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     

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.     

风沙运动的电场-流场耦合模型及气固两相流数值模拟

沙尘暴和尘卷风等风沙运动的静电场是空气流场中沙粒间的碰撞摩擦带电及沙粒粒径的分层效应引起的, 本文耦合沙粒摩擦荷电模型和风沙运动气固两相流模型, 提出了离散单元法与计算流体动力学结合的数值方法. 数值模拟计算表明电荷呈中性的沙粒临界直径为300 μm; 在充分发展的水平风沙流中, 细小的沙粒带负电, 较大直径的沙粒带正电, 所模拟的沙粒带电的荷质比及水平风洞试验段的电场强度与实验测量值一致, 验证了风沙运动的电场-流场耦合模型及数值计算方法的合理性. 本文基于沙粒摩擦荷电机理的风沙运动气固两相流模型提供了理解风沙运动静电场产生的一种物理机理.     

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.     

Effect of particle size distribution on the polarity of triboelectric charging in granular insulator systems

Triboelectric charging occurs in granular insulating systems even when all particles are composed of identical material. A simple model is used here to address triboelectric charging in such systems. The basis of the model is the existence of electrons trapped in high-energy states, which can be released during collisions with another particle and transferred to the other particle. This model shows that triboelectric charging in insulator systems composed of particles of identical material can be attributed to a distribution of particle sizes, such that smaller particles tend to charge negatively and larger particles tend to charge positively. This polarity of charging has been observed in field studies of sand storms, dust devils and volcanic plumes, and most laboratory experiments on triboelectric charging in granular systems.     

Impact on soft sand: void collapse and jet formation

Very fine sand is prepared in a well-defined and fully decompactified state by letting gas bubble through it. After turning off the gas stream, a steel ball is dropped on the sand. On impact of the ball, sand is blown away in all directions ("splash") and an impact crater forms. When this cavity collapses, a granular jet emerges and is driven straight into the air. A second jet goes downwards into the air bubble entrained during the process, thus pushing surface material deep into the ground. The air bubble rises slowly towards the surface, causing a granular eruption. In addition to the experiments and the discrete particle simulations we present a simple continuum theory to account for the void collapse leading to the formation of the upward and downward jets.     

The song of dunes as a wave-particle mode locking

Singing dunes, which emit a loud sound as they avalanche, constitute a striking and poorly understood natural phenomenon. We show that, on the one hand, avalanches excite elastic waves at the surface of the dune, whose vibration produces the coherent acoustic emission in the air. The amplitude of the sound (approximately 105 dB) saturates exactly when the vibration makes the grains take off the flowing layer. On the other hand, we show that the sound frequency (approximately 100 Hz) is controlled by the shear rate inside the sand avalanche, which for granular matter is equivalent to the mean rate at which grains make collisions. This proves the existence of a feedback of elastic waves on particle motion, leading to a partial synchronization of the avalanching sand grains. It suggests that the song of dunes results from a wave-particle mode locking.     

Convection in a vibrated granular layer

When a granular layer is submitted to an oscillating acceleration with a peak value larger than gravity, a large scale motion develops. This movement is in some ways similar to the one displayed by a liquid heated from below, and it is called granular convection. Different conditions beside the parameters of the forcing can affect it, such as the presence of an interstitial gas or the roughness of the walls. We have carried out an experiment to study the convective movement of a granular layer with a temporal resolution high enough to describe the motion of individual grains within one oscillating period. We also present experimental results concerning the friction that the lateral walls exert on the grains and its relevance on granular convection.     

颗粒物质(上)

颗粒物质是地球上存在最多、最为人们所熟悉的物质类型之一．大量颗粒组成的离散态物质体系具有特别的性质和运动规律．颗粒物质表现出许多不同于固、液、气物质的奇特现象和独特的运动规律．由于对颗粒物质运动规律的理解具有重要科学意义和应用背景，近十年来颗粒物质研究逐步成为物理学研究中的一个活跃领域．文章综述了颗粒物质的一些主要特性，如颗粒物质的静态性质、振动行为、流动特性等，其中也包括文章作者的一些新近研究结果．限于篇幅，文章分为上、下两部分发表．第一部分在对颗粒物质作一般介绍后讨论颗粒物质的静态特性，第二部分则主要讨论颗粒物质振动时的行为和流动性质．     

Stability and bifurcations of a stationary state for an impact oscillator

The motion of a vibroimpacting one-degree-of-freedom model is analyzed. This model is motivated by the behavior of a shearing granular material, in which a transitional phenomenon is observed as the concentration of the grains decreases. This transition changes the motion of a granular assembly from an orderly shearing between two blocks sandwiching a single layer of grains to a chaotic shear flow of the whole granular mass. The model consists of a mass-spring-dashpot assembly that bounces between two rigid walls. The walls are prescribed to move harmonically in opposite phases. For low wall frequencies or small amplitudes, the motion of the mass is damped out, and it approaches a stationary state with zero velocity and displacement. In this paper, the stability of such a state and the transition into chaos are analyzed. It is shown that the state is always changed into a saddle point after a bifurcation. For some parameter combinations, horseshoe-like structures can be observed in the Poincare sections. Analyzing the stable and unstable manifolds of the saddle point, transversal homoclinic points are found to exist for some of these parameter combinations. (c) 1994 American Institute of Physics.     

Sound speed in air-filled sand and 03ine shallow-layer sandy sediments

Based on the author's theory for acoustic propagation in granular media and by employing the extinction theorem, the sound speed formulae in these media were derived. The numerical computations of sound speed in 03ine sediments and air-filled sand were carried out, and the results demonstrated that under the normal atmosphere the sound speed in air- filled sand is lower than the sound speed in the air. The numerical results also indicated that the influence of scattering interaction between the grains upon the sound speed in the 03ine shallow-layer sandy sediments has to be taken into account; however, the influence of the viscous-wave interaction can be neglected. The theoretical results obtained from the rigid-granular model seem to match the measured data better than from the elastic-granular model, even the latter model fits better for the real situation, indicating further measurements are necessary in order to gain an insight into this problem thoroughly. Through an analysis of experimental data published in journals a conclusion can be drawn that the theory of granular media is suited to deal with the problems of the sound propagation in air-filled sand better than the theory of porous media.     

Measurement and simulation of sand saltation movement under fluctuating wind in a natural field environment

Extensive research on the near surface movement of sand particles has focused on wind tunnel experiments, theoretical analysis, and numerical simulation of sand saltation under ideal and controllable conditions. Most field observations are results on the average rate of sand transport over some hours or the whole day. However, researchers found recently that the effect of turbulent characteristics of near surface wind in real atmospheric boundary layers on the sand transport rate was obvious. The turbulent characteristics would cause a significant discrepancy between field observation and simulation of sand transport rate. In this work, a field experiment in a real-time system was designed to synchronously measure physical quantities, such as fluctuating wind velocity in the near surface region, sand transport intensity, temperature, and humidity, with the frequency of 1 Hz, at two points on a homogeneous flat sand surface located in the Minqin area, which is between the edges of the Badain Jaran Desert and the Tengger Desert. The relationship between the saltation events and some physical properties, such as the fluctuating wind velocity, temperature, and humidity, was studied. On the basis of the field observation results, a numerical model was developed to simulate sand movement under the fluctuating wind. The overall features of the experimental measurements were reproduced by simulation.     

Remarks on the Idea of Spontaneous Break-Down of Symmetry,Cosmic Variability of Eddington's Number,Mach's Idea Concering the Origin of Inertia,and Field Equations Describing Global and Local Gravitational Fields

Subject is considered on the level of classical field theory. We start from some aspects of the theory of ferromagnets. Their counterpart in classical field theory is pointed out using the over simplified model of a selfinteracting scalar field. The ground state (“vacuum expection value”) of the scalar field is interpreted as cosmic background field, which can be considered as constant for local physical phenomena. In practice, however, it is a function of the age of universe. Which kind of function it could be is suggested by a discussion of the cosmic variability of Eddington's number γ = 10⁴⁰, which refers to Dirac's consideration of this problem. But contrary to Dirac's assumption that atomic quantities are constant, we suppose that the inertial mass of elementary particles is a function of the age of universe. The cosmic gravitational field is described by other equations than the gravitational field created by local matter distributions. The field equations for the local gravitational field we start from reduce to Einstein's equations, if we neglect the possible influence of the universe on local phenomena. In case that the cosmic matter is homogeneously and isotropically distributed, the field equations for the cosmic gravitational field permit only such a time dependent solution the three-spaces of which are linearly expanding and spherically closed. The different field equations for cosmic and local gravitational fields are considered approximations of more fundamental field equations which approximately split into two sets of equations, if it is possible to contrast local physical systems with the universe. The described cosmological model taken as a basis, the inertial mass of elementary particles becomes a function of the matter density creating the cosmic gravitational field. This could be considered as, at least, partly realisation of Mach's idea concerning the origin of inertia. Starting from the interpretation of the ground state (vacuum expection value) as a function of a certain cosmic background field, more realistic gage field models could give the following picture of cosmic development: In the far past there was a state of the universe characterized by enormous contraction of matter. In this stage of development, it was impossible to contrast particles with the universe. Matter expands and it becomes possible to contrast certain physical systems with the universe. But the ground state is such a symmetric one that only fields with vanishing rest mass can be contrasted with the universe (ferromagnet above Curie temperature). With further expansion of the universe the ground state will lose certain symmetry properties. By this it becomes possible that you get the impression there are particles with nonvanishing rest mass (ferromagnet below Curie temperature). Finally, the influence of the universe on local physical systems goes to zero with further expansion. Especially, this means the inertial mass of elementary particles goes to zero, too (Curie temperature of ferromagnetic material goes to zero with cosmic expansion).     

颗粒物质在冲击作用下的堆积分布

沙堆在冲击作用下的行为和静态沙堆的行为有着很大的不同.通过管道产生“高斯冲击”(速度水平分量成高斯分布)来研究沙堆堆积时的分布情况，发现沙堆自身的稳定性和外界冲击是影响沙堆形状的两大重要因素.给出了沙堆在冲击作用下高度随时间的演化方程.通过该方程，成功地得到了沙堆中心点的高度与外界参量之间的关系，并且提出了一种节能高效的颗粒混合方法. 关键词： 颗粒物质 堆积 高斯分布 冲击     

Granular statistical mechanics – a personal perspective

The science of granular matter has expanded from an activity for specialised engineering applications to a fundamental field in its own right. This has been accompanied by an explosion of research and literature, which cannot be reviewed in one paper. A key to progress in this field is the formulation of a statistical mechanical formalism that could help develop equations of state and constitutive relations. This paper aims at reviewing some milestones in this direction. An essential basic step toward the development of any static and quasi-static theory of granular matter is a systematic and useful method to quantify the grain-scale structure and we start with a review of such a method. We then review and discuss the ongoing attempt to construct a statistical mechanical theory of granular systems. Along the way, we will clarify a number of misconceptions in the field, as well as highlight several outstanding problems.     

Flowing Sand—A Possible Physical Realization of Directed Percolation

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches, leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.     

Compactivity and transmission of stress in granular materials

We outline a statistical-mechanical theory of granular materials. Stress propagation and force fluctuations in static granular media are still poorly understood. We develop the statistical-mechanical theory that delivers the fundamental equations of stress equilibrium. The formalism is based on the assumptions that grains are rigid, cohesionless, and that friction is perfect. Since grains are assumed perfectly rigid, no strain or displacement field can enter the equations for static equilibrium of the stress field. The complete system of equations for the stress tensor is derived from the equations of intergranular force and torque balance, given the geometric specification of the material. These new constitutive equations are indeed fundamental and are based on relations between various components of the stress tensor within the material, and depend on the topology of the granular packing. The problem of incorporating into the formalism the "no tensile forces" constraint is considered. The compactivity concept is reviewed. We discuss the relation between the concept of compactivity and the problem of stress transmission. (c) 1999 American Institute of Physics.     

Open problems in active chaotic flows: Competition between chaos and order in granular materials

There are many systems where interaction among the elementary building blocks-no matter how well understood-does not even give a glimpse of the behavior of the global system itself. Characteristic for these systems is the ability to display structure without any external organizing principle being applied. They self-organize as a consequence of synthesis and collective phenomena and the behavior cannot be understood in terms of the systems' constitutive elements alone. A simple example is flowing granular materials, i.e., systems composed of particles or grains. How the grains interact with each other is reasonably well understood; as to how particles move, the governing law is Newton's second law. There are no surprises at this level. However, when the particles are many and the material is vibrated or tumbled, surprising behavior emerges. Systems self-organize in complex patterns that cannot be deduced from the behavior of the particles alone. Self-organization is often the result of competing effects; flowing granular matter displays both mixing and segregation. Small differences in either size or density lead to flow-induced segregation and order; similar to fluids, noncohesive granular materials can display chaotic mixing and disorder. Competition gives rise to a wealth of experimental outcomes. Equilibrium structures, obtained experimentally in quasi-two-dimensional systems, display organization in the presence of disorder, and are captured by a continuum flow model incorporating collisional diffusion and density-driven segregation. Several open issues remain to be addressed. These include analysis of segregating chaotic systems from a dynamical systems viewpoint, and understanding three-dimensional systems and wet granular systems (slurries). General aspects of the competition between chaos-enhanced mixing and properties-induced de-mixing go beyond granular materials and may offer a paradigm for other kinds of physical systems. (c) 2002 American Institute of Physics.     

The statistical mechanics of granular systems composed of elongated grains

In this paper we will suggest a model for the packing properties and phase behaviour of a granular material whose constituents are elongated in nature, using the concepts of configurational statistical mechanics. We will show that, depending upon the shape of the grains, the systems need not necessarily undergo a discontinuous first-order phase transition (even at minimum close packing). We will also briefly discuss the relationship between this model and more conventional models, such as Onsager's hard rod model.     

Granular flow from a silo: Discrete-particle simulations in three dimensions

Molecular (or granular) dynamics methods are used to study the gravity-driven flow of granular material through a horizontal aperture in three dimensions. The grains are spherical and modeled using a short-range repulsive interaction, together with normal and tangential frictional damping forces. The material is contained in a rough-walled cylindrical container with a circular hole in its base, and to permit flow measurements under steady-state conditions a continuous feed approach is employed in which exiting grains are replaced at the upper surface of the material. The dependence of flow velocity and discharge rate on aperture diameter is found to agree with experiment; other quantities such as the kinetic energy and pressure distributions are also examined. Received 5 June 2000 and Received in final form 21 September 2000