二维圆盘颗粒体系声学行为的数值研究

刘晓宇; 张国华; 孙其诚; 赵雪丹; 刘尚

doi:10.7498/aps.66.234501

摘要

数值测量了卸载过程中二维单分散圆盘颗粒系统的横波、纵波声速、声衰减系数、非线性系数随压强的变化以及声衰减系数随频率的变化.结果表明，二维（2D）圆盘颗粒体系的横波、纵波声速均随压强呈分段幂律标度：当压强P -4时，横波、纵波声速随压强的增大而减小；当P > 10-4时，有vt～ P0.202，vl～ P0.338.进一步得到其剪切模量和体积模量的比值G/B也随压强呈幂律标度，G/B ～ P-0.502，暗示在低压强下，与三维（3D）球形颗粒体系类似，2D圆盘颗粒体系也处于L玻璃态.水平激励和垂直激励下2D圆盘颗粒系统的衰减系数随频率变化也呈现分段行为：当频率f f变化；当f > 0.05时，横波纵波的衰减系数α ～ f；当f > 0.35时，横波衰减系数αT～ f2，纵波衰减系数αL～ f1.5.此外，竖直水平激励下的2D圆盘颗粒系统的非线性系数和衰减系数随压强也呈现与声速类似的分段规律：当P -4时，横波非线性系数βT～ P-0.230，其余都不随压强变化.当P > 10-4时，两者均随压强增大呈幂律减小：βT～ P-0.703，βL～ P-0.684，αT～ P-0.099，αL～ P-0.105.进而得到2D圆盘颗粒系统中散射相关的特征长度l*随压强呈幂律标度，当P -4时，l*～ P-0.595；当P > 10-4时，l*～ P0.236.

关键词:

颗粒物质 /
声速 /
非线性 /
声衰减

Abstract

The transversal and longitudinal wave velocities, the acoustic attenuation coefficients, the nonlinear coefficients at different pressures and the acoustic attenuation coefficient as a function of frequency in a two-dimensional (2D) monodisperse disc system are numerically calculated. The results show that the transversal and longitudinal wave velocities both exhibit a piecewise power law with pressure P. When P -4, the velocity decreases with the increase of pressure in the 2D disc granular system, and when P > 10-4, the transversal wave velocity Vt and longitudinal wave velocity Vl show the scaling power laws, i.e., νt~P0.202 and vl~P0.338, respectively. The ratio of the shear modulus to the bulk modulus G/B shows a power law scaling with the pressure, G/B~P-0.502, implying that the system lies in an L glass state at low pressure, similar to that of a three-dimensional (3D) spherical granular system. The attenuation coefficients (αT, αL) of the horizontal excitation and vertical excitation also show the picecewise behaviors with the change of frequency f. When f f. When f > 0.05, α ∝ fTα, αL ∝ f. And when f > 0.35, αT ∝ f2 and αL ∝ f1.5. In addition, the nonlinear coefficient and the attenuation coefficient of the 2D disc granular system under the vertical and horizontal excitation both also show a piecewise law behavior with pressure, similar to that of the acoustic velocity. When P -4, only the transversal nonlinear coefficient changes according to βT ∝ P-0.230, while the other coefficient has no change. When P > 10-4, the attenuation coefficients and nonlinear coefficients decrease according to their power law with the increase of pressure, i.e., βT ∝ P-0.703, βL ∝ P-0.684, αT ∝ P-0.099, αL ∝ P-0.105. The characteristic length l*, which characterizes the disordered structure responsible for the scattering, also decreases according to power law with the increase of pressure, when P -4, l* ∝ P-0.595; when P > 10-4, l* ∝ P0.236.

Keywords:

作者及机构信息

1.
北京科技大学物理系, 北京 100083;

2.
清华大学, 水沙科学与水利水电工程国家重点实验室, 北京 100084

通信作者: 张国华, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ; 孙其诚, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ;

基金项目: 国家自然科学基金（批准号：11272048，11572178，91634202）资助的课题.

Authors and contacts

1.
Department of Physics, University of Science and Technology Beijing, Beijing 100083, China;

2.
State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Corresponding author: Zhang Guo-Hua, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ; Sun Qi-Cheng, zhguohua@sas.ustb.edu.cn;qcsun@tsinghua.edu.cn ;

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272048, 11572178, 91634202).

参考文献

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[5]	Xu N 2011 Front. Phys. 6 109
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[10]	Sussman D M, Goodrich C P, Liu A J, Nagel S R 2015 Soft Matter 11 2745
[11]	Wyart M, Nagel S R, Witten T A 2005 Europhys. Lett. 72 486
[12]	Wyart M, Silbert L, Nagel S 2005 Phys. Rev. E 72 051306
[13]	Silbert L, Liu A, Nagel S 2005 Phys. Rev. Lett. 95 098301
[14]	Vitelli V 2010 Soft Matter 6 3007
[15]	Mizuno H, Silbert L E, Sperl M 2016 Phys. Rev. Lett. 116 068302
[16]	Merkel A, Tournat V, Gusev V 2014 Phys. Rev. E 90 023206
[17]	Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[18]	Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 234501 (in Chinese)[张祺, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 234501]
[19]	Zheng H P 2014 Chin. Phys. B 23 054503
[20]	Vitelli V, Xu N, Wyart M, Liu A J, Nagel S R 2010 Phys. Rev. E 81 021301
[21]	Somfai E, Roux J N, Snoeijer J, van Hecke M, van Saarloos W 2005 Phys. Rev. E 72 021301
[22]	Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[23]	Zhang P, Zhao X D, Zhang G H, Zhang Q, Sun Q C, Hou Z J, Dong J J 2016 Acta Phys. Sin. 65 024501 (in Chinese)[张攀, 赵雪丹, 张国华, 张祺, 孙其诚, 侯志坚, 董军军 2016 物理学报 65 024501]
[24]	Lherminier S, Planet R, Simon G, Vanel L, Ramos O 2014 Phys. Rev. Lett. 113 098001
[25]	West B J, Shlesinger M F 1984 J. Stat. Phys. 36 779
[26]	Langlois V, Jia X 2015 Phys. Rev. E 91 022205
[27]	Hong J 2005 Phys. Rev. Lett. 94 108001
[28]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301
[29]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[30]	Brunet T, Jia X, Johnson P A 2008 Geophys. Res. Lett. 35 L19308

施引文献

[1]	Liu A J, Nagel S R 1998 Nature 396 21
[2]	Henkes S, Chakraborty B 2005 Phys. Rev. Lett. 95 198002
[3]	O'Hern C S, Silbert L E, Nagel S R 2003 Phys. Rev. E 68 011306
[4]	O'Hern C, Langer S, Liu A, Nagel S 2002 Phys. Rev. Lett. 88 075507
[5]	Xu N 2011 Front. Phys. 6 109
[6]	Ikeda A, Berthier L 2015 Phys. Rev. E 92 012309
[7]	Wang X, Zheng W, Wang L, Xu N 2015 Phys. Rev. Lett. 114 035502
[8]	Coulais C, Behringer R P, Dauchot O 2014 Soft Matter 10 1519
[9]	Karimi K, Maloney C E 2015 Phys. Rev. E 92 022208
[10]	Sussman D M, Goodrich C P, Liu A J, Nagel S R 2015 Soft Matter 11 2745
[11]	Wyart M, Nagel S R, Witten T A 2005 Europhys. Lett. 72 486
[12]	Wyart M, Silbert L, Nagel S 2005 Phys. Rev. E 72 051306
[13]	Silbert L, Liu A, Nagel S 2005 Phys. Rev. Lett. 95 098301
[14]	Vitelli V 2010 Soft Matter 6 3007
[15]	Mizuno H, Silbert L E, Sperl M 2016 Phys. Rev. Lett. 116 068302
[16]	Merkel A, Tournat V, Gusev V 2014 Phys. Rev. E 90 023206
[17]	Zhang Q, Li Y, Hou M, Jiang Y, Liu M 2012 Phys. Rev. E 85 031306
[18]	Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 234501 (in Chinese)[张祺, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 234501]
[19]	Zheng H P 2014 Chin. Phys. B 23 054503
[20]	Vitelli V, Xu N, Wyart M, Liu A J, Nagel S R 2010 Phys. Rev. E 81 021301
[21]	Somfai E, Roux J N, Snoeijer J, van Hecke M, van Saarloos W 2005 Phys. Rev. E 72 021301
[22]	Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[23]	Zhang P, Zhao X D, Zhang G H, Zhang Q, Sun Q C, Hou Z J, Dong J J 2016 Acta Phys. Sin. 65 024501 (in Chinese)[张攀, 赵雪丹, 张国华, 张祺, 孙其诚, 侯志坚, 董军军 2016 物理学报 65 024501]
[24]	Lherminier S, Planet R, Simon G, Vanel L, Ramos O 2014 Phys. Rev. Lett. 113 098001
[25]	West B J, Shlesinger M F 1984 J. Stat. Phys. 36 779
[26]	Langlois V, Jia X 2015 Phys. Rev. E 91 022205
[27]	Hong J 2005 Phys. Rev. Lett. 94 108001
[28]	Wang P J, Li Y D, Xia J H, Liu C S 2008 Phys. Rev. E 77 060301
[29]	Wang P J, Xia J H, Li Y D, Liu C S 2007 Phys. Rev. E 76 041305
[30]	Brunet T, Jia X, Johnson P A 2008 Geophys. Res. Lett. 35 L19308

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