地方综合性院校开展数学建模协会活动的实践与研究

简要介绍了济南大学数学建模协会的开展情况,分析了地方综合性院校开展建模协会时存在的困难,指出了做好建模协会工作应当遵循的一些原则.     

Effect of Nanopores on the Phonon Conductivity of Crystalline CoSb3: A Molecular Dynamics Study

Molecular dynamics simulations have been performed to investigate the effect of nanometer-size pores on the phonon conductivity of single-crystal bulk CoSb₃. The cylindrical pores are uniformly distributed along two vertical principal crystallographic directions of a square lattice. Because pore diameter and porosity are two key factors that could affect the performance of the materials, they were varied individually in the ranges a ₀–6a ₀ and 0.1–5%, respectively, where a ₀ is the lattice constant of CoSb₃. The simulation results indicate that the phonon conductivity of nanoporous CoSb₃ is significantly lower than that of no-pore CoSb₃. The reduction of phonon conductivity in this simulation was consistent with the ballistic–diffusive microscopic effective medium model, demonstrating the ballistic character of phonon transport when the phonon mean-free-path is comparable with or larger than the pore size. Reducing pore diameter or increasing porosity are alternative means of effective reduction of the thermal conductivity of CoSb₃. These results are expected to provide a useful basis for the design of high-performance skutterudites.     

Molecular Dynamics Study of the Effects of Nanopores on the Tensile Mechanical Properties of Crystalline CoSb3

The effects of nanometer-size pores on the uniaxial tensile mechanical properties of single-crystal bulk CoSb₃ were investigated by classical molecular dynamics simulation. The pores were assumed to be cylindrical and uniformly distributed along two vertical principal crystallographic directions of a square lattice. The dependence of the effects of pores on pore diameter and porosity was examined separately, by varying pore diameter and porosity in the ranges a ₀–6a ₀ and 0.1–5%, respectively, where a ₀ is the lattice constant of CoSb₃. The results from simulation indicate that, at constant porosity, Young’s modulus remains almost constant whereas ultimate strength decreases as pore diameter increases. At constant pore diameter, Young’s modulus decreases monotonically as porosity increases exponentially; interestingly, variation of the ultimate strength is negligible. Numerically, the mechanical performance of systems containing nanopores is still desirable, although no better than that of the no-pore system. The results provide useful information for realistic application of skutterudites.     

磁尾中性片处一种反常电阻机制

本文在平板模型近似下探讨了磁尾中性片非绝热离子逆磁漂移不稳定性及其反常电阻。该不稳定性是由非绝热离子逆磁漂移激发的,非绝热离子的轨道漂移共振大大增强了不稳定性强度。相应的反常电阻率为10⁴(Q·m)量级,与触发磁尾磁场重联所需电阻值相近。     

EFFECTS OF MODE LOCALIZATION ON INPUT-OUTPUT DIRECTIONAL PROPERTIES OF STRUCTURES

The singular-value decomposition (SVD) is employed to study the effects of localization phenomena on input-output relationships, and power and energy transmission ratios of structures. For weakly and strongly coupled systems, existence of strong localization of singular vectors and abrupt veering of singular value loci are shown. Occurrence of strong localization causes abrupt changes in input-output directional properties. In contrast to eigenvalues, singular values do not veer away by introducing a disorder in weakly coupled systems. In particular, the use of singular values and vectors is computationally advantageous in considering multiple load cases. While eigenvalue-based analyses give information about the resonance frequencies and vibration modes of a structure, singular values of the structure are related to the forced response characteristics and give the dynamic behavior in the frequency domain. Representative examples in structural dynamics are presented.     

新显色剂PMNHA的合成、分析鉴定及其在分光光度测定钒中的应用

用1－甲基－2－萘甲酰基替换N－苯甲酰苯基羟胺（BPHA）的苯甲酰基，合成了一种新显色剂N－苯基－1－甲氧基－2－萘甲酰氧肟酸（N-phenyl-1-methoxy-2-naphthoyl hydroxamic acid，缩写为PMNHA）。根据元素分析、差热分析、质谱分析、核磁共振、红外光谱分析，确定PMNHA的组成和结构为 。该试剂的三氯甲烷溶液能很快从2.25-4.50mol/L HCl中萃取钒（V）的紫色配合物，其配合物最大吸收在540nm，很多外来离子，特别是大量的钛不干扰钒的测定，钒含量在0－28μg·g^-1范围遵守比耳定律。我们建立了一个高选择性和简便的用显色剂PMNHA分光光度测定钒的方法。     

Costas阵列编码与线性调频SFR信号分析

线性调频-Costas频率步进雷达信号是一种很有研究价值的雷达信号。针对线性调频-Costas频率步进雷达信号的需要研究总结了一套生成N阶Costas序列的方法，同时结合实际需要生成了多组64阶Costas序列。这些Costas阵列是具有良好相关特性的最佳离散信号，将Costas阵列编码与线性调频频率步进雷达信号结合起来构成了线性调频-Costas频率步进雷达信号。通过对该信号的模糊特性的理论和仿真结果的分析表明，这种信号不仅能够较大地抑制信号的模糊旁瓣的幅度。而且能解决距离-速度的多普勒耦合问题。     

1MeV Si+衬底加温注入Al0.3Ga0.7As/GaAs超晶格和GaAs的晶格损伤研究

用卢瑟福背散射／沟道技术研究了１ＭｅＶＳｉ⁺在衬底加温和室温下以不同剂量注入Ａｌ_0.3Ｇ_0.7Ａｓ／ＧａＡｓ超晶格和ＧａＡｓ后的晶格损伤。在衬底加温下，观察到Ａｌ_0.3Ｇａ_0.7Ａｓ／ＧａＡｓ超晶格和ＧａＡｓ都存在一个动态退火速率与缺陷产生速率相平衡的剂量范围，以及两种速率失去平衡的临界剂量。超晶格比ＧａＡｓ更难以损伤，并且它的两种速率失去平衡的临界剂量也大于ＧａＡｓ中的相应临界剂量，用热尖峰与碰撞模型解释了晶格损伤积累与注入剂量和衬底温度的关系。用ＣＮＤＯ／２量子化学方法计算了ＧａＡｓ和Ａｌ_xＧａ_1-xＡｓ中化学键的相对强度，并根据计算结果解释了注入过程中Ａｌ_0.3Ｇａ_0.7Ａｓ／ＧａＡｓ超晶格和ＧａＡｓ中晶格损伤程度的差别。 关键词：