The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by a basic fact: mathematicians and computers are physical objects subject to the laws of physics. Through an analysis of the Turing machine, it becomes evident that Turing and his contemporaries overlooked a physical possibility: information carriers can be quantum systems. As a result, computing models like the Turing machine can only process classical information, limiting their computing power. Gödel's incompleteness theorem highlights the basic fact that mathematicians and computers are made up of finite numbers of atoms and molecules. They can only start with a finite number of axioms, use a finite number of symbols and deduction rules, and arrive at theorems with a finite number of steps. While the number of proofs may be infinite after including all future mathematicians and computers, they must still be enumerable. In contrast, the number of mathematical statements is uncountable, meaning that there will always be mathematical statements that cannot be proved true or false. Just as Landauer claimed that information is physical, mathematics is also physical, limited or empowered by the physical entities that carries it out or embodies it.
In this paper,an optimization design method for high field superconducting magnet with ferromagnetic shield is discussed.Firstly,the analytical formula for calculating the magnetic field at any space point is derived based on the equivalent magnetic charge model.Then the validity and accuracy of the formula are discussed by comparing the results with that of the finite element method(FEM)for the same model.Finally,a joint optimization of MRI magnet system with ferromagnetic shielding is carried out in order to improve the homogeneity of magnetic field in the DSV(diameter of spherical volum)region and enhance the field intensity in the center.
钙钛矿结构LaNiO3因其高电导的金属性输运行为,有望作为电极材料在今后的氧化物器件工艺中发挥重要作用.为了细致认识氧缺位对其金属输运的影响,本文采用溶胶凝胶法在氧气、空气和真空等气氛下烧结获得具有不同缺氧量的LaNiO3-δ薄膜,并利用Mn3+的还原性进一步调整其缺氧量δ.对这些样品的电阻率温度关系测量结果表明,缺氧量δ＞0.1后薄膜的高温电阻率开始超过Mott-Ioffe-Regel极限,变成"坏金属";增大δ至0.2,薄膜的低温剩余电阻率大幅度上升,说明氧空位分布无序性导致的载流子局域化有明显作用.以上样品的金属输运都呈非费米液体行为.继续增加氧缺位浓度,样品电阻率在低温～30 K以下呈绝缘体温度关系,同时高温金属态转变为费米液体行为,说明钙钛矿结构镍酸盐的金属-绝缘体转变与费米液体输运之间或存在关联性.
AuCu3型超导体兼具非平庸的拓扑能带,是近期受到关注的拓扑超导体候选材料之一.理论预言SrPb3具有非平庸的拓扑能带,然而,实验上尚未得到证实.本工作观察到德哈斯-范阿尔芬振荡,验证了 SrPb3中电子能带的非平庸拓扑性质.通过分析提取出两个振荡频率Fα=3.54 T和Fβ=7.43 T.进一步利用Lifshitz-Kosevich公式以及朗道量子化理论,得到两个对应费米面的载流子有效质量分别为m*α=0.006m.和m*β=0.008mo,同时它们的贝里相位分别为φαβ=(1.32±0.25)π和χβB=(1.10±0.25)π.这些结果表明SrPb3中存在有效质量接近于零的相对论费米子和非平庸拓扑能带.SrPb3中超导电性与非平庸拓扑能带的共存,为研究超导与拓扑的关联以及探索拓扑超导体提供新的研究体系.
以YBCO(YBa2Cu3O7-δ)为代表的二代高温超导带材因具有高临界转变温度、高临界磁场和强载流能力,受到了国际学界高度关注,在各个领域具有广泛的应用前景.二代高温超导带材在绕制、冷却和运行过程中会受到不同来源的外力作用,且超导带材的韧性、延展性较差,因此其机械性能是影响安全性与设备运行可靠性的关键.本文基于二代超导带材各向异性的特点,对超导带材轴向、横向、弯曲三个方向的静态机械性能及疲劳性能进行了介绍.同时,也对超导带材各方向机械性能的测试方法、影响因素及机理进行了总结.
