Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Energetic potential of hexogen constructed by machine learning

Wang Peng-Ju Fan Jun-Yu Su Yan Zhao Ji-Jun

Citation:

Energetic potential of hexogen constructed by machine learning

Wang Peng-Ju, Fan Jun-Yu, Su Yan, Zhao Ji-Jun
PDF
HTML
Get Citation
  • 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX) or hexogen, a high-insensitivity explosive, the accurately description of its energy and properties is of fundamental significance in the sense of security and application. Based on the machine learning method, high-dimensional neural network is used to construct potential function of RDX crystal. In order to acquire enough data in neural network learning, based on the four known crystal phases of RDX, the structural global search is performed under different spatial groups to obtain 15199 structure databases. Here in this study, we use nearby atomic environment to build 72 different basis functions as input neurons, in which the 72 different basis functions represent the interaction with nearby atoms for each type of element. Among them, 90% data are randomly set as training set, and the remaining 10% data are taken as test set. To obtain the better training effect, 9 different neural network structures carry out 2000 step iterations at most, thereby the 30-30-10 hidden layer structure has the lower root mean square error (RMSE) after the 1847 iterations compared with the energies from first-principles calculations. Thus, the potential function fitted by 30-30-10 hidden layer network is chosen in subsequent calculations. This constructed potential function can reproduce the first-principles results of test set well, with the RMSE of 59.2 meV/atom for binding energy and 7.17 eV/Å for atomic force. Especially, the RMSE of the four known RDX crystal phases from 1 atm to 6 GPa are 10.0 meV/atom and 1.11 eV/Å for binding energy and atomic force, respectively, indicating that the potential function has a better description of the known structures. Furthermore, we also propose four additional RDX crystal phases with lower enthalpy, which may be alternative crystal phases undetermined in experiment. In addition, based on molecular dynamics simulation with this potential function, the α-phase RDX crystal can stay stable for a few ps, further proving the applicability of our constructed potential function.
      Corresponding author: Su Yan, su.yan@dlut.edu.cn ; Zhao Ji-Jun, zhaojj@dlut.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 91961204), the Science Challenge Project (Grant No. TZ2016001), and the Fundamental Research Funds for the Central Universities, China (Grant No. DUT20ZD207)
    [1]

    王泽山 2006 含能材料概论 (哈尔滨: 哈尔滨工业大学出版社) 第4−8页

    Wang Z S 2006 Introduction to Energetic Material (Harbin: Harbin Institute of Technology Press) pp4−8 (in Chinese)

    [2]

    Infante-Castillo R, Pacheco-Londono L C, Hernandez-Rivera S P 2010 J. Mol. Struct. 970 51Google Scholar

    [3]

    Figueroa-Navedo A M, Ruiz-Caballero J L, Pacheco-Londono L C, Hernandez-Rivera S P 2016 Cryst. Growth Des. 16 3631Google Scholar

    [4]

    Choi C S, Prince E 1972 Acta Crystallogr., Sect. B: Struct. Sci. B 28 2857

    [5]

    Torres P, Mercado L, Cotte I, Hernandez S P, Mina N, Santana A, Chamberlain R T, Lareau R, Castro M E 2004 J. Phys. Chem. B 108 8799Google Scholar

    [6]

    Millar D I A, Oswald I D H, Francis D J, Marshall W G, Pulham C R, Cumming A S 2009 Chem. Commun. 5 562

    [7]

    Gao C, Yang L, Zeng Y, Wang X, Zhang C, Dai R, Wang Z, Zheng X, Zhang Z 2017 J. Phys. Chem. C 121 17586Google Scholar

    [8]

    Dreger Z A, Gupta Y M 2010 J. Phys. Chem. A 114 8099Google Scholar

    [9]

    Sorescu D C, Rice B M 2016 J. Phys. Chem. C 120 19547Google Scholar

    [10]

    Munday L B, Chung P W, Rice B M, Solares S D 2011 J. Phys. Chem. B 115 4378Google Scholar

    [11]

    Weingarten N S, Sausa R C 2015 J. Phys. Chem. A 119 9338Google Scholar

    [12]

    Mathew N, Picu R C 2011 J. Chem. Phys. 135 024510Google Scholar

    [13]

    Davidson A J, Oswald I D H, Francis D J, Lennie A R, Marshall W G, Millar D I A, Pulham C R, Warren J E, Cumming A S 2008 CrystEngComm 10 162Google Scholar

    [14]

    Ciezak J A, Jenkins T A 2008 Propellants Explos. Pyrotech. 33 390Google Scholar

    [15]

    Millar D I A, Oswald I D H, Barry C, Francis D J, Marshall W G, Pulham C R, Cumming A S 2010 Chem. Commun. 46 5662Google Scholar

    [16]

    Sorescu D C, Rice B M, Thompson D L 1997 J. Phys. Chem. B 101 798Google Scholar

    [17]

    Sorescu D C, Rice B M, Thompson D L 2000 J. Phys. Chem. B 104 8406Google Scholar

    [18]

    Guo Y, Thompson D L 1999 J. Phys. Chem. B 103 10599Google Scholar

    [19]

    Liu H, Zhao J, Ji G, Gong Z, Wei D 2006 Physica B 382 334Google Scholar

    [20]

    Kohno Y, Ueda K, Imamura A 1996 J. Phys. Chem. 100 4701Google Scholar

    [21]

    Duan X H, Li W P, Pei C H, Zhou X Q 2013 J. Mol. Model. 19 3893Google Scholar

    [22]

    Lysne P C, Hardesty D R 1973 J. Chem. Phys. 59 6512Google Scholar

    [23]

    Strachan A, van Duin A C T, Chakraborty D, Dasgupta S, Goddard W A 2003 Phys. Rev. Lett. 91 098301Google Scholar

    [24]

    van Duin A C T, Dasgupta S, Lorant F, Goddard W A 2001 J. Phys. Chem. A 105 9396Google Scholar

    [25]

    Guo F, Cheng X L, Zhang H 2012 J. Phys. Chem. A 116 3514Google Scholar

    [26]

    Wood M A, van Duin A C T, Strachan A 2014 J. Phys. Chem. A 118 885Google Scholar

    [27]

    Butler K T, Davies D W, Cartwright H, Isayev O, Walsh A 2018 Nature 559 547Google Scholar

    [28]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129Google Scholar

    [29]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [30]

    Rupp M, Tkatchenko A, Mueller K R, von Lilienfeld O A 2012 Phys. Rev. Lett. 108 058301Google Scholar

    [31]

    Bartok A P, Payne M C, Kondor R, Csanyi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

    [32]

    Vu K, Snyder J C, Li L, Rupp M, Chen B F, Khelif T, Mueller K R, Burke K 2015 Int. J. Quantum Chem. 115 1115Google Scholar

    [33]

    Hansen K, Montavon G, Biegler F, Fazli S, Rupp M, Scheffler M, von Lilienfeld O A, Tkatchenko A, Mueller K-R 2013 J. Chem. Theory Comput. 9 3404Google Scholar

    [34]

    Schuett K T, Arbabzadah F, Chmiela S, Mueller K R, Tkatchenko A 2017 Nat. Commun. 8 13890Google Scholar

    [35]

    Musil F, De S, Yang J, Campbell J E, Day G M, Ceriotti M 2018 Chem. Sci. 9 1289Google Scholar

    [36]

    Schran C, Behler J, Marx D 2020 J. Chem. Theory Comput. 16 88Google Scholar

    [37]

    Elton D C, Boukouvalas Z, Butrico M S, Fuge M D, Chung P W 2018 Sci. Rep. 8 9059Google Scholar

    [38]

    Akkermans R L C, Spenley N A, Robertson S H 2013 Mol. Simul. 39 1153Google Scholar

    [39]

    Day G M, Motherwell W D S, Ammon H L, Boerrigter S X M, Della Valle R G, Venuti E, Dzyabchenko A, Dunitz J D, Schweizer B, van Eijck B P, Erk P, Facelli J C, Bazterra V E, Ferraro M B, Hofmann D W M, Leusen F J J, Liang C, Pantelides C C, Karamertzanis P G, Price S L, Lewis T C, Nowell H, Torrisi A, Scheraga H A, Arnautova Y A, Schmidt M U, Verwer P 2005 Acta Crystallogr., Sect. B: Struct. Sci. 61 511Google Scholar

    [40]

    宋华杰, 李华, 张平, 杨延强, 黄风雷 2018 含能材料 26 1006

    Song H, Li H, Zhang P, Yang Y, Huang F 2018 Chin. J. Energ. Mater. 26 1006

    [41]

    Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169Google Scholar

    [42]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [43]

    Blochl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [44]

    Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135Google Scholar

    [45]

    Artrith N, Urban A, Ceder G 2017 Phys. Rev. B 96 014112Google Scholar

    [46]

    Behler J 2015 Int. J. Quantum Chem. 115 1032Google Scholar

    [47]

    Montavon G, Genevive B O, Müller K R (Eds.) 2012 Neural Networks: Tricks of the Trade, Lecture Notes in Computer Science (Ed. 2) (Vol. 7700) (Berlin Heidelberg: Springer-Verlag) p19

    [48]

    Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533Google Scholar

    [49]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

  • 图 1  高维神经网络结构示意图, C代表原子坐标, G代表基底函数, H代表隐藏层神经元, E代表原子能量, 下角标1, 2, ···, n为原子序号, ET为体系总能量

    Figure 1.  Structure of high-dimensional neural network. C, G, H, and E represent coordinates of atom, basis functions, hidden layer neurons, and energy of atom, respectively. Subscripts, 1, 2, ···, n are the serial numbers of atoms, and ET is the total energy of the system.

    图 2  (a) α相RDX晶体结构示意图; (b) 4种常见RDX分子构型示意图[10], 白球代表氢原子, 灰球代表碳原子, 蓝球代表氮原子, 红球代表氧原子

    Figure 2.  (a) Structure of α-RDX crystal; (b) structures of four usual types of RDX molecules.[10] The white, grey, blue, and red balls represent hydrogen, carbon, nitrogen, and oxygen atoms, respectively.

    图 3  (a) 9种隐藏层结构在400代之后测试集最低RMSE随迭代步数变化示意图; (b) 30-30-10隐藏层网络结构在1500代之后训练集和测试集RMSE随迭代步数变化示意图

    Figure 3.  (a) Diagram of test set lowest RMSEs variation along with training iteratons of nine types hidden layer neural structures after 400 iterations; (b) diagram of training and test sets RMSEs variation along with training iteratons of 30-30-10 hidden layer neural structures after 1500 iterations.

    图 4  (a) 训练集(黑色叉)和测试集(红色十字)所有结构第一性原理计算形成能和机器学习计算形成能对应关系图; (b) 训练集(黑色叉)和测试集(红色十字)所有结构第一性原理计算原子受力和机器学习计算原子受力对应关系示意图

    Figure 4.  (a) Correlation of machine learning binding energies with the corresponding ab initio reference energies for all structures in the training (black skew crosses) and testing (red crosses) sets; (b) correlation of machine learning atomic forces with the corresponding ab initio reference forces for all structures in the training (black skew crosses) and testing (red crosses) sets.

    图 5  0 K下4种已知RDX晶型在标准大气压到6 GPa压强下机器学习计算结合能的误差

    Figure 5.  Errors of machine learning binding energies of four known RDX crystals from 1 atm to 6 GPa at 0 K.

    图 6  (a) 4种RDX晶型结构示意图; (b) 7—10 GPa下4种晶型第一性原理计算(黑色方块)和机器学习势函数计算(红色圆圈)的焓值

    Figure 6.  (a) Structures of four RDX crystals; (b) enthalpies from 7 to 10 GPa calculated by ab initio (black block) and machine learning potential (red circle).

    图 7  (a) α相RDX 2 × 2 × 2晶胞在NVT系综下分子动力学模拟温度随时间变化图; (b) 压强随时间变化图

    Figure 7.  Variations in time of the temperature (a) and pressure (b) in the NVT ensemble for 2 × 2 × 2 α-RDX crystal.

    表 1  4×3个G2型径向基函数((1a)式)中η取值

    Table 1.  η of 4 × 3G2 type radial basis functions (Eq. (1a)).

    No.1—45—89—12
    η20.0032140.2142641.428426
    DownLoad: CSV

    表 2  10 × 6个G4型角向基函数((1b)式)中η, λ, ζ取值

    Table 2.  η, λ, and ζ of 10 × 6 G4 type angular basis functions (Eq. (1b)).

    No.13—2223—3233—4243—5253—6263—72
    η/10-4 Å23.573.573.573.573.573.57
    λ–1.01.0–1.01.0–1.01.0
    ζ1.01.02.02.04.04.0
    DownLoad: CSV

    表 3  训练集与测试集机器学习计算形成能和原子受力与第一性原理计算比较MAE和RMSE

    Table 3.  MAE and RMSE of machine learning binding energies and atomic forces corresponding ab initio reference energies and forces in the training and test sets.

    Energy/meV·atom1Force/eV·Å1
    MAERMSEMAERMSE
    Training set29.247.12.229.45
    Test set35.159.22.247.17
    DownLoad: CSV
  • [1]

    王泽山 2006 含能材料概论 (哈尔滨: 哈尔滨工业大学出版社) 第4−8页

    Wang Z S 2006 Introduction to Energetic Material (Harbin: Harbin Institute of Technology Press) pp4−8 (in Chinese)

    [2]

    Infante-Castillo R, Pacheco-Londono L C, Hernandez-Rivera S P 2010 J. Mol. Struct. 970 51Google Scholar

    [3]

    Figueroa-Navedo A M, Ruiz-Caballero J L, Pacheco-Londono L C, Hernandez-Rivera S P 2016 Cryst. Growth Des. 16 3631Google Scholar

    [4]

    Choi C S, Prince E 1972 Acta Crystallogr., Sect. B: Struct. Sci. B 28 2857

    [5]

    Torres P, Mercado L, Cotte I, Hernandez S P, Mina N, Santana A, Chamberlain R T, Lareau R, Castro M E 2004 J. Phys. Chem. B 108 8799Google Scholar

    [6]

    Millar D I A, Oswald I D H, Francis D J, Marshall W G, Pulham C R, Cumming A S 2009 Chem. Commun. 5 562

    [7]

    Gao C, Yang L, Zeng Y, Wang X, Zhang C, Dai R, Wang Z, Zheng X, Zhang Z 2017 J. Phys. Chem. C 121 17586Google Scholar

    [8]

    Dreger Z A, Gupta Y M 2010 J. Phys. Chem. A 114 8099Google Scholar

    [9]

    Sorescu D C, Rice B M 2016 J. Phys. Chem. C 120 19547Google Scholar

    [10]

    Munday L B, Chung P W, Rice B M, Solares S D 2011 J. Phys. Chem. B 115 4378Google Scholar

    [11]

    Weingarten N S, Sausa R C 2015 J. Phys. Chem. A 119 9338Google Scholar

    [12]

    Mathew N, Picu R C 2011 J. Chem. Phys. 135 024510Google Scholar

    [13]

    Davidson A J, Oswald I D H, Francis D J, Lennie A R, Marshall W G, Millar D I A, Pulham C R, Warren J E, Cumming A S 2008 CrystEngComm 10 162Google Scholar

    [14]

    Ciezak J A, Jenkins T A 2008 Propellants Explos. Pyrotech. 33 390Google Scholar

    [15]

    Millar D I A, Oswald I D H, Barry C, Francis D J, Marshall W G, Pulham C R, Cumming A S 2010 Chem. Commun. 46 5662Google Scholar

    [16]

    Sorescu D C, Rice B M, Thompson D L 1997 J. Phys. Chem. B 101 798Google Scholar

    [17]

    Sorescu D C, Rice B M, Thompson D L 2000 J. Phys. Chem. B 104 8406Google Scholar

    [18]

    Guo Y, Thompson D L 1999 J. Phys. Chem. B 103 10599Google Scholar

    [19]

    Liu H, Zhao J, Ji G, Gong Z, Wei D 2006 Physica B 382 334Google Scholar

    [20]

    Kohno Y, Ueda K, Imamura A 1996 J. Phys. Chem. 100 4701Google Scholar

    [21]

    Duan X H, Li W P, Pei C H, Zhou X Q 2013 J. Mol. Model. 19 3893Google Scholar

    [22]

    Lysne P C, Hardesty D R 1973 J. Chem. Phys. 59 6512Google Scholar

    [23]

    Strachan A, van Duin A C T, Chakraborty D, Dasgupta S, Goddard W A 2003 Phys. Rev. Lett. 91 098301Google Scholar

    [24]

    van Duin A C T, Dasgupta S, Lorant F, Goddard W A 2001 J. Phys. Chem. A 105 9396Google Scholar

    [25]

    Guo F, Cheng X L, Zhang H 2012 J. Phys. Chem. A 116 3514Google Scholar

    [26]

    Wood M A, van Duin A C T, Strachan A 2014 J. Phys. Chem. A 118 885Google Scholar

    [27]

    Butler K T, Davies D W, Cartwright H, Isayev O, Walsh A 2018 Nature 559 547Google Scholar

    [28]

    Blank T B, Brown S D, Calhoun A W, Doren D J 1995 J. Chem. Phys. 103 4129Google Scholar

    [29]

    Behler J, Parrinello M 2007 Phys. Rev. Lett. 98 146401Google Scholar

    [30]

    Rupp M, Tkatchenko A, Mueller K R, von Lilienfeld O A 2012 Phys. Rev. Lett. 108 058301Google Scholar

    [31]

    Bartok A P, Payne M C, Kondor R, Csanyi G 2010 Phys. Rev. Lett. 104 136403Google Scholar

    [32]

    Vu K, Snyder J C, Li L, Rupp M, Chen B F, Khelif T, Mueller K R, Burke K 2015 Int. J. Quantum Chem. 115 1115Google Scholar

    [33]

    Hansen K, Montavon G, Biegler F, Fazli S, Rupp M, Scheffler M, von Lilienfeld O A, Tkatchenko A, Mueller K-R 2013 J. Chem. Theory Comput. 9 3404Google Scholar

    [34]

    Schuett K T, Arbabzadah F, Chmiela S, Mueller K R, Tkatchenko A 2017 Nat. Commun. 8 13890Google Scholar

    [35]

    Musil F, De S, Yang J, Campbell J E, Day G M, Ceriotti M 2018 Chem. Sci. 9 1289Google Scholar

    [36]

    Schran C, Behler J, Marx D 2020 J. Chem. Theory Comput. 16 88Google Scholar

    [37]

    Elton D C, Boukouvalas Z, Butrico M S, Fuge M D, Chung P W 2018 Sci. Rep. 8 9059Google Scholar

    [38]

    Akkermans R L C, Spenley N A, Robertson S H 2013 Mol. Simul. 39 1153Google Scholar

    [39]

    Day G M, Motherwell W D S, Ammon H L, Boerrigter S X M, Della Valle R G, Venuti E, Dzyabchenko A, Dunitz J D, Schweizer B, van Eijck B P, Erk P, Facelli J C, Bazterra V E, Ferraro M B, Hofmann D W M, Leusen F J J, Liang C, Pantelides C C, Karamertzanis P G, Price S L, Lewis T C, Nowell H, Torrisi A, Scheraga H A, Arnautova Y A, Schmidt M U, Verwer P 2005 Acta Crystallogr., Sect. B: Struct. Sci. 61 511Google Scholar

    [40]

    宋华杰, 李华, 张平, 杨延强, 黄风雷 2018 含能材料 26 1006

    Song H, Li H, Zhang P, Yang Y, Huang F 2018 Chin. J. Energ. Mater. 26 1006

    [41]

    Kresse G, Furthmuller J 1996 Phys. Rev. B 54 11169Google Scholar

    [42]

    Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865Google Scholar

    [43]

    Blochl P E 1994 Phys. Rev. B 50 17953Google Scholar

    [44]

    Artrith N, Urban A 2016 Comput. Mater. Sci. 114 135Google Scholar

    [45]

    Artrith N, Urban A, Ceder G 2017 Phys. Rev. B 96 014112Google Scholar

    [46]

    Behler J 2015 Int. J. Quantum Chem. 115 1032Google Scholar

    [47]

    Montavon G, Genevive B O, Müller K R (Eds.) 2012 Neural Networks: Tricks of the Trade, Lecture Notes in Computer Science (Ed. 2) (Vol. 7700) (Berlin Heidelberg: Springer-Verlag) p19

    [48]

    Rumelhart D E, Hinton G E, Williams R J 1986 Nature 323 533Google Scholar

    [49]

    Plimpton S 1995 J. Comput. Phys. 117 1Google Scholar

  • [1] Du Bo-Chuan, Tian Pu. Variational analysis and AI algorithm implementation of free energy landscapes of molecular system. Acta Physica Sinica, 2024, 73(6): 068702. doi: 10.7498/aps.73.20231800
    [2] Song Tian-Shu, Xia Hui. Study on dynamic scaling behavior of Villain-Lai-Das Sarma equation based on numerically stable nueral networks. Acta Physica Sinica, 2024, 73(16): 160501. doi: 10.7498/aps.73.20240852
    [3] Ouyang Xin-Jian, Zhang Yan-Xing, Wang Zhi-Long, Zhang Feng, Chen Wei-Jia, Zhuang Yuan, Jie Xiao, Liu Lai-Jun, Wang Da-Wei. Modeling ferroelectric phase transitions with graph convolutional neural networks. Acta Physica Sinica, 2024, 73(8): 086301. doi: 10.7498/aps.73.20240156
    [4] Li Rui, Xu Bang-Lin, Zhou Jian-Fang, Jiang En-Hua, Wang Bing-Hong, Yuan Wu-Jie. A synaptic plasticity induced change in synaptic intensity variation and neurodynamic transition during awakening-sleep cycle. Acta Physica Sinica, 2023, 72(24): 248706. doi: 10.7498/aps.72.20231037
    [5] Zeng Qi-Yu, Chen Bo, Kang Dong-Dong, Dai Jia-Yu. Large scale and quantum accurate molecular dynamics simulation: Liquid iron under extreme condition. Acta Physica Sinica, 2023, 72(18): 187102. doi: 10.7498/aps.72.20231258
    [6] Peng Ya-Jing, Sun Shuang, Liu Wei-Na, Liu Yu-Hui. Initial dynamic response and reaction mechanism of cyclotrimethylenetrinitramine under shock loading. Acta Physica Sinica, 2021, 70(15): 158202. doi: 10.7498/aps.70.20201279
    [7] Chong Tao, Mo Jian-Jun, Zheng Xian-Xu, Fu Hua, Zhao Jian-Heng, Cai Jin-Tao. Dynamic behaviors of RDX single crystal under ramp compression. Acta Physica Sinica, 2020, 69(17): 176101. doi: 10.7498/aps.69.20200318
    [8] Sun Li-Wang, Li Hong, Wang Peng-Jun, Gao He-Bei, Luo Meng-Bo. Recognition of adsorption phase transition of polymer on surface by neural network. Acta Physica Sinica, 2019, 68(20): 200701. doi: 10.7498/aps.68.20190643
    [9] Peng Ya-Jing, Sun Shuang, Song Yun-Fei, Yang Yan-Qiang. Coherent anti-Stokes Raman scattering spectrum of vibrational properties of liquid nitromethane molecules. Acta Physica Sinica, 2018, 67(2): 024208. doi: 10.7498/aps.67.20171828
    [10] Wei De-Zhi, Chen Fu-Ji, Zheng Xiao-Xue. Internet public opinion chaotic prediction based on chaos theory and the improved radial basis function in neural networks. Acta Physica Sinica, 2015, 64(11): 110503. doi: 10.7498/aps.64.110503
    [11] Peng Ya-Jing, Jiang Yan-Xue. Analyses of the influences of molecular vacancy defect on the geometrical structure, electronic structure and vibration characteristics of Hexogeon energetic material. Acta Physica Sinica, 2015, 64(24): 243102. doi: 10.7498/aps.64.243102
    [12] Ge Wei-Kuan, Xue Yun, Lou Zhi-Mei. Generalized gradient representation of holonomic mechanical systems. Acta Physica Sinica, 2014, 63(11): 110202. doi: 10.7498/aps.63.110202
    [13] Hui Zhi-Xin, He Peng-Fei, Dai Ying, Wu Ai-Hui. Molecular dynamics simulation of the thermal conductivity of silicon functionalized graphene. Acta Physica Sinica, 2014, 63(7): 074401. doi: 10.7498/aps.63.074401
    [14] Wang Wen-Ting, Hu Bing, Wang Ming-Wei. Femtosecond laser fine machining of energetic materials. Acta Physica Sinica, 2013, 62(6): 060601. doi: 10.7498/aps.62.060601
    [15] Wang Rong, Wu Ying, Liu Shao-Bao. Effect of ion channel random blocking on the spatiotemporal dynamics of neuronal network. Acta Physica Sinica, 2013, 62(22): 220504. doi: 10.7498/aps.62.220504
    [16] Zhou Nai-Gen, Hu Qiu-Fa, Xu Wen-Xiang, Li Ke, Zhou Lang. A comparative study of different potentials for molecular dynamics simulations of melting process of silicon. Acta Physica Sinica, 2013, 62(14): 146401. doi: 10.7498/aps.62.146401
    [17] Li Hui-Shan, Li Peng-Cheng, Zhou Xiao-Xin. Role of potential function in high order harmonic generation of model hydrogen atoms in intense laser field. Acta Physica Sinica, 2009, 58(11): 7633-7639. doi: 10.7498/aps.58.7633
    [18] Chen Yu-Xiang, Xie Guo-Feng, Ma Ying, Zhou Yi-Chun. Molecular-dynamics simulation of the structure and elastic constants of barium titanium. Acta Physica Sinica, 2009, 58(6): 4085-4089. doi: 10.7498/aps.58.4085
    [19] Peng Ya-Jing, Liu Yu-Qiang, Wang Ying-Hui, Zhang Shu-Ping, Yang Yan-Qiang. Thermal dynamic analysis of picosecond and nanosecond single pulse laser flash-heating of Al/NC nanoenergetic composites. Acta Physica Sinica, 2009, 58(1): 655-661. doi: 10.7498/aps.58.655
    [20] Wang Rui-Min, Zhao Hong. The role of neuron transfer function in artificial neural networks. Acta Physica Sinica, 2007, 56(2): 730-739. doi: 10.7498/aps.56.730
Metrics
  • Abstract views:  8773
  • PDF Downloads:  328
  • Cited By: 0
Publishing process
  • Received Date:  09 May 2020
  • Accepted Date:  06 July 2020
  • Available Online:  27 November 2020
  • Published Online:  05 December 2020

/

返回文章
返回