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.     

分仓颗粒布居分聚现象的通量模型

置于以窗口连接的分隔仓中振动驱动的颗粒气体会出现颗粒在两仓中布居分聚现象,被形象地称为麦克斯韦妖现象.通量模型的建立是理解麦克斯韦妖现象的关键问题.Eggers以颗粒气体动力学为基础得出了简化的理论模型.该模型可以很好地得到分仓中颗粒的布居分聚现象,然而似乎无法用于预测两种颗粒在分仓体系中的布居振荡现象.通过实验研究,测量了颗粒气体的流通量曲线,改进了Eggers模型.改进的模型可以很好地得到两种颗粒在分仓体系中的布居振荡现象. 关键词： 颗粒气体 耗散 通量模型     

Directed segregation in compartmentalized bi-disperse granular gas

A bi-disperse granular gas in an asymmetrical two-compartment system is studied experimentally. The presence of asymmetry within the range of our experimental parameters results in a directed segregated state and a directed clustering state. This deterministic system does not depend on the initial conditions. A modified flux model based on Lohse's flux model for bi-disperse granular gases is derived. The modified flux model explains qualitatively the experimental results.     

剪切振动下湿颗粒的力学谱

在恒温25 ℃剪切振动条件下,测量不同水分含量的NaCl湿颗粒体系的力学谱（能量耗散tanφ和剪切模量G）.研究发现,随着剪切振幅增大,NaCl湿颗粒体系的剪切模量G和能量耗散tanφ都表现出类似于干颗粒体系的阻塞（Jamming）转变行为.随着体系中水含量的增大,湿颗粒体系的剪切模量G和能量耗散tanφ在质量分数约等于11%的临界水浓度下均出现一个峰值,且峰位与应变振幅无关,表明此时颗粒之间主要的作用力发生了变化.     

Breakdown of energy equipartition in a 2D binary vibrated granular gas

We report experiments on the equipartition of kinetic energy in a mixture of pairs of different types of grains vibrated in two dimensions. In general, the two types of grains do not attain the same granular temperature, T(g) = 1/2m. However, the temperature ratio is constant in the bulk of the system and independent of the vibration velocity. The ratio depends strongly on the ratio of mass densities of the grains, but not on their inelasticity. Also, the temperature ratio is insensitive to compositional variables such as the number fraction of each component and the total number density. We conclude that a single granular temperature, as traditionally defined, does not characterize a multicomponent mixture.     

准静态颗粒介质的弹性势能弛豫分析

颗粒体系是典型的多体相互作用体系, 具有多重的能量亚稳态. 对于准静态颗粒体系, 引入构型颗粒温度T_c描述弹性势能涨落. 本文认为平衡的体系具有一定的构型颗粒温度T_a, 其量值反映了其结构特征. 当外界扰动激发的构型颗粒温度超出T_a时, 产生不可逆过程. 通过对应力松弛过程的分析, 发现(T_c-T_a)激发了弹性弛豫, 且(T_c-T_a)越大则松弛过程中应力变化越大, 最终构型颗粒温度T_c→T_a时,宏观应力松弛结束,体系达到新的能量亚稳态.     

Modifying the structural phase state of fine-grained titanium under conditions of ion irradiation

The results from quantitative investigations into the structural phase state of finely dispersed titanium before and after implantation with aluminum ions are presented. Two types of ??-Ti grains differing by phase composition, defect structure, and size are distinguished in the structure: fine grains in the range of 0.1?C0.5 ??m and coarse grains in the range of 0.5?C5 ??m. The presence of two types of TiO₂ particles in the material, i.e., rounded particles found at dislocations in the bulk of the ??-Ti grains and lamellar particles found only inside coarse ??-Ti grains, is established. The formation of the Ti₃Al phase is observed in the form of lamellar inclusions along the grain boundaries and rounded particles in triple joints. It is found that the particles of the TiAl₃ phase are isolated with a smaller volume fraction than the Ti₃Al phase; they are localized along the boundaries of coarse grains of the titanium matrix. It is established that the granular state and defect structure of the material change substantially after ion irradiation; i.e., the dislocation density and the fields of internal stresses in fine grains grow considerably, relative to the initial state of titanium.     

Free cooling of the one-dimensional wet granular gas

The free cooling behavior of a wet granular gas is studied in one dimension. We employ a particularly simple model system in which the interaction of wet grains is characterized by a fixed energy loss assigned to each collision. Macroscopic laws of energy dissipation and cluster formation are studied on the basis of numerical simulations and mean-field analytical calculations. We find a number of remarkable scaling properties which may shed light on earlier unexplained results for related systems.     

Observation of the condensation of a gas of interacting grains

We consider an ensemble of grains that interact through a dipole-dipole interaction. A granular gas is formed by the vertical motion of a piston at the bottom boundary of the system. The interaction between the grains is controlled by an horizontally applied magnetic field. When the speed of the piston is decreased, we observe a transition from a low density to a high density phase. When the interaction between grains is weak, the transition is continuous. It is discontinuous for stronger interaction. The phase diagram displays strong similarities with the ones observed for usual equilibrium phase transitions.     

Dressed Josephson junction network models and low-field magnetic response of high-Tc granular superconductors

A bare three-dimensional model, in which grains are reduced to points, cannot fully account for the magnetic properties of granular superconductors. A dressed version of these network models is proposed to discuss the quantitative link between the low-field magnetic response of high-T_c superconducting granular samples and the characteristic properties of Josephson junction network models. By means of dressed models, the temperature dependence of the d.c. field-cooled susceptibility of a simple three-dimensional granular system, consisting of eight grains in a cubic arrangement, is studied.     

Upward penetration of grains through a granular medium

We study experimentally the creeping penetration of guest (percolating) grains through densely packed granular media in two dimensions. The evolution of the system of the guest grains during the penetration is studied by image analysis. To quantify the changes in the internal structure of the packing, we use Voronoï tessellation and a certain shape factor which is a clear indicator of the presence of different underlying substructures (domains). We first consider the impact of the effective gravitational acceleration on upward penetration of grains. It is found that the higher effective gravity increases the resistance to upward penetration and enhances structural organization in the system of the percolating grains. We also focus our attention on the dependence of the structural rearrangements of percolating grains on some parameters like polydispersity and the initial packing fraction of the host granular system. It is found that the anisotropy of penetration is larger in the monodisperse case than in the bidisperse one, for the same value of the packing fraction of the host medium. Compaction of initial host granular packing also increases anisotropy of penetration of guest grains. When a binary mixture of large and small guest grains is penetrated into the host granular medium, we observe size segregation patterns.     

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.     

Arches and contact forces in a granular pile

Assemblies of granular particles mechanically stable under their own weight contain arches. These are structural units identified as sets of mutually stable grains. It is generally assumed that these arches shield the weight above them and should bear most of the stress in the system. We test such hypothesis by studying the stress born by in-arch and out-of-arch grains. We show that, indeed, particles in arches withstand larger stresses. In particular, the isotropic stress tends to be larger for in-arch grains whereas the anisotropic component is marginally distinguishable between the two types of particles. The contact force distributions demonstrate that an exponential tail (compatible with the maximization of entropy under no extra constraints) is followed only by the out-of-arch contacts. In-arch contacts seem to be compatible with a Gaussian distribution consistent with a recently introduced approach that takes into account constraints imposed by the local force balance on grains.     

The morphology of tin cluster assembled films and the effect of nitrogen

Thin films produced by depositing tin clusters with sizes between 5 and 10 nm onto silicon nitride substrates were found to be highly coalesced resulting in grains with sizes ~30 nm. Exposing the clusters to nitrogen before they were deposited significantly reduced the coalescence between them and resulted in granular films where the clusters mostly retained their shape. This is due to a small amount of tin nitride forming in the clusters. The coalesced and granular films were used to fabricate tin oxide gas sensors. This was done by depositing the two types of films onto silicon nitride chips and then oxidising them by baking at 250 °C for 24 h. It was found that the sensors composed of uncoalesced clusters were much more sensitive to hydrogen. This was attributed to the smaller grain size and the larger surface area of the granular films.     

On the development of inhomogeneities in freely evolving granular gases: The shear state and beyond

The understanding of the mechanisms leading to the formation of inhomogeneities in freely evolving granular gases is important to establish, for instance, the time scale for pattern formation. In this work, the shear state of an isolated granular gas will be analyzed. This is a two-band shear state with a steady density profile and an average temperature that decays in time with a Haff like law, but controlled by the viscosity of the gas. Hydrodynamics predicts that this state can only exist if the size of the system is larger than the critical size for the stability of the homogeneous cooling state, and expressions for the hydrodynamic fields in the limit of not too large inhomogeneities can be obtained. The theoretical predictions are compared with computer simulation results of a system of inelastic hard disks for several values of the coefficient of restitution, well beyond the quasi-elastic limit. It will be shown that the shear state is indeed exhibited by the system if its size is larger, but not much larger, than the critical size. The behaviour of the system and the way in which it deviates from the shear state as its size is increased will also be discussed.     

Origin of density clustering in a freely evolving granular gas

The physical mechanisms leading to the development of density inhomogeneities in a freely evolving low density granular gas are investigated. By means of the direct simulation Monte Carlo method, numerical solutions of the inelastic Boltzmann equation are constructed for both a perturbed system and also for an initially homogeneous state. Analysis of the Fourier components of the fields indicates that the nonlinear coupling contributions of the transversal velocity play a crucial role in the initial setup of clustering. A simple hydrodynamic model is proposed to describe what is observed in the simulations. Finally, the nature of the inhomogeneous state is briefly discussed.     

Self-Organization in a Granular Medium by Internal Avalanches

Internal avalanches of grain displacements can be created inside a granular material kept in a bin in two ways: (i) by removing a randomly selected grain at the bottom of the bin; and (ii) by breaking a stable arch of grains clogging a hole at the bottom of the bin. Repeated generation of such avalanches leads the system to a steady state. It is relevant to ask whether this state is a critical state, as in self-organized criticality (SOC). We review here some recent studies of this problem using cellular automata and hard-disc models.     

Phase Transition and Critical Phenomenon Occurring in Granular Matter

We investigate the granular flow states in a channel with bottleneck by molecular dynamics simulations.Our study is restricted only on a selected key area rather than on the whole system to focus on the flow properties of a single granular state.A random force field is introduced to control the granular temperature.It is also pointed out that the flow rate in the granular flow can be correlated with the pressure,which leads us to carry out a comprehensive study similar to the classical study for general liquid-gas phase transition.Our results show that the dilute flow state and the dense flow state of the granules are similar to the gas state and the liquid state of general substances,respectively,and the properties of phase transition and critical phenomenon are also similar to those occurring in general substances.     

Multipartite Quantum Clock Synchronization under The Influence of Unruh Thermal Noise

A protocol for multipartite quantum clock synchronization is performed under the influence of Unruh thermal noise. The dynamics of multipartite quantum system consisting of Unruh–DeWitt detectors when one of the detectors is accelerated are obtained. To estimate the time difference between the clocks, the time probability is calculated and how the probability is influenced by the Unruh thermal noise and other factors is analyzed. It is shown that both relativistic motion and interaction between the atom and the external scalar field affect the choice of optimal number of excited atoms in the initial state, which leads to a higher clock adjustment accuracy. Time probabilities for different types of initial states approach the same value in the limit of infinite acceleration, while tend to different minimums with increasing number of atoms. In addition, the accuracy of clock synchronization using a pair of entangled clocks in two‐party system is always higher than in a multipartite system, while the optimal Z‐type multipartite initial state always performs better than the W‐type state.     

Air-Driven Segregation in Binary Granular Mixtures with Same Size but Different Densities

We investigate the segregation effect of binary granular mixtures with the same size but different densities under vibration at different air pressures. Our experiments show that the segregation state is seriously dependent on the air pressure and there is a new type of partially segregated state at high air pressure, which has the characteristic that the lighter grains tend to stay at the bottom and form a pure layer, while heavier grains and remained lighter ones tend to rise and to form a mixed layer on the top of the system. We redefine the order parameter to study the variation of the segregation effect with the air pressure and vibration parameter in detail. Finally, the mechanism of the air-driven segregation is illustrated by the faster acceleration due to the airflow through the granular bed for lighter particles.