Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.     

静态堆积颗粒中的力链分布

颗粒物质是由众多离散颗粒组成的软凝聚态物质,涉及多个物理层次结构和机制,是多尺度问题. 首先阐述了颗粒物质多尺度力学的研究框架,指出颗粒间接触力链构成的细观尺度是核心,颗粒物质显示出的独特静态堆积特性和动态流变特性都与细观尺度力链的复杂演变规律直接相关. 围绕着定量描述力链特征这一目标,采用严格的球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下12000个球心共面的二维等径颗粒静态堆积进行了离散动力学模拟,对力链分布特征、接触力规律等做了量化分析,考察了颗粒 关键词： 颗粒物质 力链 离散模型 多尺度力学     

双轴压缩下颗粒物质剪切带的形成与发展

本文采用离散元方法,研究了双轴压缩的颗粒体系在刚性边界约束下,局部剪切带的形成和发展过程,注重分析了细观的体积分数、配位数、颗粒旋转角度等参数以及力链结构形态的演变.并从颗粒体系jamming 相图中J点附近的边壁压强和配位数随体积分数的标度规律出发,分析了剪切带内外的体积分数和配位数的变化.结果表明:剪切带形成于颗粒体系的塑性变形开始阶段,此时体系发生剪胀,颗粒体积分数减小,颗粒体系抵抗旋转的能力降低,开始出现细小剪切带,随着轴向应变的继续,细小剪切带发生连接,最终导致贯穿性优势剪切带形成 关键词： 颗粒物质 力链 双轴压缩 剪切带     

Interior dynamics of subharmonious surface wave in an idealized bidimensional granular layer

In this paper, high-speed photography was used to investigate the intrinsic dynamics of subharmonious surface wave in a vertical vibrated and idealized bidimensional granular layer. Using the high-speed photography, velocity fields of the granular layer at different stages through two cycles were obtained, which show the continuous particle motions during a cycle. From the velocity fields, a crystal structure in the wave-hollow was observed, which is reported for the first time. Furthermore, quantitative results of kinetic energy distribution in the layer were calculated, which shows temporal correspondence with the evolution of the wave pattern.     

Oscillatory patterns in a rotating aqueous suspension

Suspensions of granular material in glycerin-water mixtures agitated in horizontally aligned rotating tubes show a whole variety of patterns. The stationary pattern of a homogeneous distribution and a chain of rings have been investigated before. Here we report on two types of oscillatory states in the same system. For a certain range of the rotation frequency and sufficiently high viscosity traveling waves propagate with constant velocity back and forth along the tube in an almost homogeneous distribution of sedimenting particles. The transition from a stationary to the traveling-wave state is found to be an imperfect supercritical bifurcation. The dependence of the wave length and speed on the tube's rotation frequency and the dynamic viscosity of the fluid are determined. Experiments with low viscosities show no traveling waves but low-frequency oscillations, when the previously known chain of rings undergoes a secondary instability.     

一些典型的软物质物理中的非平衡自组织现象

在软物质物理中经常有自组织(self-organization)现象发生.这一现象通常在非平衡的过程中产生,并生成非常美丽和有趣的图案与结构.具体例子包括胶体颗粒的扩散限制凝聚(diffusion limited aggregation,DLA),Hele-Shaw盒中产生的流体分形结构,凝胶的形成(gelation),生物体自组织聚集,以及颗粒类物质(granular material)运动产生的规则图案等.这些现象在软物质物理研究中产生了很多重要结果.文章以比较浅显的文字介绍这些软物质物理中的非平衡自组织现象.     

Hydraulic theory for a debris flow supported on a collisional shear layer

We consider a heap of grains driven by gravity down an incline. We assume that the heap is supported at its base on a relatively thin carpet of intensely sheared, highly agitated grains that interact through collisions. We adopt the balance laws, constitutive relations, and boundary conditions of a kinetic theory for dense granular flows and determine the relationship between the shear stress, normal stress, and relative velocity of the boundaries in the shear layer in an analysis of a steady shearing flow between identical bumpy boundaries. This relationship permits us to close the hydraulic equations governing the evolution of the shape of the heap and the velocity distribution at its base. We integrate the resulting equations numerically for typical values of the parameters for glass spheres. (c) 1999 American Institute of Physics.     

Magnetization transfer MRI of mouse brain reveals areas of high neural density

Extending applications of magnetization transfer contrast (MTC) in magnetic resonance imaging (MRI) of the human central nervous system, this work quantitatively describes MTC of the murine brain. As a novel finding, complementing T₁- and T₂-weighted MRI, MTC allows for the distinction of densely packed gray matter from normal gray and white matter. Examples include the Purkinje cell layer and the granular cell layer in the mouse cerebellum as well as the delineation of the CA3 subfield of the hippocampus relative to surrounding hippocampal gray matter and white matter tracts such as the hippocampal fimbria. Using a kainate lesion model, the CA3 hyperintensities in MTC and T₁-weighted MRI are assigned to the densely packed somata of pyramidal cells.     

Darwin curves and galaxy arms

In the natural world, there exists one kind of structure which is beyond the scope of human laboratorial experiment. It is the structure of galaxies which is usually composed of billions of stars. Spiral galaxies are flat disk-shaped. There are two types of spiral galaxies. The spiral galaxies with some bar-shaped pattern are called barred spirals, and the ones without the pattern are called ordinary spirals. Longer-wavelength galaxy images (infrared, for example) show that ordinary spiral galaxies are basically an axi-symmetric disk that is called exponential disk. For a planar distribution of matter, Jin He defined Darwin curves in the plane as such that the ratio of the matter densities at both sides of the curve is constant along the curve. Therefore, the arms of ordinary spiral galaxies are Darwin curves. Now an important question is that: Are the arms of barred spiral galaxies the Darwin curves too? Fortunately, Jin He designed a piece of Galaxy Anatomy graphic software. With the software, not only can people simulate the stellar density distribution of barred spiral galaxies but also can draw the Darwin curves of the simulated galaxy structure. This paper shows partial evidence that the arms of galaxy NGC 3275, 4548 and 5921 follow Darwin curves.     

Pattern Formation in a Vibrated Granular Layer on an Inclined Base

We carry out the simulations of pattern formation in a two-dimensional vibrated granular layer on an inclined base by molecular dynamics. It is found that the maximum amplitude of the pattern is greater at the lower part than at the higher part of the base, and is proportional to the thickness of the layer. Meanwhile, the wavelength varies non-monotoniclly as the inclined angle of the base is increased.     

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.     

阻尼对水平滚筒内二元颗粒体系径向分离模式形成的影响

采用离散单元数学模型对一充装量为50%的水平薄滚筒内S形二元颗粒体系的分离模式进行了数值模拟试验,研究了不同碰撞阻尼参数下的分离过程,分析了阻尼对分离过程及分离模式的影响.模拟结果表明阻尼对滚筒内颗粒的分离过程及分离模式影响很大,在S形二元颗粒体系水平薄滚筒内,阻尼可控制渗透和离析的协同作用以及自由表面层的流动形式,最终影响分离模式的形成;当阻尼太大时分离模式只能形成月亮模式,阻尼太小时可形成不明显的花瓣模式,只有当阻尼在适当的范围内,自由表面流动层形成雪崩流型式时,分离模式才会呈现规则的花瓣模式,试验结 关键词： 滚筒 模式形成 径向分离 离散单元法     

Softening induced instability of a stretched cohesive granular layer

We report on a cellular pattern which spontaneously forms at the surface of a thin layer of a cohesive granular material submitted to in-plane stretching. We present a simple model in which the mechanism responsible of the instability is the "strain softening" exhibited by humid granular materials above a typical strain. Our analysis indicates that such a type of instability should be observed in any system presenting a negative stress sensitivity to strain perturbations.     

Granular Rayleigh-Taylor instability: experiments and simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.     

Kinetic theory for sheared granular flows

Rapid granular flows are far-from-equilibrium-driven dissipative systems where the interaction between the particles dissipates energy, and so a continuous supply of energy is required to agitate the particles and facilitate the rearrangement required for the flow. This is in contrast to flows of molecular fluids, which are usually close to equilibrium, where the molecules are agitated by thermal fluctuations. Sheared granular flows form a class of flows where the energy required for agitating the particles in the flowing state is provided by the mean shear. These flows have been studied using the methods of kinetic theory of gases, where the particles are treated in a manner similar to molecules in a molecular gas, and the interactions between particles are treated as instantaneous energy-dissipating binary collisions. The validity of the assumptions underlying kinetic theory, and their applicability to the idealistic case of dilute sheared granular flows are first discussed. The successes and challenges for applying kinetic theory for realistic dense sheared granular flows are then summarised.     

Free surface waves in wall-bounded granular flows

We report free-surface waves in granular flows near boundaries in an inclined chute. The chevron-shaped traveling waves spontaneously develop at inclinations close to the angle of repose for both steady and accelerating flows. Two distinct regimes are characterized by internal angle and frequency variations. Experimental measurements indicate that subsurface circulation driven by velocity gradients near frictional walls plays a central role in the pattern formation mechanism, suggesting that wave generation is controlled by the granular analog of a fluid boundary layer.     

离散颗粒层被横向推移过程中的力学行为研究

研究发现,颗粒物质层被匀速推移挤压过程中,所需推移力先以线性规律增加,在某一确定点后,则会以指数规律增加.而颗粒物质是由众多离散颗粒组成的软凝聚态物质,其宏观上反映的是离散颗粒的个体性质和凝聚态物质的集体效应.颗粒与颗粒之间以及颗粒与边界之间的细观尺度接触力链的构成以及演变规律将会直接影响各种宏观受力情况,其摩擦力与挤压力便是力链的主要构成形式.围绕着定量描述细观力链特征,从而揭示力的变化规律这一目标,采用计算机模拟的方法,依照球形颗粒Hertz法向接触理论和Mindlin-Deresiewicz切向接触理论,对重力作用下不同数目的三维等径球体颗粒层的推移情况进行了离散元仿真模拟,量化分析了推移力变化规律、各摩擦力变化规律以及力链分布规律,发现摩擦力与挤压力在颗粒堆积的不同阶段对力链的构成起到了不同的主次作用,使得力链发生强弱演变,从而发现了推移颗粒物质层时推移力的变化规律及原因.这些结果有利于从力链角度揭示颗粒内部和颗粒与各边界之间的受力情况.     

颗粒物质内自旋小球运动行为的数值模拟研究

针对大耳沙蜥在沙子中的运动行为,以球形物体为研究对象,利用3维离散元数值模拟程序LIGGGHTS模拟了旋转运动模式对颗粒物质中球形物体平动和上升/下降行为的影响,定量分析了旋转速度以及颗粒间摩擦系数等因素的具体影响.研究结果表明:球形物体与颗粒物质基底颗粒间的摩擦系数以及球形物体的自转角速度对球形物体的运动有明显影响,摩擦系数越大物体运动越明显,自转角速度越大物体运动越明显.该结果比较好地解释了沙漠生物外表具有鳞片的原因.