二维有摩擦颗粒体系振动态密度与玻色峰的研究  

Vibrational density of states and boson peak in two-dimensional frictional granular assemblies

作　　者：牛晓娜[1] 张国华[1] 孙其诚[2] 赵雪丹[1] 董远湘[1] 

机构地区：[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

出　　处：《物理学报》2016年第3期206-213,共8页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:11272048;51239006);欧盟Marie Curie国际合作项目(批准号:IRSES-294976)资助的课题~~

摘　　要：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μ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μ的增大,区分德拜标度与态密度平台的过渡频率ω*与玻色峰频率ωBP均向低频移动,玻色峰高度D(ωBP)/ωBP逐渐增加.主要原因是μ增大导致颗粒体系无序程度增加(平均配位数减小)而在ω>ω*处出现了大量额外模式.模式分析表明:低频(ω<1.0)模式主要是以平动为主的混合模式,中频(1.0<ω<4.0)模式主要是以平动为主的混合局域化模式,高频(ω>4.0)振动模式几乎为纯转动的局域化模式;并且随μ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 μ of disk on mechanical and geometrical properties of these systems under isotropic confining are studied.Results show that at a fixed pressure,withμ increasing from 0.001 to 1.0,the crossover frequency ω~＊,which separates the Debye scale region from the platform of vibrational density of states,and the boson peak ω_（BP） gradually shift towards lower frequency,and the intensity of the boson peak D（ω_（BP））/ω_（BP） increases.These results are mainly attributed to the fact that the system becomes more and more disordered with the increase of μ（i.e.,the decrease of the average coordination number）,resulting in more excess modes at ω 〉 ω~＊.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（ω1=0.15,ω2=1.5 and ω3 = 6.0） for configurations with μ= 0.001 and μ=1.0,respectively.Mode analysis results show that the mode at low（ω〈 1.0） has a mixed translational-rotational but translational-dominated character;the mode at intermediate frequency（1.0 〈ω〈 4.0） is localized and has a mixed translational-rotational but translational-dominated character;and the mode at high frequency（ω〉 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 μ increases,implying that the rotational modes play more important role in the system with higher friction coefficient.

关 键 词：颗粒物质 振动态密度 玻色峰 模式分析 

分 类 号：TB34[一般工业技术—材料科学与工程]