Vibrations and diverging length scales near the unjamming transition

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition.     

Force Distributions near Jamming and Glass Transitions

We calculate the distribution of interparticle normal forces P(F) near the glass and jamming transitions in model supercooled liquids and foams, respectively. P(F) develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of P(F) was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress, and density lends credence to the recently proposed generalized jamming phase diagram.     

Rotating bearings in regular and irregular granular shear packings

For 2D regular dense packings of solid mono-size non-sliding disks there is a mechanism for bearing formation under shear that can be explained theoretically. There is, however, no easy way to extend this model to include random dense packings which would better describe natural packings. A numerical model that simulates shear deformation for both near-regular and irregular packings is used to demonstrate that rotating bearings appear roughly with the same density in random and regular packings. The main difference appears in the size distribution of the rotating clusters near the jamming threshold. The size distribution is well described by a scaling form with a large-size cut-off that seems to grow without bounds for regular packings at the jamming threshold, while it remains finite for irregular packings. At packing densities above the jamming transition there can be no shear, unless the disks are allowed to break. Breaking of disks induces a large number of small local bearings. Clusters of rotating particles may contribute to e.g. pre-rupture yielding in landslides, snow avalanches and to the formation of aseismic gaps in tectonic fault zones.     

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.     

Jamming and crystallization in athermal polymer packings

Dense packings of chains of hard spheres possess characteristic features that do not have a counterpart in corresponding packings of monomeric spheres especially near the maximally random jammed (MRJ) state. From the modelling perspective the additional requirement that spheres keep their connectivity while maximizing the occupied volume fraction imposes severe constraints on generation algorithms of dense chain configurations. The extremely sluggish dynamics imposed by the uncrossability of chains precludes the use of deterministic or stochastic dynamics to generate all but dilute polymer packings. As a viable alternative, especially tailored chain-connectivity-altering Monte Carlo (MC) algorithms have been developed that bypass this kinetic hindrance and have actually been able to produce packings of hard-sphere chains in a volume fraction range spanning from infinite dilution up to the MRJ state. Such very dense athermal polymer packings share a number of structural features with packings of monomeric hard spheres, but also display unique characteristics due to the constraints imposed by connectivity. We give an overview of the most relevant results of our recent modeling work on packings of freely-jointed chains of tangent hard spheres about the MRJ state, local structure, chain dimensions and their scaling with density, topological constraints in the form of entanglements and knots, contact network at jamming, and entropically driven crystallization.     

Relationship between vibrations and dynamical heterogeneity in a model glass former: Extended soft modes but local relaxation

We study the relation between short-time vibrational modes and long-time relaxational dynamics in a kinetically constrained lattice gas with harmonic interactions between neighbouring particles. We find a correlation between the location of the low- (high-) frequency vibrational modes and regions of high (low) propensity for motion. This is similar to what was observed in continuous force systems, but our interpretation is different: in our case relaxation is due to localised excitations which propagate through the system; these localised excitations act as background disorder for the elastic network, giving rise to anomalous vibrational modes. Our results provide an example whereby a correlation between spatially extended low-frequency modes and high-propensity regions does not imply that relaxational dynamics originates in extended soft modes but rather belies their common origin. We consider other measures of elastic heterogeneity, such as non-affine displacement fields and mode localisation lengths, and discuss implications of our results to interpretations of dynamic heterogeneity more generally.     

Elegance of disordered granular packings: a validation of Edward's hypothesis

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming a constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly related to the coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states.     

Understanding the low-frequency quasilocalized modes in disordered colloidal systems

In disordered colloidal systems, we experimentally measure the normal modes with the covariance matrix method and clarify the origin of low-frequency quasilocalization at the single-particle level. We observe important features from both jamming and glass simulations: There is a plateau in the density of states [D(ω)] which is suppressed upon compression, as predicted by jamming; within the same systems, we also find that the low-frequency quasilocalization originates from the large vibrations of defective structures coupled with transverse excitations, consistent with a recent glass simulation. The coexistence of these features demonstrates an experimental link between jamming and glass. Extensive simulations further show that such a structural origin of quasilocalization is universally valid for various temperatures and volume fractions.     

Numerical study of the stress response of two-dimensional dense granular packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.     

Dense packing in the monodisperse hard-sphere system: A numerical study

We report a numerical study of the close packing of monodisperse hard spheres. The close packings of hard spheres are produced by the Lubachesky-Stillinger (LS) compression algorithm and span the range from the disordered states to the ordered states. We provide quantitative evidence for the claim that the density and structural order of the arrested close packing can be determined by the compression rate, i.e., with slower rates producing denser and more ordered structures. Through deeply analyzing the structure of the resulting arrested close packings, a transition region has been identified in the plane of density and reciprocal compression rate, in between what have been historically thought of as amorphous and crystalline packings. We also find clear system size dependences in studying the structural properties of the packings from the disordered ones to the ordered ones. These detailed investigations, on the structure of the arrested close packings, may provide a link between the glassy states and the crystalline states in the hard spheres.     

Tapped granular packings described as complex networks

Abstract

We characterize the structure of simulated two-dimensional granular packings using concepts from complex networks theory. The packings are generated by a simulated tapping protocol, which allows us to obtain states in mechanical equilibrium in a wide range of densities. We show that our characterization method is able to discriminate non-equivalent states that have the same density. We do this by examining differences in the topological structure of the contact network of the packings. In particular, we find that the polygons of the network are specially sensitive probes for the contact structure. Additionally, we compare the network properties obtained in two different scenarios: the tapped and a compressed system.     

Protocol dependence of mechanical properties in granular systems

We study the protocol dependence of the mechanical properties of granular media by means of computer simulations. We control a protocol of realizing disk packings in a systematic manner. In 2D, by keeping material properties of the constituents identical, we carry out compaction with various strain rates. The disk packings exhibit the strain rate dependence of the critical packing fraction above which the pressure becomes non-zero. The observed behavior contrasts with the well-studied jamming transitions for frictionless disk packings. We also observe that the elastic moduli of the disk packings depend on the strain rate logarithmically. Our results suggest that there exists a time-dependent state variable to describe macroscopic material properties of disk packings, which depend on its protocol.     

Critical scaling in linear response of frictionless granular packings near jamming

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.     

Calculating vibrational mode contributions to sound absorption in excitable gas mixtures by decomposing multi-relaxation absorption spectroscopy

Sound relaxational absorption spectroscopy of excitable gas mixtures is potentially applied for gas composition detection. The relaxation of vibrational modes of gas molecules determines the sound relaxational absorption. However, to our knowledge, the contribution of each vibrational mode available in gas mixtures to sound multi-relaxation absorption has not been calculated in existing literature. In this paper, based on the decoupled expression of the effective isochoric molar heat for a gas mixture, a sound multi-relaxation absorption spectrum is decomposed into the sum of single-relaxation spectra. From this decomposable characteristic, the contribution of each vibrational mode available in the gaseous medium to the multi-relaxation absorption is obtained at room temperature. For various gas compositions including carbon dioxide, methane, nitrogen etc., the calculated contributions of vibrational modes are verified by the comparison with experiment data. We prove the following views with quantifiable outcomes that the primary molecular relaxation process associated with the lowest mode plays the major role in acoustic relaxational absorption of gas mixtures; the mode with lower vibrational frequency provides higher contribution to the primary relaxation process. This work could provide a deeper insight into the relationship between the sound relaxational absorption spectroscopy and gas molecules.     

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.     

Why is random close packing reproducible?

We link the thermodynamics of colloidal suspensions to the statistics of regular and random packings. Random close packing has defied a rigorous definition yet, in three dimensions, there is near universal agreement on the volume fraction at which it occurs. We conjecture that the common value of phi{rcp} approximately 0.64 arises from a divergence in the rate at which accessible states disappear. We relate this rate to the equation of state for a hard-sphere fluid on a metastable, noncrystalline branch.     

Observability of order parameter collective modes in heavy fermion superconductors

The effect of impurity scattering on the dynamics of the order parameter ofa “bnon-s-wave” anisotropic superconducting state is considered. It is found that near T_c and for realistic scattering rates the dynamics of all non-Goldstone order parameter components is purely relaxational. At sufficient low temperatures pair vibration modes with frequency ω∼δ are found to be weakly damped even though ωτ may be much less than unity.     

Local anisotropy in globally isotropic granular packings

We report on two-dimensional computer simulations of frictionless granular packings at various area fractions φ above the jamming point φ(c). We measure the anisotropy in coarse-grained stress ε(s) and shear modulus ε(m) as functions of coarse-graining scale, R. ε(s) can be collapsed onto a master curve after rescaling R by a characteristic length scale ξ and ε(s) by an anisotropy magnitude A. Both A and ξ accelerate as φ→φ(c) from above, consistent with a divergence at φ(c). ε(m) shows no characteristic length scale and has a nontrivial power-law form, ε(m)~R(-0.62), over almost the entire range of R at all φ. These results suggest that the force chains present in the spatial structure of the quenched stress may be governed by different physics than the anomalous elastic response near jamming.     

Repulsive contact interactions make jammed particulate systems inherently nonharmonic

Many jammed particulate systems, such as granular and colloidal materials, interact via repulsive contact forces. We find that these systems possess no harmonic regime in the large system limit (N→∞) for all compressions Δ? studied, and at jamming onset Δ?→0 for all N. We perform fixed energy simulations following perturbations with amplitude δ along eigendirections of the dynamical matrix. The fluctuations abruptly spread to all modes for δ≈δ(c) (where a single contact breaks) in contrast to linear and weakly nonlinear behavior. For δ > δ(c), all discrete modes disappear into a continuous frequency band. <δ(c)> scales with 1/N and Δ?, which limits harmonic behavior to only overcompressed systems. The density of vibrational modes deviates strongly from that predicted from the dynamical matrix when the system enters the nonharmonic regime, which significantly affects its mechanical and transport properties.     

CuCl催化苯腙和丙炔酸甲酯Michael加成反应的机理研究

本文采用密度泛函理论(DFT)中的M05方法针对性的研究了以CuCl为催化剂催化苯腙和丙炔酸甲酯发生Michael加成的微观反应机理.采用Gaussian09程序,使用6-31+G*(Cu采用赝势基组LanL2DZ)对化学反应过程中的反应物、中间体、过渡态分子的几何构型进行了优化,同时进行了频率计算,所有过渡态都有唯一虚频,中间体和过渡态分子结构的合理性得到了确认.通过自然键轨道(NBO)理论分析了分子轨道间的相互作用.通过理论计算发现CuCl催化苯腙和丙炔酸甲酯发生Michael加成反应的位点在苯腙的N原子上,反应的速控步骤活化能为34.86 kcal/mol,相关的理论研究结果与实验反应现象相吻合.