Collision statistics of clusters: from Poisson model to Poisson mixtures

doi:10.1088/1674-1056/19/2/023602

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 23602-023602.doi: 10.1088/1674-1056/19/2/023602

Collision statistics of clusters: from Poisson model to Poisson mixtures

Sascha Vongehr, 唐少春, 孟祥康

National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China

收稿日期:2009-06-16 修回日期:2009-07-15 出版日期:2010-02-15 发布日期:2010-02-15

Collision statistics of clusters: from Poisson model to Poisson mixtures

Sascha Vongehr, Tang Shao-Chun(唐少春), and Meng Xiang-Kang(孟祥康)^†

National Laboratory of Solid State Microstructures, Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, China

Received:2009-06-16 Revised:2009-07-15 Online:2010-02-15 Published:2010-02-15

摘要/Abstract

摘要： Clusters traverse a gas and collide with gas particles. The gas particles are absorbed, and the clusters become hosts. If the clusters are size-selected, the number of guests will be Poisson distributed. We review this by showcasing four laboratory procedures that all rely on the validity of the Poisson model. The effects of a statistical distribution of the clusters' sizes in a beam of clusters are discussed. We derive the average collision rates. Additionally, we present Poisson mixture models that also involve standard deviations. We derive the collision statistics for common size distributions of hosts and also for some generalizations thereof. The models can be applied to large noble gas clusters traversing doping gas. While outlining how to fit a generalized Poisson to the statistics, we still find even these Poisson models to be often insufficient.

Abstract: Clusters traverse a gas and collide with gas particles. The gas particles are absorbed, and the clusters become hosts. If the clusters are size-selected, the number of guests will be Poisson distributed. We review this by showcasing four laboratory procedures that all rely on the validity of the Poisson model. The effects of a statistical distribution of the clusters' sizes in a beam of clusters are discussed. We derive the average collision rates. Additionally, we present Poisson mixture models that also involve standard deviations. We derive the collision statistics for common size distributions of hosts and also for some generalizations thereof. The models can be applied to large noble gas clusters traversing doping gas. While outlining how to fit a generalized Poisson to the statistics, we still find even these Poisson models to be often insufficient.

Key words: collision statistics, helium droplets, clusters, Poisson statistics

中图分类号: (Atomic and molecular clusters)

36.40.-c

31.15.bt (Statistical model calculations (including Thomas-Fermi and Thomas-Fermi-Dirac models)) 02.50.-r (Probability theory, stochastic processes, and statistics)

Sascha Vongehr, 唐少春, 孟祥康. Collision statistics of clusters: from Poisson model to Poisson mixtures[J]. 中国物理B, 2010, 19(2): 23602-023602.

Sascha Vongehr, Tang Shao-Chun(唐少春), and Meng Xiang-Kang(孟祥康). Collision statistics of clusters: from Poisson model to Poisson mixtures[J]. Chin. Phys. B, 2010, 19(2): 23602-023602.

参考文献 26

[1]	Villarica M, Casey M J, Goodisman J and Chaiken J 1993 J. Chem. Phys. 98 4610
[2]	Wang C R, Huang R B, Liu Z Y and Zheng L S 1994 Chem. Phys. Lett. 227 103
[3]	Limpert E, Stahel W A and Abbt M 2001 BioScience 51 341
[4]	Toennies J P and Vilesov A F 2004 Angew. Chem. Int. Ed. 4 3 2622
[5]	Stienkemeier F and Lehmann K K 2006 J. Phys. B 39 R127
[6]	Vongehr S and Kresin V V 2003 J. Chem. Phys. 119 11124
[7]	Lewerenz M, Schilling B and Toennies J P 1995 J. Chem. Phys. 102 8191
[8]	Quaas N 1997 Bericht 101, Max Planck Institut für Str?mungsforschung,G?ttingen
[9]	Berkeling K, Helbing R, Kramer K, Pauly H, Schlier Ch and Toschek P 1962 Z. Phys. 166 406
[10]	Hess H, Larsen D S and Scheidemann A A 1999 Philos. Mag. B 79 1437
[11]	Knuth E L and Henne U 1999 J. Chem. Phys. 110 2664
[12]	Brink D M and Stringari S 1990 Z. Phys. D: Atomic, Mol. Clusters 15 257
[13]	Harms J, Toennies J P and Dalfovo F 1998 Phys. Rev. B 58 3341
[14]	Braun A 2004 Dissertation}, Lausanne, EPFL 2967 1
[15]	Willmot G E 1986 ASTIN Bulletin 16 S59
[16]	Willmot G E 1987 Scandinavian Actuarial Journal} 113
[17]	Seshadri V 1983 Can. J. Stat. 11 131
[18]	Seshadri V 1998 The Inverse Gaussian Distribution} (New York: Springer)
[19]	Yang S, Brereton S M and Ellis A M 2005 Rev. Sci. Instrum. 76 104102
[20]	Iwase K and Hirano K 1990 Jpn. J. Appl. Stat. 19 163
[21]	Kawamura T and Iwase K 2003 J. Jpn. Stat. Soc. 3 3 95
[22]	Sichel H S 1992 Information Processing & Management 28 5
[23]	Consul P C and Shoukri M M 1985 Commun. in Stat. -- Simul. andComput. 141533
[24]	Vongehr S 2005 Dissertation} (USC, Los Angeles)
[25]	Barranco M, Guardiola R, Hernandez S, Mayol R, Navarro Jand Pi M 2006 J. Low Temp. Phys. 142 1
[26]	Willmot G E 1993 Scandinavian Actuarial Journal 114

Collision statistics of clusters: from Poisson model to Poisson mixtures

Collision statistics of clusters: from Poisson model to Poisson mixtures

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 26

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Yuanqi Jiang(蒋元祺), Ping Peng(彭平). Predicting novel atomic structure of the lowest-energy Fe_nP_13-n(n=0-13) clusters: A new parameter for characterizing chemical stability[J]. 中国物理B, 2023, 32(4): 47102-047102.
[2]	Famin Yu(于法民), Zhonghua Liu(刘中华), Jiarui Li(李佳芮), Wanrong Huang(黄婉蓉), Xinrui Yang(杨欣瑞), and Zhigang Wang(王志刚). Bottom-up design and assembly with superatomic building blocks[J]. 中国物理B, 2022, 31(12): 128107-128107.
[3]	Ioan Baldea. Chemical bonding in representative astrophysically relevant neutral, cation, and anion HC_nH chains[J]. 中国物理B, 2022, 31(12): 123101-123101.
[4]	Runxiao Zhang(张润潇), Zi Liu(刘姿), Xin Hu(胡昕), Kun Xie(谢鹍), Xinyue Li(李新月), Yumin Xia(夏玉敏), and Shengyong Qin(秦胜勇). Two-dimensional Sb cluster superlattice on Si substrate fabricated by a two-step method[J]. 中国物理B, 2022, 31(8): 86801-086801.
[5]	Tonghe Ying(应通和), Jianbao Zhu(朱健保), and Wenguang Zhu(朱文光). Machine learning potential aided structure search for low-lying candidates of Au clusters[J]. 中国物理B, 2022, 31(7): 78402-078402.
[6]	Dong-Lin Luan(栾栋林), Ya-Bin Wang(王亚斌), Guo-Meng Li(李果蒙), Lei Yuan(袁磊), and Jun Chen(陈军). Plasticity and melting characteristics of metal Al with Ti-cluster under shock loading[J]. 中国物理B, 2021, 30(7): 73103-073103.
[7]	Songül Taran, Ali Kemal Garip, Haydar Arslan. A theoretical study on chemical ordering of 38-atom trimetallic Pd-Ag-Pt nanoalloys[J]. 中国物理B, 2020, 29(7): 77801-077801.
[8]	田永红, 孙伟国, 陈伯乐, 金圆圆, 卢成. Cluster structure prediction via CALYPSO method[J]. 中国物理B, 2019, 28(10): 103104-103104.
[9]	张鸽, 盛勇. Density functional study on the bimetallic Ti_mZr_n (n+m ≤ 5) clusters and their interactions with H₂[J]. 中国物理B, 2018, 27(9): 93601-093601.
[10]	Francisco E Jorge, José R da Costa Venâncio. Structure, stability, catalytic activity, and polarizabilities of small iridium clusters[J]. 中国物理B, 2018, 27(6): 63102-063102.
[11]	刘珂, 胡丽娟, 张巧凤, 谢耀平, 高超, 董海英, 梁婉怡. Effect of Ni and vacancy concentration on initial formation of Cu precipitate in Fe-Cu-Ni ternary alloys by molecular dynamics simulation[J]. 中国物理B, 2017, 26(8): 83601-083601.
[12]	马丽, 金雪玲, 杨慧慧, 王小霞, 杜宁, 陈宏善. Dissociation of H₂ on Mg-coated B₁₂C₆N₆[J]. 中国物理B, 2017, 26(6): 68801-068801.
[13]	邵桂芳, 朱梦, 上官亚力, 李文然, 张灿, 王玮玮, 李玲. Structural optimization of Au-Pd bimetallic nanoparticles with improved particle swarm optimization method[J]. 中国物理B, 2017, 26(6): 63601-063601.
[14]	刘秀英, 于景新, 李晓东, 刘桂成, 李晓凤, Joong-Kee Lee. Effect of metal catalyst on the mechanism of hydrogen spillover in three-dimensional covalent-organic frameworks[J]. 中国物理B, 2017, 26(2): 27302-027302.
[15]	Francisco E Jorge, Luiz G M de Macedo. Dipole (hyper) polarizabilities of neutral silver clusters[J]. 中国物理B, 2016, 25(12): 123102-123102.