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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 物理学报 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 物理学报 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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