三维等熵欧拉方程组解的爆破

研究了带阻尼项的三维等熵欧拉方程组初值问题经典解的爆破.在M(0)0条件下,若初始动量的某些泛函足够大时,得到了其经典解在有限时间内必定发生爆破的结论.     

Thermodynamic coefficients of ideal Fermi gas

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low-temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg .     

双温度氩-氮等离子体热力学和输运性质计算

获得覆盖较宽温度和压力范围内的等离子体热力学和输运性质是开展等离子体传热和流动过程数值模拟的必要条件.本文通过联立Saha方程、道尔顿分压定律以及电荷准中性条件求解等离子体组分;采用理想气体动力学理论计算等离子体热力学性质;基于Chapman-Enskog方法求解等离子体输运性质.利用上述方法计算了压力为0.1, 1.0和10.0 atm (1 atm=101325 Pa),电子温度在300—30000 K范围内,非局域热力学平衡(电子温度不等于重粒子温度)条件下氩-氮等离子体的热力学和输运性质.结果表明压力和非平衡度会影响等离子体中各化学反应过程,从而对氩-氮等离子体的热力学及输运性质有较大的影响.在局域热力学平衡条件下,计算获得的氩-氮等离子体输运性质和文献报道的数据符合良好.     

超临界CO2布雷登循环热电联供系统多目标优化

本文研究了以超临界CO₂布雷登循环为原动机的热电联供系统,对系统主要运行参数进行了分析,得到运行参数对于系统热力学性能和经济性能的影响规律。同时,以一次能源利用率和单位输出成本作为目标函数,采用多目标遗传算法对系统进行了优化;在优化结果的基础上,通过TOPSIS法决策出最优解,并与单目标最优解进行对比。结果表明,透平进口温度、透平进口压力和压缩机进口温度的增大有利于系统效率的提高;作为代价,成本也相应增加。在热电比0~4范围内,尽可能增大热电比能够最大程度上降低系统的单位输出成本,提高能源的利用率。     

非化学计量对铁氧化物还原热力学平衡的影响

铁氧化物是具有非化学计量比的化合物,非化学计量对铁氧化物的还原过程带来一系列影响。本文采用Dieckmann缺陷模型和Weiss的浮氏体理想固溶体模型分别对非化学计量比的磁铁矿和浮氏体进行了热力学计算。同时根据电荷守恒和物质守恒,对铁氧化物固溶体的综合缺陷度δ与还原失重率和亚铁含量的关系进行了分析,以期对实验终产物的判定提供依据。通过理论分析与计算,最终明确了不同化学计量比的磁铁矿和浮氏体在不同温度下的平衡还原势PCO(H2),即相应的优势区图。在给定还原势的纯赤铁矿等温还原过程(未有金属Fe生成时),当失重率小于6%时,还原产物属于Fe3+占优势的磁铁矿区域;当失重率高于6%时,反应进入Fe2+占优势的浮氏体区域。     

Fe--Sialon复合材料中 Fe3 Si 合成热力学分析及实验验证

对淤泥沙原料中Fe3 O4及其中间产物FeO和Fe可能参与的反应进行了热力学分析。结合绘制的不同CO分压下Fe-Si体系在C和SiO2过量下的优势区相图及Fe-O-N体系热力学参数状态图,得出体系中Fe元素最终以Fe3 Si形式存在,为淤泥沙合成O′-Sialon-SiC-Fe3 Si (即Fe-Sialon)复合材料提供了热力学理论依据。在热力学分析的基础上,以淤泥沙为主要原料,采用碳热还原氮化法制备了Fe-Sialon复合材料,并借助X射线衍射仪和扫描电子显微镜对烧结体的物相和显微形貌进行了表征,得出产物的主晶相为O′-Sialon,还含有少量的SiC和Fe3 Si相,晶粒呈现为纤维状、絮状或短柱状,与热力学分析结果( Fe元素最终以Fe3 Si存在)吻合。     

一类非线性斯图谟—刘维尔问题正解的存在性

本文讨论了非线性斯图谟-刘维尔方程[p(x)u'(x)]'+f[u(x)]=0在两端固定边条件下的边值问题,当p(x)是区间[0,1]上的分段线性函数时,其正解存在。     

分担依赖于函数的常数亚纯函数正规族

研究关于分担值的亚纯函数族的正规性,证明了如下结果:设k,n(≥k+3)是两个正整数,F为单位圆盘Δ内的一族亚纯函数,如果对于每一个f∈F,f的零点重级≥k,且存在仅依赖于f的非零有穷复数bf,cf满足:bf/cf是一个常数;min{σ(0,bf),σ(0,cf),σ(bf,cf)}≥m,这里m0;对于每一对f,g∈F,有f(k)-1/bfn-1fn=cfg(k)-1/bgn-1gn=cg,那么F在Δ内正规.     

Synthesis,characterization, speciation and biological studies on metal chelates of 1-benzoyl(1,2,4-triazol-3-yl)thiourea

Proton-ligand association constants of 1-benzoyl(1,2,4-triazol-3-yl)thiourea (BTTU) and its complex formation constants with some bivalent metal ions Ni(II), Co(II), Mn(II), Zn(II), and Cu(II), have been determined potentiometrically in 50% EtOH–H₂O and 0.1 M NaNO₃. The complexes formed in solution have a stoichiometry of 1:1 and 1:2 [M:L], where M represents the metal ion and L the BTTU ligand. The corresponding thermodynamic parameters are derived and discussed. The complexes are stabilized by enthalpy changes and the results suggest that complexation is an enthalpy-driven process. The effects of metal ion, ionic radius, electronegativity, and nature of ligand on the formation constants are discussed. The formation constants of the complexes with 3d transition metals follow the order Mn²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺ > Zn²⁺. The metal complexes were synthesized and characterized by elemental analyses, conductance, IR, ¹H NMR, and magnetic measurements. The low magnetic moment of 0.11 BM for the Cu(II) complex is suggestive of dimerization through Cu–Cu interaction. The concentration distribution diagrams of the complexes were evaluated. The ligands and their metal complexes have been screened in vitro against some bacteria and fungi.     

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method (ICM), a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements: the weak material element method and the tiny section element method. Three criteria (no structural singularity, no violated constraints and no change of structural weight) are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.The project supported by the National Natural Science Foundation of China (10472003) and Beijing Natural Science Foundation (3042002) The English text was polished by Yunming Chen.