Michio Otsuki, Hisao Hayakawa
The existence of universal scaling in the vicinity of the jamming transition of sheared granular materials is predicted by a phenomenology. The critical exponents are explicitly determined, which are independent of the spatial dimension. The validity of the theory is verified by the molecular dynamics simulation.
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The critical rheology of sheared frictional granular materials near jamming transition is numer- ically investigated. It is confirmed that there exist a true critical density which characterizes the onset of the yield stress, and two fictitious critical densities which characterize the scaling laws of rheological properties. We find the existence of a hysteresis loop between two of the critical densities for each friction coefficient. It is noteworthy that the critical scaling law for frictionless jamming transition seems to be still valid even for frictional jamming despite using fictitious c…
We study numerically a system of athermal, overdamped, frictionless spheres, as in a non-Brownian suspension, in two and three dimensions. Compressing the system isotropically at a fixed rate $\dotε$, we investigate the critical behavior at the jamming transition. The finite compression rate introduces a control timescale, which allows one to probe the critical timescale associated with jamming. As was found previously for steady-state shear-driven jamming, we find for compression-driven jamming that pressure obeys a critical scaling relation as a function of packing fraction $ϕ$ and compressi…
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 non-affine 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.
Universal Jamming Criticality and Self-Organizing Principles from Disorder to the Limit of Perfect Crystalline Order
研究聚焦弹性阻塞堆积，系统调结构揭示通用特性，证明力学性能受阻塞临界性支配，发现配位数分布等，为无序固体刚性提出组织机制，强调阻塞物理相关性并补充自组织原理。
We carry out numerical simulations to study transport behavior about the jamming transition of a model granular material in two dimensions at zero temperature. Shear viscosity ηis computed as a function of particle volume density ρand applied shear stress σ, for diffusively moving particles with a soft core interaction. We find an excellent scaling collapse of our data as a function of the scaling variable σ/|ρ_c-ρ|^Δ, where ρ_c is the critical density at σ=0 ("point J"), and Δis the crossover scaling critical exponent. Our results show that jamming is a true critical phenomenon, extending to …
We numerically study the jamming transition in particulate systems with attraction by investigating their mechanical response at zero temperature. We find three regimes of mechanical behavior separated by two critical transitions--connectivity and rigidity percolation. The transitions belong to different universality classes than their lattice counterparts, due to force balance constraints. We also find that these transitions are unchanged at low temperatures and resemble gelation transitions in experiments on colloidal and silica gels.
We investigate the glass and the jamming transitions of hard spheres in finite dimensions $d$, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite $d$. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent $ν=2/d$, which we verify through finite size scaling, and standard critical exponents…
We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. There is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the canonical power-law scalings of the contact number and elastic moduli break down at low pressure. These quantities exhibit scaling collapse with a non-trivial scaling function, demonstrating that the jamming transition can be considered a phase transition. Scaling is achieved as a function of N in both 2 and 3 dimensions,…
Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound ef…
The jamming transition of non-spherical particles is fundamentally different from the spherical case. Non-spherical particles are hypostatic at their jamming points, while isostaticity is ensured in the case of the jamming of spherical particles. This structural difference implies that the presence of asphericity affects the critical exponents related to the contact number and the vibrational density of states. Moreover, while the force and gap distributions of isostatic jamming present power-law behaviors, even an infinitesimal asphericity is enough to smooth out these singularities. In a rec…
The jamming transition of particles with finite-range interactions is characterized by a variety of critical phenomena, including power law distributions of marginal contacts. We numerically study a recently proposed simple model of jamming, which is conjectured to lie in the same universality class as the jamming of spheres in all dimensions. We extract numerical estimates of the critical exponents, θ = 0.451 $\pm$ 0.006 and γ = 0.404 $\pm$ 0.004, that match the exponents observed in sphere packing systems. We analyze finite-size scaling effects that manifest in a subcritical cutoff regime an…
We carry out a finite size scaling analysis of the jamming transition in frictionless bi-disperse soft core disks in two dimensions. We consider two different jamming protocols: (i) quench from random initial positions, and (ii) quasistatic shearing. By considering the fraction of jammed states as a function of packing fraction for systems with different numbers of particles, we determine the spatial correlation length critical exponent $ν\approx 1$, and show that corrections to scaling are crucial for analyzing the data. We show that earlier numerical results yielding $ν<1$ are due to the imp…
Universal scaling function ansatz for finite-temperature jamming
本文将非零温度下的堵塞转变纳入标度假设框架，通过引入具有两个分支的普适标度函数统一了自由能热力学导数的四个标度指数区域，并利用危险无关变量解释了两个分支具有不同指数的异常特征。
Gardner transition coincides with the emergence of jamming scalings in hard spheres and disks
该研究发现硬球、硬盘有限维玻璃中Gardner转变与两种jamming标度的出现同步，可据此提取结构序参量，表明该转变是jamming转变的前兆，为相关实验检测提供了便捷方法。
Active Jamming at Criticality
研究活性力或热涨落下二维活性软球系统的堵塞临界行为，发现其标度规律仍可由平均场描述，突显非晶结构的关键作用。
We study the effect of dilute pinning on the jamming transition. Pinning reduces the average contact number needed to jam unpinned particles and shifts the jamming threshold to lower densities, leading to a pinning susceptibility, $χ_p$. Our main results are that this susceptibility obeys scaling form and diverges in the thermodynamic limit as $χ_p \propto |ϕ- ϕ_c^\infty|^{-γ_p}$ where $ϕ_c^\infty$ is the jamming threshold in the absence of pins. Finite-size scaling arguments yield these values with associated statistical (systematic) errors $γ_p = 1.018 \pm 0.026 (0.291) $ in $d=2$ and $γ_p =…
We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined.
Critical behaviors of sheared dense and frictionless granular materials in the vicinity of the jamming transition are numerically investigated. From the extensive molecular dynamics simulation, we verify the validity of the scaling theory near the jamming transition proposed by Otsuki and Hayakawa (Prog. Theor. Phys., 121, 647 (2009)). We also clarify the critical behaviors of the shear viscosity and the pair correlation function based on both a phenomenology and the simulation.
We discuss the physics of crystals with small polydispersity near the jamming transition point. For this purpose, we introduce an effective single-particle model taking into account the nearest neighbor structure of crystals. The model can be solved analytically by using the replica method in the limit of large dimensions. In the absence of polydispersity, the replica symmetric solution is stable until the jamming transition point, which leads to the standard scaling of perfect crystals. On the contrary, for finite polydispersity, the model undergoes the full replica symmetry breaking (RSB) tr…
In Phys. Rev. Lett. 96, 035702 (2006) we introduced a class of kinetically constrained models which display a dynamical glass transition. We focused on a particular example: the "knights" model. As correctly pointed out by Jeng and Schwarz cond-mat/0612484, we overlooked some additional directed frozen structures of the knights model which are not simple directed percolation (DP) paths: these "thicker" directed structures lower the critical density. Here we argue that, nevertheless, the full directed processes are in the DP universality class and the T-junctions between perpendicular segments …
Extensive numerical simulations in the past decades proved that the critical exponents of the jamming of frictionless spherical particles remain unchanged in two and three dimensions. This implies that the upper critical dimension is $d_u=2$ or lower. In this work, we study the jamming transition below the upper critical dimension. We investigate a quasi-one-dimensional system: disks confined in a narrow channel. We show that the system is isostatic at the jamming transition point as in the case of standard jamming transition of the bulk systems in two and three dimensions. Nevertheless, the s…
We investigate universal features of the jamming transition in granular materials, colloids and glasses. We show that the jamming transition in these systems has common features: slowing of response to external perturbation, and the onset of structural heterogeneities.
We examine the structure of the distribution of single particle displacements (van-Hove function) in a broad class of materials close to glass and jamming transitions. In a wide time window comprising structural relaxation, van-Hove functions reflect the coexistence of slow and fast particles (dynamic heterogeneity). The tails of the distributions exhibit exponential, rather than Gaussian, decay. We argue that this behavior is universal in glassy materials and should be considered the analog, in space, of the stretched exponential decay of time correlation functions. We introduce a dynamical m…
Critical behavior of soft repulsive particles after quench of temperature near the jamming trasition is numerically investigated. It is found that the plateau of the mean square displacement of tracer particles and the pressure satisfy critical scaling laws. The critical density for the jamming transition depends on the protocol to prepare the system, while the values of the critical exponents which are consistent with the prediction of a phenomenology are independent of the protocol.
We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents $β=0$, $γ= 2$, $α= 0$ and the finite size scaling exponent $ν^* = 2/d$ for values of the spatial dimension $d \geq 2$. We argue that the upper critical dimension is $d_u=2$ and the connectedness length exponent is $ν=1$.
We study the rheology of amorphous packings of soft, frictionless particles close to jamming. Implementing a quasistatic simulation method we generate a well defined ensemble of states that directly samples the system at its yield-stress. A continuous jamming transition from a freely-flowing state to a yield stress situation takes place at a well defined packing fraction, where the scaling laws characteristic of isostatic solids are observed. We propose that long-range correlations observed below the transition are dominated by this isostatic point, while those that are observed above the tran…
Recently, we proposed a universal scaling framework that shows shear thickening in dense suspensions is governed by the crossover between two critical points: one associated with frictionless isotropic jamming and a second corresponding to frictional shear jamming. Here, we show that orthogonal perturbations to the flows, an effective method for tuning shear thickening, can also be folded into this universal scaling framework. Specifically, we show that the effect of adding in orthogonal shear perturbations (OSP) can be incorporated by simply altering the scaling variable to include a multipli…
In this work we provide an overview of jamming transitions in two dimensional systems focusing on the limit of frictionless particle interactions in the absence of thermal fluctuations. We first discuss jamming in systems with short range repulsive interactions, where the onset of jamming occurs at a critical packing density and where certain quantities show a divergence indicative of critical behavior. We describe how aspects of the dynamics change as the jamming density is approached and how these dynamics can be explored using externally driven probes. Different particle shapes can produce …
Granular packings display the remarkable phenomenon of dilatancy [1], wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, as also the related phenomenon of shear-induced jamming, requires frictional interactions [2, 3]. Here, we investigate the occurrence of dilatancy and shear jamming in frictionless packings. We show that the existence of isotropic jamming densities ϕj above the minimal density, the J-point density ϕJ [4, 5], leads both to the emergence of shear-induced jamming and dilatancy. Packings at ϕJ form a significan…
Vibrational similarities in jamming-unjamming of polycrystalline and disordered granular packings
通过离散元模拟发现，多晶与无序颗粒堆积体在堵塞-去堵塞循环中低频振动指数变化不同，但距堵塞密度相同距离处指数与历史无关，表明振动特征可恢复。
We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(ϕ,F)$: at low $ϕ$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $ϕ$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy w…
We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, phi = phi_J). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near phi_J is divided in three differen…
Like other critical phenomena, the jamming transition accompanies the divergence of the relaxation time $τ$. A recent numerical study of frictionless spherical particles proves that $τ$ is inversely proportional to the lowest non-zero eigenvalue $λ_1$ of the dynamical matrix. In this note, we derive the scaling of $λ_1$ below the jamming transition point $φ_J$ by solving the linearized dynamical equation. The resultant critical exponent agrees with a previous theoretical result for sheared suspension obtained by applying the virtual work theorem to a simple shear, highlighting the universality…
Jamming is a first-order transition with quenched disorder in amorphous materials sheared by cyclic quasistatic deformations
本研究针对阻塞相变的属性争议，通过对循环准静态剪切的二维、三维非晶体系开展标度分析，证明阻塞是伴随淬火无序的一级相变，为其研究提供了新的理论框架。
It is shown that the fluctuations of the jamming coverage upon Random Sequential Adsorption ($σ_{θ_J}$), decay with the lattice size according to the power-law $σ_{θ_J} \propto L^{-1 / ν_J}$, with $ν_{J} = 2 / (2D - d_f)$, where $D$ is the dimension of the substrate and $d_{\rm f}$ is the fractal dimension of the set of sites belonging to the substrate where the RSA process actually takes place. This result is in excellent agreement with the figure recently reported by Vandewalle {\it et al} ({\it Eur. Phys. J.} B. {\bf 14}, 407 (2000)), namely $ν_J = 1.0 (1)$ for the RSA of needles with $D = …
While the glass transition at non-zero temperature seems to be hard to access for experimental, theoretical, or simulation studies, jamming at zero temperature has been explored in great detail. It is a widely discussed question whether this athermal jamming transition is related to the glass transition. Motivated by the exploration of the energy landscape that has been successfully used to describe athermal jamming, we introduce a new method to determine whether the configuration space of a soft sphere system can be explored within a reasonable timescale or not, i.e., whether the system is er…
Universal scaling of shear thickening transitions
该研究将剪切增稠解释为刚性转变的前兆，提出基于无摩擦堵塞点到摩擦剪切堵塞的普适交叉标度函数的黏度理论，并通过实验证实不同悬浮液系统的黏度可坍缩为单一普适曲线。
We investigate experimentally the mechanical response of a monolayer of bi-disperse frictional grains to an inhomogeneous shear perturbation across the jamming transition. We inflate an intruder inside the packing and use photo-elasticity and tracking techniques to measure the induced shear strain and stresses at the grain scale. We quantify experimentally the constitutive relations for strain amplitudes as low as 0.001 and for a range of packing fractions within 2% variation around the jamming transition. At the transition strong nonlinear effects set in : both the shear modulus and the dilat…
We investigate the jamming transition in packings of emulsions and granular materials via molecular dynamics simulations. The emulsion model is composed of frictionless droplets interacting via nonlinear normal forces obtained using experimental data acquired by confocal microscopy of compressed emulsions systems. Granular materials are modeled by Hertz-Mindlin deformable spherical grains with Coulomb friction. In both cases, we find power-law scaling for the vanishing of pressure and excess number of contacts as the system approaches the jamming transition from high volume fractions. We find …
We demonstrate that a highly frustrated anisotropic Josephson junction array(JJA) on a square lattice exhibits a zero-temperature jamming transition, which shares much in common with those in granular systems. Anisotropy of the Josephson couplings along the horizontal and vertical directions plays roles similar to normal load or density in granular systems. We studied numerically static and dynamic response of the system against shear, i. e. injection of external electric current at zero temperature. Current-voltage curves at various strength of the anisotropy exhibit universal scaling feature…
Recent computer simulations have uncovered the striking difference between the jamming transition of spherical and non-spherical particles. While systems of spherical particles are isostatic at the jamming point, systems of nonspherical particles are not: the contact number and shear modulus of the former exhibit a square root singularity near jamming, while those of the latter are linearly proportional to the distance from jamming. Furthermore, while our theoretical understanding of jamming of spherical particles is well developed, the same is not true for nonspherical particles. To understan…
Non-Hermitian Random Matrix Theory of Jamming in Active Disordered Media
该研究基于非厄米随机矩阵理论，构建活性阻塞系统力学的理论框架，通过推导自洽方程揭示活性非互易性正则化软模发散，得到力学柔量标度律及活性阻塞点附近的标度形式。
This paper illustrates how the tools of equilibrium statistical mechanics can help to explain a far-from-equilibrium problem: the jamming transition in frictionless granular materials. Edwards ideas consist of proposing a statistical ensemble of volume and stress fluctuations through the thermodynamic notion of entropy, compactivity, X, and angoricity, A (two temperature-like variables). We find that Edwards thermodynamics is able to describe the jamming transition (J-point). Using the ensemble formalism we elucidate the following: (i)We test the combined volume-stress ensemble by comparing th…
Jamming transition and normal modes of polydispersed soft particle packing
研究多分散软颗粒在二维空间中的聚集转变，发现颗粒分散性显著影响接触力、局部配位及聚集密度，但压力和弹性模量的临界标度不受颗粒尺寸分布影响，振动密度态也对分散性不敏感。
We consider the rheology of soft-core frictionless disks in two dimensions in the neighborhood of the athermal jamming transition. From numerical simulations of bidisperse, overdamped, particles, we argue that the divergence of the viscosity below jamming is characteristic of the hard-core limit, independent of the particular soft-core interaction. We develop a mapping from soft-core to hard-core particles that recovers all the critical behavior found in earlier scaling analyses. Using this mapping we derive a duality relation that gives the exponent of the non-linear Herschel-Bulkley rheology…
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 using fully equilibrium statistical mechanics and develop a microscopic many-body 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 predictions for microscopic correlation functions of jammed states that are amenable to experimental verifica…
We investigate the dynamics of soft sphere liquids through computer simulations for spatial dimensions from $d =3$ to $8$, over a wide range of temperatures and densities. Employing a scaling of density-temperature dependent relaxation times, we precisely identify the density $ϕ_0$ which marks the ideal glass transition in the hard sphere limit, and a crossover from sub- to super-Arrhenius temperature dependence. The difference between $ϕ_0$ and the athermal jamming density $ϕ_J$, small in 3 and 4 dimensions, increases with dimension, with $ϕ_0 > ϕ_J$ for $d > 4$. We compare our results with r…
We report an analytical study of the vibrational spectrum of the simplest model of jamming, the soft perceptron. We identify two distinct classes of soft modes. The first kind of modes are related to isostaticity and appear only in the close vicinity of the jamming transition. The second kind of modes instead are present everywhere in the glass phase and are related to the hierarchical structure of the potential energy landscape. Our results highlight the universality of the spectrum of normal modes in disordered systems, and open the way towards a detailed analytical understanding of the vibr…
A review on shear jamming
本文综述剪切阻塞的实验、模拟与理论进展，通过广义相图统一无摩擦与有摩擦体系，并阐明其临界性、弹性及与多种流变现象的联系。
In this thesis I present most of the results obtained during my PhD, where I worked on different subjects regarding jamming in systems of frictionless spheres. In particular, I focused on microscopic properties of jammed packings, such as the distribution of contact forces and interparticle gaps, as well as the single particle dynamics that occur near the jamming point. Several of these results have already been presented in Refs. [1,2], but here I include a more detailed analysis of some of them. Besides, all the results of the second chapter are new, even if related to such works.
Microrheology near jamming
本研究针对阻塞转变附近微流变学中广义斯托克斯关系（GSR）的有效性问题，建立线性响应理论形式体系并结合数值模拟，证实微流变与宏观流变的标度律一致，且通过渐近与位移场分析解释了二者的等效性。
Random sequential addition (RSA) models are used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the algebraic time dependence of the asymptotic jamming coverage as $t\to\infty$. For the RSA of monodisperse non-spherical particles the scaling is generally believed to be $~t^{-ν}$, where $ν=1/d_{\rm f}$ for a particle with $d_{\rm f}$ degrees of freedom. While the $d_{\rm f}=1$ result of spheres (Renyi's classical car parking problem) can be derived analytically, evidence for the $1/d_{\rm f}$ scaling for arbitrary particle shapes has s…
Dislocation assemblies exhibit a jamming or yielding transition at a critical external shear stress value $σ=σ_c$. Nevertheless the nature of this transition has not been ascertained. Here we study the heterogeneous and collective nature of dislocation dynamics within a crystal plasticity model close to $σ_c$, by considering the first-passage properties of the dislocation dynamics. As the transition is approached in the moving phase, the first passage time distribution exhibits scaling, and a related peak {\it dynamical} susceptibility $χ_4^*$ diverges as $χ_4^* \sim (σ-σ_c)^{-α}$, with $α\app…
Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically rel…
Jamming and percolation of three-dimensional (3D) $k \times k \times k $ cubic objects ($k^3$-mers) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The $k^3$-mers were irreversibly deposited into the lattice. Jamming coverage $θ_{j,k}$ was determined for a wide range of $k$ ($2 \leq k \leq 40$). $θ_{j,k}$ exhibits a decreasing behavior with increasing $k$, being $θ_{j,k=\infty}=0.4204(9)$ the limit value for large $k^3$-mer sizes. In addition, a finite-size scaling analysis of the jamming transition was carried out, an…
A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics
该研究构建合成细胞模拟物融合单层，通过调控自推进持续时间，发现由细胞形状驱动且与密度无关的重入型堵塞转变，并用模拟解释动力学异质性。
Shear hardening in frictionless amorphous solids near the jamming transition
本文通过数值模拟与弹性理论研究深度退火无摩擦堆积体的剪切硬化，揭示键数增加及键取向各向异性、长程关联两个微观起源，补充了阻塞转变的临界普适规律。
We present a novel mechanism for the anomalous behaviour of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a crossover temperature above which the specific heat scales linearly with temperature while below it a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) The marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-…
Microscopically grounded constitutive model for dense suspensions of soft particles below jamming
本文提出一个基于微观机制的构型模型，用于描述致密软粒子悬浊液在阻尼转变以下的流变学特性，预测了剪切稀释和正应力差异等行为。
Anomalous Criticality of Absorbing State Transition toward Jamming
研究通过重新审视偏置随机组织模型，揭示高密度下与Manna universality类不符的临界异常，发现晶化破坏吸收过渡，而密集二元混合物出现新的动态universality类。
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