Complex force network in marginally and deeply jammed solids

This paper studies the force network properties of marginally and deeply jammed packings of frictionless soft particlesfrom the perspective of complex network theory. We generate zero-temperature granular packings at different pressures by minimizing the inter-particle potential energy. The force networks are constructed as nodes representing particles and links representing normal forces between the particles. Deeply jammed solids show remarkably different behavior from marginally jammed solids in their degree distribution, strength distribution, degree correlation, and clustering coefficient. Bimodal and multi-modal distributions emerge when the system enters the deep jamming region. The results also show that small and large particles can show different correlation behavior in this simple system.     

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.     

Definition and properties of ideal amorphous solids

It is proposed that two ideal amorphous structures, type I and type II, based on maximally random jammed packing of spheres of equal size, form a distinct class of ideal amorphous solids. The ideal amorphous structures contain wide variations in local density, limited by the condition of solidity. Four distinct characteristics, based on statistical geometry and topology, are shown to define this class. Voronoi tessellations carried out on simulated cells of random packed spheres and amorphous polymers give a broad distribution of individual volumes, skewed, with a tail at the high volume end.     

Rheology of dense granular mixtures: boundary pressures

Models for dense sheared granular materials indicate that their rheological properties depend on particle size, but the representative size for mixtures is not obvious. Here, we computationally study pressure on a boundary due to sheared granular mixtures to determine its dependence on particle size distribution. We find that the pressure does not depend monotonically on average particle size. Instead it has an additional dependence on a measure of the effective free volume per particle we adapt from an expression for packing of monosized particles near the jammed state.     

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     

Jamming I: A volume function for jammed matter

We introduce a “Hamiltonian”-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed systems. At the microscopic level, we show that the volume function is the Voronoi volume associated to each particle and in turn we provide an analytical formula for the Voronoi volume in terms of the contact network, valid for any dimension. We then develop a statistical theory for the probability distribution of the volumes in 3d to calculate an average volume function coarse-grained at a mesoscopic level. The salient result is the discovery of a mesoscopic volume function inversely proportional to the coordination number. Our analysis is the first step toward the calculation of macroscopic observables and equations of state using the statistical mechanics of jammed matter, when supplemented by the condition of mechanical equilibrium of jamming that properly defines jammed matter at the ensemble level.     

Scaling theory of polymer thermodiffusion

The motion of a linear polymer chain in a good solvent under a temperature gradient is examined theoretically by breaking up the flexible chain into Brownian rigid rods, and writing down an equation of motion for each rod. The motion is driven by two forces. The first one is Waldmann’s thermophoretic force (stemming from the departure of the solvent’s molecular-velocity distribution from Maxwell’s equilibrium distribution) which here is extrapolated to a dense medium. The second force is due to the fact that the viscous friction varies with position owing to the temperature gradient, which brings an important correction to the Stokes law of friction. We use scaling considerations relying upon disparate length scales and omitting non-universal numerical prefactors. The present scaling theory is compared with recent experiments on the thermodiffusion of polymers and is shown to account for (i) the existence of both signs of the thermodiffusion coefficient of long chains, (ii) the order of magnitude of the coefficient, (iii) its independence of the chain length in the high-polymer limit and (iv) its dependence on the solvent viscosity.     

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.     

On the extension of the Boltzmann equation to include pair correlations

The derivation of kinetic equations, including the effects of pair correlations, for a gas of particles interacting via purely repulsive forces is reported. An additional assumption on the form of the two-particle distribution function yields the Enskog equation for a dense hard-sphere gas. However, the true two-particle distribution function is not of this form.     

Surface relief gratings in photoaddressable polymers generated by cw holography

Surface relief gratings (SRGs) are a widely observed phenomenon in holographic experiments with photoaddressable polymers. This article proposes a model which is able to explain the observed effects in cw experiments. It is based on forces in an electrical field which are caused by the inhomogeneous spatial distribution of the refractive index and the permittivity in the illuminated sample. Received: 11 September 2000 / Revised version: 5 December 2000 / Published online: 21 February 2001     

Freezing transition in bi-directional CA model for facing pedestrian traffic

We present a bi-directional cellular automaton (CA) model for facing traffic of pedestrians on a wide passage. The excluded-volume effect and bi-directionality of facing traffic are taken into account. The CA model is not stochastic but deterministic. We study the jamming and freezing transitions when pedestrian density increases. We show that the dynamical phase transitions occur at three stages with increasing density. There exist four traffic states: the free traffic, jammed traffic 1, jammed traffic 2, and frozen state. At the frozen state, all pedestrians stop by preventing from going ahead each other. At three transitions, the pedestrian flow changes from the free traffic through the jammed traffic 1 and jammed traffic 2, to the frozen state.     

Transition from the Compact to the Dense Phase of Two-Dimensional Polymers

We present a unifying picture of the compact, dense, and dilute phases of two-dimensional polymers. The lattice dependence of the scaling exponents for compact polymers is reconciled with their universality in the dense and dilute cases. In particular, we show that violations of the fully packing constraint in the compact phase can be interpreted as magnetic screening in the associated Coulomb gas, which induces a flow to either the dense or the dilute phase. When more than one flavor of polymers is present the flow away from the compact phase leads to a decoupling of the flavors, and the central charge decreases by an integer. If charge asymmetry develops, the polymer flavors may independently flow to either of the two noncompact phases.     

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.     

Modeling the capability of penetrating a jammed crowd to eliminate freezing transition

Frozen state from jammed state is one of the most interesting aspects produced when simulating the multidirectional pedestrian flow of high density crowds. Cases of real life situations for such a phenomenon are not exhaustively treated.Our observations in the Hajj crowd show that freezing transition does not occur very often. On the contrary, penetrating a jammed crowd is a common aspect. We believe the kindness of pedestrians facing others whose walking is blocked is a main factor in eliminating the frozen state as well as in relieving the jammed state. We refine the social force model by incorporating a new social force to enable the simulated pedestrians to mimic the real behavior observed in the Hajj area.Simulations are performed to validate the work qualitatively.     

双分散颗粒体系在临界堵塞态的结构特征

堵塞行为是颗粒体系中一种常见的现象,其力学性质与堆积结构的关联非常复杂.本文采用离散元法研究了由两种不同半径颗粒组成的二维双分散无摩擦球形颗粒体系在临界堵塞态所呈现的结构特征,讨论了大小颗粒粒径比与大颗粒百分比对临界堵塞态的影响.数值模拟结果表明,当粒径比小于1.4时,临界平均接触数与大颗粒百分比关系不大,当粒径比大于1.4时随着大颗粒百分比的增大临界平均接触数先减小再增大.而临界体积分数在粒径比小于1.8时随着大颗粒百分比的增加先减小后增大,大于1.8时又基本不随大颗粒百分比而变化.大颗粒百分比在接近0或1时,系统近似为单分散体系,临界平均接触数与体积分数基本不随半径比的增大而变化;在接近0.5时,临界平均接触数随着半径比的增大逐渐减小,而临界体积分数则是先减小后增大.文中对大-小颗粒这一接触类型的百分比也进行了探讨,其值随着大颗粒百分比的增大呈二次函数的变化趋势,粒径比对这一变化趋势只有较小的影响.     

Nonequilibrium fluctuation relation for sheared micellar gel in a jammed state

We show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress, and in all cases show similar symmetry properties as predicted by the Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear-rate fluctuations increase with the decrease of the system size.     

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.     

Statistics of crumpled paper

A statistical study of crumpled paper is allowed by a minimal 1D model: a self-avoiding line bent at sharp angles--in which the elastic energy resides--put in a confining potential. Many independent equilibrium configurations are generated numerically and their properties are investigated. At small confinement, the distribution of segment lengths is log-normal in agreement with previous predictions and experiments. At high confinement, the system approaches a jammed state with a critical behavior, whereas the length distribution follows a gamma law in which the parameter is predicted as a function of the number of layers in the system.     

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.     

基于容栅位移传感器的管路堵塞监测系统设计

现有的氮磷营养盐原位监测仪存在不足,其进样管路在受污染的水体中容易被堵塞,针对此问题提出了一种基于容栅位移传感器的管路堵塞监测系统。通过容栅位移传感器采集位移信号,经过滑动滤波以后输入STM32单片机处理,对数据分析处理后得到管路形变特征参数,进而判断管路堵塞状态,并启动滤膜更换装置更换过滤膜,排除堵塞保证机器顺利运行。系统测试和实验结果表明:容栅测位移法在非介入式管路堵塞测量中完全可行,为小管径胶管的在线堵塞检测提供了一种新的方法。