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利用颗粒离散元方法, 研究了由2048个有摩擦的单分散圆盘颗粒组成的体系在各向同性压缩条件下, 颗粒摩擦系数 对颗粒体系结构与振动特性的影响. 结果表明: 固定压强下, 随 的增大, 区分德拜标度与态密度平台的过渡频率* 与玻色峰频率BP均向低频移动, 玻色峰高度D(BP) / BP 逐渐增加. 主要原因是 增大导致颗粒体系无序程度增加(平均配位数减小)而在 * 处出现了大量额外模式. 模式分析表明: 低频( 1.0)模式主要是以平动为主的混合模式, 中频(1.0 4.0)模式主要是以平动为主的混合局域化模式, 高频( 4.0) 振动模式几乎为纯转动的局域化模式; 并且随的增大, 低频下平动模式更加局域化, 同时低频转动模式的贡献也逐渐增加, 暗示在高摩擦系数下低频转动模式产生更重要的影响.In this paper, the two-dimensional granular assemblies composed of 2048 mono-dispersed frictional disks are simulated by the discrete element method. A set of eigenvalues and corresponding eigenvectors is obtained by diagonalizing the Hessian matrix for each stable configuration. The effects of the friction coefficient of disk on mechanical and geometrical properties of these systems under isotropic confining are studied. Results show that at a fixed pressure, with increasing from 0.001 to 1.0, the crossover frequency *, which separates the Debye scale region from the platform of vibrational density of states, and the boson peak BP gradually shift towards lower frequency, and the intensity of the boson peak D(BP) / BP increases. These results are mainly attributed to the fact that the system becomes more and more disordered with the increase of (i.e., the decrease of the average coordination number), resulting in more excess modes at *. For a better understanding of the different vibration modes of the two-dimensional frictional granular systems, we plot the polarization vector diagrams for different frequencies ( 1 = 0.15, 2 = 1.5 and 3 = 6.0) for configurations with = 0.001 and = 1.0, respectively. Mode analysis results show that the mode at low ( 1.0) has a mixed translational-rotational but translational-dominated character; the mode at intermediate frequency (1.0 4.0) is localized and has a mixed translational-rotational but translational-dominated character; and the mode at high frequency ( 4.0) have a strongly rotational in character. It is worth noting that the low-frequency modes become more localized and the rotational participation fraction also increases as increases, implying that the rotational modes play more important role in the system with higher friction coefficient.
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Keywords:
- granular matter /
- vibrational density of states /
- boson peak /
- mode analysis
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[1] OHern C S, Silbert L E, Nagel S R 2003 Phys. Rev. E 68 011306
[2] Wyart M, Nagel S R, Witten T A 2005 Europhys. Lett. 72 486
[3] Xu N, Wyart M, Liu A J, Nagel S R 2007 Phys. Rev. Lett. 98 175502
[4] Ghosh A, Chikkadi V K, Schall P, Kurchan J, Bonn D 2010 Phys. Rev. Lett. 104 248305
[5] Tan P, Xu N, Schofield A B, Xu L 2012 Phys. Rev. Lett. 108 095501
[6] Zargar R, Russo J, Schall P, Tanaka H, Bonn D 2014 Europhys. Lett. 108 38002
[7] Liu H X, Chen K, Hou M Y 2015 Acta Phys. Sin. 64 116302 (in Chinese) [刘海霞, 陈科, 厚美瑛 2015 64 116302]
[8] Schober H R, Laird B B 1991 Phys Rev. B 44 6746
[9] Schober H R, Oligschleger C 1996 Phys Rev B 53 11469
[10] Ruffl B, Parshin D A, Courtens E, Vacher R 2008 Phys. Rev. Lett. 100 015501
[11] Tanguy A, Wittmer J P, Leonforte F, Barrat J L 2002 Phys. Rev. B 66 174205
[12] Gurevich V L, Parshin D A, Schober H R 2003 Phys. Rev. B 67 094203
[13] Elliott S R 1992 Europhys. Lett. 19 201
[14] Wyart M, Silbert L E Nagel S R, Witten T A 2005 Phys. Rev. E 72 051306
[15] Flores-Ruiz H M, Naumis G G 2011 Phys Rev B 83 184204
[16] Zhang G H, Sun Q C, Shi Z P, Feng X, Gu Q, Jin F 2014 Chin. Phys. B 23 076301
[17] Leonforte F 2011 J. Non-Cryst. Solids 357 552
[18] Premkumar L, Das S P 2015 Phys. Lett. A 379 1073
[19] Feng X, Zhang G H, Sun Q C 2013 Acta Phys. Sin. 62 184501 (in Chinese) [冯旭, 张国华, 孙其诚 2013 62 184501]
[20] Xu N 2011 Front. Phys. China 6 109
[21] Somfai E, van Hecke M, Ellenbroek W G, Shundyak K, van Saarloos W 2007 Phys. Rev. E 75 020301
[22] Song C, Wang P, Makse H A 2008 Nature 453 629
[23] Henkes S, Shundyak K, van Saarloos W, van Hecke M 2010 Soft Matter 6 2935
[24] Stillinger F H Weber T A 1984 Science 225 4666
[25] Gao G J, Bławzdziewicz J, OHern C S 2006 Phys. Rev. E 74 061304
[26] Shintani H, Tanaka H 2008 Nature Mater. 7 870
[27] Schreck C F Bertrand T, OHern C S, Shattuck M D 2011 Phys. Rev. Lett. 107 078301
[28] Henkes S, van Hecke M, van Saarloos W 2010 Europhys. Lett. 90 14003
[29] Goodrich C P, Liu A J, Nagel S R 2014 Nature Phys. 10 578
[30] Srivastava D, Sarkar S K 2012 Phys. Rev. B 85 024206
[31] Chen K, Ellenbroek W G, Zhang Z, Chen D T, Yunker P J, Henkes S, Brito C, Dauchot O, van Saarloos W, Liu A J, Yodh A G 2010 Phys. Rev. Lett. 105 025501
[32] Xu N, Vitelli V, Liu A J, Nagel S R 2010 Europhys. Lett. 90 56001
[33] Chen K, Still T, Schoenholz S, Aptowicz K B, Schindler M, Maggs A C, Liu A J, Yodh A G 2013 Phys. Rev. E 88 022315
[34] Zeravcic Z, Xu N, Liu A J, Nagel S R, van Saarloos W 2009 Europhys. Lett. 87 26001
[35] Yunker P J, Chen K, Zhang Z, Ellenbroek W G, Liu A J, Yodh A G 2011 Phys. Rev. E 83 011403
[36] Papanikolaou S, OHern C S, Shattuck M D 2013 Phys. Rev. Lett. 110 198002
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