New jamming scenario: from marginal jamming to deep jamming

We study the properties of jammed packings of frictionless spheres over a wide range of volume fractions. There exists a crossover volume fraction which separates deeply jammed solids from marginally jammed solids. In deeply jammed solids, all the scalings presented in marginally jammed solids are replaced with remarkably different ones with potential independent exponents. Correspondingly, there are structural changes in the pair distribution function associated with the crossover. The normal modes of vibration of deeply jammed solids also exhibit some anomalies, e.g., strengthened quasilocalization and the absence of Debye-like density of states at low frequencies. Deeply jammed systems may thus be cataloged to a new class of amorphous solids.     

Jamming of packings of frictionless particles with and without shear

By minimizing the enthalpy of packings of frictionless particles, we obtain jammed solids at desired pressures and hence investigate the jamming transition with and without shear. Typical scaling relations of the jamming transition are recovered in both cases. In contrast to systems without shear, shear-driven jamming transition occurs at a higher packing fraction and the jammed solids are more rigid with an anisotropic force network. Furthermore, by introducing the macrofriction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixed pressure.     

Entropy of jammed matter

We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using volume fluctuation analysis and graph theoretical methods. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter. At the mesoscopic level the entropy vanishes at random close packing, while the microscopic states contribute to a finite entropy. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits.     

Jamming III: Characterizing randomness via the entropy of jammed matter

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the definition of a volume function that is dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, which explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. The mesoscopic theory reproduces the simulations results in shape well, though a difference in magnitude implies that the entire entropy of the packing may not be captured by the methods presented herein. We discuss possible extensions to the present mesoscopic approach describing packings from random loose packing (RLP) to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to face-centered cubic (FCC) packing.     

Transients in sheared granular matter

As dense granular materials are sheared, a shear band and an anisotropic force network form. The approach to steady-state behavior depends on the history of the packing and the existing force and contact network. We present experiments on shearing of dense granular matter in a 2D Couette geometry in which we probe the history and evolution of shear bands by measuring particle trajectories and stresses during transients. We find that when shearing is stopped and restarted in the same direction, steady-state behavior is immediately reached, in agreement with the typical assumption that the system is quasistatic. Although some relaxation of the force network is observed when shearing is stopped, quasistatic behavior is maintained because the contact network remains essentially unchanged. When the direction of shear is reversed, a transient occurs in which stresses initially decrease, changes in the force network reach further into the bulk, and particles far from the wheel become more mobile. This occurs because the force network is fragile to changes transverse to the force network established under previous shear; particles must rearrange before becoming jammed again, thereby providing resistance to shear in the reversed direction. The strong force network is re-established after displacing the shearing surface , where d is the mean grain diameter. Steady-state velocity profiles are reached after a shear of . Particles immediately outside of the shear band move on average less than 1 diameter before becoming jammed again. We also examine particle rotation during this transient and find that mean particle spin decreases during the transient, which is related to the fact that grains are not interlocked as strongly.Received: 5 March 2004, Published online: 24 August 2004PACS: 45.70.-n Granular systems - 83.80.Fg Granular solids     

Suppressed compressibility at large scale in jammed packings of size-disperse spheres

We analyze the large-scale structure and fluctuations of jammed packings of size-disperse spheres, produced in a granular experiment as well as numerically. While the structure factor of the packings reveals no unusual behavior for small wave vectors, the compressibility displays an anomalous linear dependence at low wave vectors and vanishes when q→0. We show that such behavior occurs because jammed packings of size-disperse spheres have no bulk fluctuations of the volume fraction and are thus hyperuniform, a property not observed experimentally before. Our results apply to arbitrary particle size distributions. For continuous distributions, we derive a perturbative expression for the compressibility that is accurate for polydispersity up to about 30%.     

Unexpected density fluctuations in jammed disordered sphere packings

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k) approximately |k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r) approximately -r(-4), and a long-ranged direct correlation function c(r).     

Microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations.     

Shocks near jamming

Nonlinear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed and demonstrate that the elementary excitations are strongly nonlinear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.     

Effective temperature and jamming transition in dense, gently sheared granular assemblies

We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.     

Order-to-disorder transition in ring-shaped colloidal stains

A colloidal dispersion droplet evaporating from a surface, such as a drying coffee drop, leaves a distinct ring-shaped stain. Although this mechanism is frequently used for particle self-assembly, the conditions for crystallization have remained unclear. Our experiments with monodisperse colloidal particles reveal a structural transition in the stain, from ordered crystals to disordered packings. We show that this sharp transition originates from a temporal singularity of the flow velocity inside the evaporating droplet at the end of its life. When the deposition speed is low, particles have time to arrange by Brownian motion, while at the end, high-speed particles are jammed into a disordered phase.     

Disks vs. spheres: Contrasting properties of random packings

Collections of random packings of rigid disks and spheres have been generated by computer using a previously described concurrent algorithm. Particles begin as infinitesimal moving points, grow in size at a uniform rate, undergo energy-onconserving collisions, and eventually jam up. Periodic boundary conditions apply, and various numbers of particles have been considered (N2000 for disks,N8000 for spheres). The irregular disk packings thus formed are clearly polycrystalline with mean grain size dependent upon particle growth rate. By contrast, the sphere packings show a homogeneously amorphous texture substantially devoid of crystalline grains. This distinction strongly influences the respective results for packing pair correlation functions and for the distributions of particles by contact number. Rapidly grown disk packings display occasional vacancies within the crystalline grains; no comparable voids of such distinctive size have been found in the random sphere packings. Rattler particles free to move locally but imprisoned by jammed neighbors occur in both the disk and sphere packings.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Jamming as a critical phenomenon: a field theory of zero-temperature grain packings

A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a nonzero value of the packing fraction. The zero-temperature constraint of force balance plays a crucial role in determining the nature of the transition. Two order parameters, , the deviation of the average number of contacts from the isostatic value, and , the average magnitude of the force per contact, characterize the transition from the jammed (high packing fraction) to the unjammed (low packing fraction state). The critical point has a mixed character with the order parameters showing a jump discontinuity but with fluctuations of the contact force diverging. At the critical point, the distribution of phi shows the characteristic plateau observed in static granular piles. The theory makes falsifiable predictions about the spatial fluctuations of the contact forces.     

Combinatorial and approximative analyses in a spatially random division process

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.     

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     

Dense and nearly jammed random packings of freely jointed chains of tangent hard spheres

Dense packings of freely jointed chains of tangent hard spheres are produced by a novel Monte Carlo method. Within statistical uncertainty, chains reach a maximally random jammed (MRJ) state at the same volume fraction as packings of single hard spheres. A structural analysis shows that as the MRJ state is approached (i) the radial distribution function for chains remains distinct from but approaches that of single hard sphere packings quite closely, (ii) chains undergo progressive collapse, and (iii) a small but increasing fraction of sites possess highly ordered first coordination shells.     

Contact forces in a granular packing

We present the results of a systematic numerical investigation of force distributions in granular packings. We find that all the main features of force transmission previously established for two-dimensional systems of hard particles hold in three-dimensional systems and for soft particles, too. In particular, the probability distribution of normal forces falls off exponentially for forces above the mean force. For forces below the mean, this distribution is either a decreasing power law when the system is far from static equilibrium, or nearly uniform at static equilibrium, in agreement with recent experiments. Moreover, we show that the forces below the mean do not contribute to the shear stress. The subnetwork of the contacts carrying a force below the mean thus plays a role similar to a fluid surrounding the solid backbone composed of the contacts carrying a force above the mean. We address the issue of the computation of contact forces in a packing at static equilibrium. We introduce a model with no local simplifying force rules, that allows for an exact computation of contact forces for given granular texture and boundary conditions. (c) 1999 American Institute of Physics.     

Jamming in two-dimensional packings

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-based on several approximations to predict the probability distribution of volumes-suggests the existence of the limiting densities of the jammed packings according to their coordination number and compactivity. This result has implications for the understanding of disordered states in the disk packing problem as well as the existence of a putative glass transition in two-dimensional systems.     

On-line Measurement of Solids Concentration or the Mean Particle Size in a Saturated Slurry Containing Background Particles Using a Turbidity Method

An on-line double-sensor turbidimeter for estimating the solids concentration or the mean particle size in a saturated slurry system in the presence of foreign insoluble particles is proposed. The correlation representing the operation of the double-sensor turbidimeter for on-line implementation is also developed. The technique relies on measuring the transmittance of an infrared light beam through the suspension, once in the presence of soluble particles and a second time when the soluble particles have completely dissolved. The device can be easily implemented on a crystallization system for monitoring and control applications. The maximum errors for solids concentration and mean particle size measurements were 13% and 7%, respectively.