物理学与美学

探索物理学中美的因素,领悟自然科学之美,激发科学创新精神。     

原子结构中的物理理论

本文较系统地介绍了有关原子结构方面的一些基础理论,由定性到定量,并应用量子力学知识描绘了原子结构状态。     

新型三曲线机构与卡西尼卵形线

本文论述了由作者发明的可绘制双纽线、纺锤线及椭圆三种曲线的新型机构的构成特点;形成这三类曲线族机构连杆上浮动点的轨迹方程式及各类曲线形成的参数 l_6(=l_5)的域值;以及与标准椭圆和卡西尼卵形线的比较。     

一类双曲方程反问题的存在性和唯一性

讨论了如何确定下述双曲方程中反问题中的未知系数ｑ（ｘ），用压缩映像原理证明了反问题的存在性和唯一性定理。     

PDE-Based Medial Axis Extraction and Shape Manipulation of Arbitrary Meshes

Shape skeletonization （i.e., medial axis extraction） is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. In this paper, the authors expand the use of diffusion equations combined with distance field information to approximate medial axes of arbitrary 3D differential properties. It offers an alternative solids represented by polygonal meshes based on their but natural way for medial axis extraction for commonly used 3D polygonal models. By solving the PDE along time axis, this system can not only quickly extract diffusion-based medial axes of input meshes, but also allow users to visualize the extraction process at each time step. In addition, the proposed model provides users a set of manipulation toolkits to sculpt extracted medial axes, then use diffusion-based techniques to recover corresponding deformed shapes according to the original input datasets. This skeleton-based shape manipulation offers a fast and easy way for animation and deformation of complicated mesh objects.     

Liquid-Liquid Equilibrium for 1-Butanol-Water-KF and 1-Butanol-Water-K2CO3 Systems

KF or K2CO3 was added into the 1-butanol-water system and two phases were formed： water-rich phase （water phase） and 1-butanol-rich phase （1-butanol phase）. The liquid liquid equilibrium （LLE） data for 1-butanol-water-KF and 1-butanol-water-K2CO3 systems were measured at 25℃ and showed that 1-butanol phase contained negligible salt and water phase contained negligible 1-butanol when the concentrations of KF and K2CO3 in the water phase were equal to or higher than 27.11% and 31.68% , respectively. Thus water could be separated efficiently from 1-butanol-water by adding KF or K2CO3 into the system. A theoretical calculation of LLE data was calculated by using the Pitzer theory to get water activity in the water phase, and by the models, such as the Wilson, NRTL or the UNIQUAC for the 1-butanol phase. For 1-hutanol-water-KF system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and Wilson equa tion, while for 1-butanol-water-K2CO3 system, the experimental data were found in good agreement with the calculated results by using Pitzer theory and UNIQUAC eauation.     

二元体系气液平衡的测定和关联

本文在实验的基础上，用威尔逊方程对异丙醇（１）－环己烷（２）、甲醇（１）－水（２）和乙醇（１）－水（２）体系的气液平衡数据进行关联和预测；计算结果和实验数据符合良好。     

关于丢番图方程x2±xy+y2=p

设p是形如6k+1的正素数,运用数论方法及计算机程序,获得了丢番图方程x2-xy+y2=p在p<100000时的满足x相似文献   

关于系船水鼓受力的数学模型

对水鼓系泊系统在外力作用下产生的位移,建立了数学模型、给出位移解析式。并通过解析式对鼓体受外力后增加吃水深度、水平位移的大小与其它参数之间的关系、锚链上的张力情况以及锚链拖地情况进行了分析。     

一种基于偏微分方程的形态学边缘检测新方法

提出一种基于偏微分方程(PDE)的形态学腐蚀算子．在边缘检测中，直接对原图像求取一阶差分，利用该形态学腐蚀算子增强边缘梯度、降低噪声的影响，突破了传统的先低通滤波后计算梯度的边缘检测思路．形态学运算不会带来边缘位置的偏移，因此能够对图像的边缘准确定位，同时具有抗噪性．将新方法的边缘检测性能和Canny算子、Log算子做了比较，结果表明提出的边缘定位方法更加准确，具有更好的抗噪性能．