The spreading of a granular mass: role of grain properties and initial conditions

We present 2D numerical simulations of the collapse and spreading of granular columns for which the final geometry of the deposit and the runout distance are studied. Both the effects of the initial geometry and the effects of the details of the interactions between the grains are investigated. The scaling of the runout distance shows both a linear and a power-law dependence on the aspect ratio of the initial column, in agreement with previous findings (Balmforth and Kerswell in J. Fluid Mech. 538, 399–428, 2004; Lajeunesse et al. in Phys. Fluids 17, 103302, 2005; Lube et al. in Phys. Rev. E 72, 041301, 2005; Staron and Hinch in J. Fluid Mech. 545, 1–27, 2005), and independently of the value of the inter-grain friction. The latter controls the prefactor of the scaling, the effective frictional properties of the flow, and its internal structure. The non-trivial mass distribution induced by the initial geom- etry of the column strongly influences the dissipation process, and is believed to control the power-law dependence of the runout distance on the column aspect ratio.     

Pressure fluctuations measurement and analysis in hydraulic jumps using a microcomputer

Abstract

This paper presents a microcomputer based data acquisition system and an analysis of pressure fluctuations in the range of weak hydraulic jumps. Statistical analysis of data shows that the distribution of pressure fluctuations follows the Gaussian probability density function. The maximum pressure fluctuation amplitude is found to be in the range of 2.5 to 3.5 times the standard deviation. The spectral analysis of data indicates that large eddies in the low frequency range of 0 to 20 Hz are predominant over the small eddies in the high frequencies. This result is also predicted by the empirical correlation coefficient. Based on cross correlation analysis, the relationship between areal pressure fluctuations and point pressure fluctuations is developed and can be used to prevent over‐designing the strength of the stilling basins. It shows that the areal pressure fluctuations decrease as the jump longitudinal dimension increases.     

Temperature fluctuations in a solid-nitrogen cooled secondary frequency standard

Liquid helium and liquid nitrogen are commonly used as coolants for highly frequency stable oscillators. In this paper, we present the use of solid nitrogen as an alternative coolant. Solid nitrogen solidifies near 52 K under vacuum and we show that the temperature fluctuations in the solid are an order of magnitude lower than in the liquid. This has the advantage of reducing the temperature control requirements necessary to limit temperature induced frequency fluctuations in cryogenic microwave resonator-oscillators.     

The frictionless rolling contact of a rigid circular cylinder on a semi-infinite granular material

The resulting flow and deformation of a semi-infinite granular material under a rolling, smooth rigid circular cylinder is investigated using a perturbation method. Based on the double-shearing theory of granular flow, complete stress and velocity fields, resistance to rolling and the permanent displacement of surface particles are determined to first order; when the internal friction angle is zero, the solutions reduce to those obtained in the corresponding analysis for Tresca or von-Mises materials. The solution scheme and the double-shearing model for granular flow both find their origins in the work of A.J.M. Spencer.     

Resonance in a granular system

The dynamics of a 3D vibrated granular system is investigated. A new effect of resonant behaviour in the granular system is reported. The resonant frequencies can cause vibro-induced segregation in a granular system.     

Dynamic and perturbative system analysis of granular material in a vibrating screen

In most particulate classification systems, feed rates in excess of 80% of the designed capacity leads to inefficiency and conversely feed rates below this value significantly diminishes the operational efficiencies. It therefore implies that maximum efficiency is only attainable at the expense of low capacity, and vice versa. This problem is caused by transience in granular flow due to start-ups and fluctuating feed-rates, in addition to fluctuations in feed material properties. If these variations are not checked, they cause instabilities, resulting in chaotic saddles responsible for in-process systemic error generation. These errors produce intermittent disruptions in production process and control. We have applied perturbation theory to study the effects of infinitesimal changes on the material balance analysis of the unit operation. The problem was identified as one of the highly multi-stable dynamic systems, characterized by ‘predator-prey’ phenomenon in dynamical systems theory. The study allowed formulation of optimal state equations, whose numerical solutions resulted in establishment of optimal operating conditions required to sustain stability, and consistently high tonnages and efficiency up to 99% simultaneously. The study also led to development of an optimization algorithm, which upon validation with experimental data showed a close relationship, with a minimal absolute error of 0.8 and a relative error of 6%. Finally, a representative case study was conducted on screen dimensioning, based on the determined parameters. Successful evolution of this methodology may be applied for up-scaling of real systems in future.     

Surface fluctuations and the inertia effect in sandpiles

We report both an experiment and numerical simulations on superficial fluctuations of a slowly driven granular system: a box filled with a certain number of layers of glass beads is tilted very slowly up to the maximum angle of stability where an avalanche is produced. The avalanche decreases the slope of the free surface of the packing until a second critical angle is reached: the angle of repose. During the build up period many rearrangements occur on the free surface. The distribution function for the observed mass fluctuations follows a power-law behavior. We reproduce this results (rearrangements and avalanche) with a cellular automata model which takes into account the transfer of momentum to layers below. It is the purpose of this work to study the transition between static and flowing states in a very slowly driven granular system. We will focus on the very reach behavior of the surface rearrangements leading up to a large slide. Received: 30 March 2000     

Stochastic fluctuations in epidemics on networks.

The effects of demographic stochasticity on the long-term behaviour of endemic infectious diseases have been considered for long as a necessary addition to an underlying deterministic theory. The latter would explain the regular behaviour of recurrent epidemics and the former the superimposed noise of observed incidence patterns. Recently, a stochastic theory based on a mechanism of resonance with internal noise has shifted the role of stochasticity closer to the centre stage, by showing that the major dynamic patterns found in the incidence data can be explained as resonant fluctuations, whose behaviour is largely independent of the amplitude of seasonal forcing, and by contrast very sensitive to the basic epidemiological parameters. Here we elaborate on that approach, by adding an ingredient which is missing in standard epidemic models, the 'mixing network' through which infection may propagate. We find that spatial correlations have a major effect on the enhancement of the amplitude and the coherence of the resonant stochastic fluctuations, providing the ordered patterns of recurrent epidemics, whose period may differ significantly from that of the small oscillations around the deterministic equilibrium. We also show that the inclusion of a more realistic, time-correlated recovery profile instead of exponentially distributed infectious periods may, even in the random-mixing limit, contribute to the same effect.     

Direct observation of critical fluctuations in a binary mixture

Microscopic observations of concentration fluctuations in the range 1–500 m have been performed in a number of binary fluids near their critical temperature (T _c). A heterodyne technique has been used. The temperature range (T-T _c = 1–25 mK) is such that the sizes of the fluctuations are larger than or equal to the correlation length, measured usually as the inverse half-width of the structure factor of the fluctuations. Image analysis has given some information about the free energy of the system determined from the intensity distribution function. Also, the shape of the fluctuations can be studied. These are self-similar over more than three decades, with a fractal dimension of D _f = 2.8. This value is compared with a number of theoretical predictions.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

The stress response of a semi-infinite micropolar granular material subject to a concentrated force normal to the boundary

We consider the problem of a two dimensional semi-infinite granular material subject to a concentrated or point force normal to the boundary. This boundary value problem was originally solved for a classical elastic material by Flamant in 1892 and, hence, is also known as the Flamant problem (Johnson [8]). In this paper, the granular material is considered as an elastic micropolar or Cosserat continuum and is represented by a particular form of the general constitutive law derived in Walsh and Tordesillas [29]. The stress distribution predicted by the model is in good agreement with experimental data for small strains. In particular, two important features that are captured by the proposed model are: (i) the presence of tensile stress response regions, and (ii) the dependence of the stresses on the microstructural properties, i.e. the particles normal, tangential and rotational stiffness constants. The proposed analysis utilizes two new stress functions, similar to Airys stress functions in classical elastic theory.The support of the US Army Research Office through a grant to AT (Grant No. DAAD19-02-1-0216) and the Melbourne Research and Development Grant scheme is gratefully acknowledged. We thank our reviewers for their useful suggestions and insightful comments.     

Large-strain dynamic cavity expansion in a granular material

The dynamic problem of the symmetric expansion of a cylindrical or spherical cavity in a granular medium is considered. The constitutive behaviour of the material is governed by a hypoplasticity relation for granular soils capable of describing both monotonic and cyclic deformation. The problem is solved numerically by a finite-difference technique. A nonreflecting boundary condition used at the outer boundary of the computational domain makes it possible to model a continuous multi-cycle loading on the cavity wall. The solution is illustrated by numerical examples. Possible geomechanical applications to the modelling of the vibratory compaction and penetration in granular soils are discussed.     

Large-strain dynamic cavity expansion in a granular material

The dynamic problem of the symmetric expansion of a cylindrical or spherical cavity in a granular medium is considered. The constitutive behaviour of the material is governed by a hypoplasticity relation for granular soils capable of describing both monotonic and cyclic deformation. The problem is solved numerically by a finite-difference technique. A nonreflecting boundary condition used at the outer boundary of the computational domain makes it possible to model a continuous multi-cycle loading on the cavity wall. The solution is illustrated by numerical examples. Possible geomechanical applications to the modelling of the vibratory compaction and penetration in granular soils are discussed.     

物料冲击破碎过程的一种非线性力模型

针对冲击破碎过程，在初步准静压破碎实验的基础上，提出了物料层的分段线性接触力模型，并引入恢复系数来表示膨胀阶段和压缩阶段之间的参数关系。应用该模型进行了单球冲击破碎的计算机模拟，证明恢复系数能宏观反映冲击破碎过程的能量损失。与线性弹簧阻尼模型相比，不但在微观过程中接触力保持正压，物料破碎会产生不可恢复的变形，更符合实验观察的实际情况，而且计算精度更高。     

Triaxial behavior of granular material under complex loading path by a new numerical true triaxial engine

A new numerical true triaxial engine based on discrete element method accounting for rolling resistance contact is developed. By this engine, we have simulated mechanical behavior of granular materials under complex stress loading path in this study. Stress-strain responses of a kind of typical granular sand under several stress loading path in meridian and deviatoric stress space are provided. The results show that the three dimensional effects like the intermediate principal stress play an important role in the modeling processes. Theoretical analysis in strength characteristic implies the strength criteria with three parameters such as unified strength criterion and van Eekelen strength criterion are capable of describing cohesionless granular material behaviors in three dimensional stress states. Moreover, the case study for Chende sand further demonstrates the numerical true triaxial engine, is a potential tool. As compared to conventional triaxial compression test, this new developed apparatus could be widely used to “measure” elastic-plastic behavior in three dimensional stress space for finite element analysis in geotechnical problems.     

Thermal fluctuations of haemoglobin from different species: adaptation to temperature via conformational dynamics

Thermodynamic stability, configurational motions and internal forces of haemoglobin (Hb) of three endotherms (platypus, Ornithorhynchus anatinus; domestic chicken, Gallus gallus domesticus and human, Homo sapiens) and an ectotherm (salt water crocodile, Crocodylus porosus) were investigated using circular dichroism, incoherent elastic neutron scattering and coarse-grained Brownian dynamics simulations. The experimental results from Hb solutions revealed a direct correlation between protein resilience, melting temperature and average body temperature of the different species on the 0.1 ns time scale. Molecular forces appeared to be adapted to permit conformational fluctuations with a root mean square displacement close to 1.2 Å at the corresponding average body temperature of the endotherms. Strong forces within crocodile Hb maintain the amplitudes of motion within a narrow limit over the entire temperature range in which the animal lives. In fully hydrated powder samples of human and chicken, Hb mean square displacements and effective force constants on the 1 ns time scale showed no differences over the whole temperature range from 10 to 300 K, in contrast to the solution case. A complementary result of the study, therefore, is that one hydration layer is not sufficient to activate all conformational fluctuations of Hb in the pico- to nanosecond time scale which might be relevant for biological function. Coarse-grained Brownian dynamics simulations permitted to explore residue-specific effects. They indicated that temperature sensing of human and chicken Hb occurs mainly at residues lining internal cavities in the β-subunits.     

单环苯并噁嗪树脂热解的ReaxFF反应动力学模拟

采用ReaxFF动力学方法模拟了非交联固化单环苯并噁嗪树脂在不同温度下的热解特性。模拟结果表明,N桥键的断裂是热解的主要引发反应,H_2,H_2O和大分子碳团簇是热解的主要产物。随着反应温度升高,H_2的数量急剧增加,而H_2O的数量反而降低,高温有利于促进相对分子质量较大的碳团簇的形成,还观察到了CO,NH_3,N_2和HCN等小分子产物。用ReaxFF动力学方法模拟所得的气体产物以及含类似石墨烯结构的碳团簇与实际实验结果一致,ReaxFF动力学模拟方法可以作为一种研究苯并噁嗪树脂高温热解反应的有效途径。     

Motion of a granular material in a tall vibrating system

The vertical motion of particles is considered for a tall vibrating system; a study is made of the effects of stress waves on the distance between the bottom of the vessel and the bottom of the bed.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 6, pp. 1048–1053, June, 1978.     

多功能阵列式触觉传感器的研究

介绍了一种以MEMS技术制作的可定量获取三维接触力信息的 4× 8阵列触觉传感器的结构与工艺 ,提出一种新颖的三维接触力信息的获取与处理方法 ,并给出了实现接触、分布压、接触总力、滑动状态等多种功能的实验结果和主要的技术指标。