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有关圆周率的碰撞问题

光滑的地面上有两个静止的小木块, 离墙近的质量为$1$Kg, 离墙远的质量为$n$kg, 现给重的木块一定的速度使其向墙壁方向运动, 假设所有的碰撞都是弹性碰撞, 那么木块之间的碰撞次数和与墙壁之间的碰撞次数是多少? 这里可以给出这样的数据.

  • n = 1, 发生3次碰撞
  • n = 1e2, 发生31次碰撞
  • n = 1e4, 发生314次碰撞
  • n = 1e6, 发生3141次碰撞
  • n = 1e8, 发生31415次碰撞

Basel问题和圆周率的关系

1734年Euler给出了Basel 问题的解答, 也就是所有正整数的平方的倒数和:

[\sum_{i=1}^{\infty}\frac{1}{i^2} = \frac{\pi^2}{6}]

publications

Atom classification model for total energy evaluation of two-dimensional multicomponent materials

Chang-Chun He, Shao-Bin Qiu, Ju-Song Yu, Ji-Hai Liao, Yu-Jun Zhao, Xiao-Bao Yang "Atom Classification Model for Total Energy Evaluation of Two-Dimensional Multicomponent Materials. " J. Phys. Chem. A 124, 22, 4506–4511 (2020)
doi: https://doi.org/10.1021/acs.jpca.0c02431

All-boron planar ferromagnetic structures: from clusters to monolayers

Chang-Chun He, Shao-Gang Xu, Yu-Jun Zhao, Hu Xu and Xiao-Bao Yang "All-boron planar ferromagnetic structures: from clusters to monolayers." Nanoscale 13, 9881-9887 (2021).
doi: https://doi.org/10.1039/D1NR00981H

Biased screening for multi-component materials with Structures of Alloy Generation And Recognition (SAGAR)

Chang-Chun He, Ji-Hai Liao, Shao-Bin Qiu, Yu-Jun Zhao, Xiao-Bao Yang 2021. "Biased screening for multi-component materials with Structures of Alloy Generation And Recognition (SAGAR). " Comput. Mater. Sci. 193, 110386 (2021)
doi: https://doi.org/10.1021/acs.jpca.0c02431

Determining ground states of alloys by a symmetry-based classification

Yu-Jie Cen*, Chang-Chun He*, Shao-Bin Qiu, Yu-Jun Zhao, and Xiao-Bao Yang "Determining ground states of alloys by a symmetry-based classification " Phys. Rev. Mater. 6, L050801 (2022).
doi: https://doi.org/10.1103/PhysRevMaterials.6.L050801

Five-fold symmetry in Au–Si metallic glass

Chang-Chun He, Shao-Gang Xu, Shao-Bin Qiu, Chao He, Yu-Jun Zhao, Xiao-Bao Yang and Hu Xu "Five-fold symmetry in Au–Si metallic glass." Nanoscale 14, 12757-12761 (2022).
doi: https://doi.org/10.1039/D2NR02975H

Multi-peak emission of In2O3 induced by oxygen vacancy aggregation

Yin-Hui Peng*, Chang-Chun He*, Yu-Jun Zhao, Xiao-Bao Yang "Multi-peak emission of In2O3 induced by oxygen vacancy aggregation." J. Appl. Phys. 133 075702 (2023).
doi: https://doi.org/10.1063/5.0135162

Influence of element substitution on structural stability and hydrogen storage performance: a theoretical and experimental study on TiCr2-xMnx alloy

Wenbin Jiang*, Changchun He*, Xiaobao Yang, Xuezhang Xiao, Liuzhang Ouyang, Min Zhu 2023. "Influence of element substitution on structural stability and hydrogen storage performance: a theoretical and experimental study on TiCr2-xMnx alloy." Renewable Energy 197, 564-573 (2023).
doi: https://doi.org/10.1016/j.renene.2022.07.113

Generalized Octet Rule with Fractional Occupancies for Boron

Shaogang Xu*, Changchun He*, Yujun Zhao, Xiaobao Yang, and Hu Xu. 2024. "Generalized Octet Rule with Fractional Occupancies for Boron." J. Am. Chem. Soc. 145(45), 25003-25009 (2023).
doi: https://doi.org/10.1021/jacs.3c10370

The synergistic effect of neutron irradiation on the tensile properties of Fe-0.74 wt.% Ni alloy: A combined study of machine-learning and molecular dynamics

Chang-Chun He, Fen Ren, Xiao-Bao Yang, Guiyi Wu, Shuyan Zhang "The synergistic effect of neutron irradiation on the tensile properties of Fe-0.74 wt.% Ni alloy: A combined study of machine-learning and molecular dynamics." Phys. Lett. A 527 129992 (2024)
doi: https://doi.org/10.1016/j.physleta.2024.129992

Entropy-driven electron density and effective model Hamiltonian for boron systems

Chang-Chun He†, Shao-Gang Xu, Yu-Jun Zhao, Hu Xu, and Xiao-Bao Yang "Entropy-driven electron density and effective model Hamiltonian for boron systems." Phys. Rev. B 111, 085408 (2025)
doi: https://doi.org/10.1103/PhysRevB.111.085408

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