴线阵列。根部呈笋状的纳米同轴线,直径约100nm,长度可以超过10μm;同轴线芯直径约50nm、壳层厚约25nm。通过X射线衍射的表征以及能量色散谱的线扫描,确定纳米同轴线的芯为Zn,壳层为Zn₂SiO₄。我们提出了一种新的生长机制,同时也为生长均匀的纳米同轴线提供一种新的技术。观察阴极荧光谱发现,纳米同轴线有三个主要发光带:强度最大的中紫外300nm发光、较弱的可见光区560nm以及红外谱区865nm的发光。对纳米同轴线截面的300nm发光峰观测发现,中紫外发光来源于Zn₂SiO₄壳层。正是这种同轴线的结构,使得其具备特殊的光学性质。     

Monte Carlo simulation of grain growth in polycrystalline materials

Understanding the kinetics of grain growth, under the influence of second phase (such as impurities, voids and bubbles) is fundamental to advances in the control of microstructural evolution. As a precursor to this objective, we have investigated the grain growth kinetics in a polycrystalline material using a standard Q-state Potts’ model under Monte Carlo settings. Based on physical reasoning, new modifications are suggested to circumvent some of the disadvantages in the basic Potts model. The efficacy of these modifications vis-à-vis the basic model is verified. The influence of second phase particles on the impurity loaded grain boundaries is investigated for the study of grain growth kinetics.     

Excess isentropic compressibility and speed of sound of the ternary mixture 2-propanol + diethyl ether + n-hexane and the constituent binary mixtures at 298.15 K

Speed of sound and densities of the ternary mixture 2-propanol + diethyl ether + n-hexane and also the binary mixtures 2-propanol + diethyl ether and 2-propanol + n-hexane have been measured at the entire composition range at 298.15 K. The excess isentropic compressibilities and the excess speed of the sound have been calculated from experimental densities and speed of sound. These excess properties of the binary mixtures were fitted to Redlich-Kister equation, while the Cibulka’s equation was used to fit the values related to the values to the ternary system. These excess properties have been used to discuss the presence of significant interactions between the component molecules in the binary mixtures and also the ternary mixtures. Speed of sound of the binary mixtures and the ternary mixture have been compared with calculated values from free length theory (FLT), collision factor theory (CFT), Nomoto’s relation (NR), Van Deal’s ideal mixing relation (IMR) and Junjie’s relation (JR). The results are used to compare the relative merits of these theories and relations in terms of the root mean square deviation relative (RMSD_r).     

Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

生长曲线模型中回归系数阵的极大似然估计的精确分布

对于生长曲线模型,基于理论发展和应用效果的考虑,本文引入了Gauss型误差．在此误差下,本文研究了模型中回归系数阵的极大似然估计的精确分布,求出了此分布的密度和特征函数．     

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency.     

经济增长与宏观经济运行模型

对国民经济进行宏观调控，如同经济增长问题一样是一个永恒问题，对宏观调控的基本内容，手段，方法，国内外学者已进行了较多的规范性讨论，尤其是在数理分析方面，也已有许多具有普遍意义的成果，但是，要把那些成果转化为“生产力”从而变成清晰的，简明的，可操作的手段和方法，尚需人们不断的探索，本文通过对国民经济运行过程中若干宏观经济变量之间的数量关系分析，并以此建立了的国民经济宏观数量模型，就是尝试性的探索。     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.