We investigate criticality near the jamming transition in both quiescent systems and those under shear by considering the effect of mechanical training on the jamming transition and nonlinear rheology. We simulate frictionless soft particles undergoing athermal quasi-static shear using initial configurations trained with athermal quasi-static cyclic volume deformations. The jamming transition density of the initial configuration $φ_{\rm J0}$ is systematically altered by tuning the ``depth'' of mechanical training. We exert a steady shear on these configurations and observe either shear jamming (gain of stiffness due to shear) or shear melting (loss of stiffness due to shear), depending on the depth of training and proximity to the jamming transition density. We also observe that the characteristic strains, at which shear jamming or melting occur, diverge at a unique density $φ_{\rm JS}$. This is due to the shift of the jamming transition density from $φ_{\rm J0}$ to $φ_{\rm JS}$ under shear, associated with loss of memory of the initial configuration. Finally, we thoroughly investigate nonlinear rheology near the jamming transition density, and contrary to previous works, we find a nonlinear ``softening'' takes place below as well as above the jamming transition density.
We investigate the criticality of the jamming transition for overdamped shear-driven frictionless disks in two dimensions for two different models of energy dissipation: (i) Durian's bubble model with dissipation proportional to the velocity difference of particles in contact, and (ii) Durian's "mean-field" approximation to (i), with dissipation due to the velocity difference between the particle and the average uniform shear flow velocity. By considering velocity correlations, finite-size behavior of pressure, and the pressure analog of viscosity, we argue that these two models share the same…
We numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction phi_J. For configurations with a fixed isotropic global stress tensor, we investigate the fluctuations of the local packing fraction phi(r) to test whether such configurations display the hyperuniformity that has been claimed to exist exactly at phi_J. For our configurations, generated by a rapid quench protocol, we find that hyperuniformity persists only out to a finite length scale, and that this length scale appears to remain finite as the s…
Numerical simulations of soft-core frictionless disks in two dimensions are carried out to study behavior of a simple liquid as a function of thermal temperature $T$, packing fraction $ϕ$, and uniform applied shear strain rate $\dotγ$. Inferring the hard-core limit from our soft-core results, we find that it depends on the two parameters $ϕ$ and $T/\dotγ$. $T/\dotγ\to 0$ defines the athermal limit in which a shear driven jamming transition occurs at a well defined $ϕ_J$. $T/\dotγ\to\infty$ defines the thermalized limit where an equilibrium glass transition may take place at a $ϕ_G$. This concl…
The jamming of bi-disperse soft core disks is considered, using a variety of different protocols to produce the jammed state. In agreement with other works, we find that cooling and compression can lead to a broad range of jamming packing fractions $ϕ_J$, depending on cooling rate and initial configuration; the larger the degree of big particle clustering in the initial configuration, the larger will be the value of $ϕ_J$. In contrast, we find that shearing disrupts particle clustering, leading to a much narrower range of $ϕ_J$ as the shear strain rate varies. In the limit of vanishingly small…
We study numerically the critical behavior and marginal stability of the shear jamming transition for frictionless soft spheres, observed to occur over a finite range of densities, associated with isotropic jamming for densities above the minimum jamming (J-point) density. Several quantities are shown to scale near the shear jamming point in the same way as the isotropic jamming point. We compute the exponents associated with the small force distribution and the interparticle gap distribution,and show that the corresponding exponents are consistent with the marginal stability condition observe…
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 macro-friction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixe…
We investigate the rigidity transition associated with shear jamming in frictionless, as well as frictional, disk packings in the quasi-static regime and at low shear rates. For frictionless disks, the transition is under quasistatic shear is discontinuous, with an instantaneous emergence of a system spanning rigid cluster at the jamming transition. For frictional systems, the transition appears continuous for finite shear rates, but becomes sharper for lower shear rates. In the quasi-static limit, it is discontinuous as in the frictionless case. Thus, our results show that the rigidity transi…
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 numerically simulate mechanically stable packings of soft-core, frictionless, bidisperse disks in two dimensions, above the jamming packing fraction $ϕ_J$. For configurations with a fixed isotropic global stress tensor, we compute the averages, variances, and correlations of conserved quantities (stress $Γ_{\cal C}$, force-tile area $A_{\cal C}$, Voronoi volume $V_{\cal C}$, number of particles $N_{\cal C}$, and number of small particles $N_{s{\cal C}}$) on compact subclusters of particles ${\cal C}$, as a function of the cluster size and the global system stress. We find several significan…
We carry out constant volume simulations of steady-state, shear driven, rheology in a simple model of bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. We carry out a detailed critical scaling analysis of our resulting data for pressure $p$ and shear stress $σ$, in order to determine the critical exponent $β$ that describes the algebraic divergence of the Bagnold transport coefficients, as the jamming transition is approached from below. We show that it is necessary, for the strain rates considered in this work, to cons…
We investigate the rheological properties of an assembly of inelastic (but frictionless) particles close to the jamming density using numerical simulation, in which uniform steady states with a constant shear rate $\dotγ$ is realized. The system behaves as a power-law fluid and the relevant exponents are estimated; e.g., the shear stress is proportional to $\dotγ^{1/δ_S}$, where $1/δ_S=0.64(2)$. It is also found that the relaxation time $τ$ and the correlation length $ξ$ of the velocity increase obeying power laws: $τ\sim\dotγ^{-β}$ and $ξ\sim\dotγ^{-α}$, where $β=0.27(3)$ and $α=0.23(3)$.
We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in…
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.
The jamming transition is accompanied by a rich phenomenology, such as hysteresis or non-local effects, which is still not well understood. Here we experimentally investigate a model frictionless granular layer flowing down an inclined plane, as a way to disentangle generic collective effects from those arising from frictional interactions. We find that thin frictionless granular layers are devoid of hysteresis, yet the layer stability is increased as it gets thinner. Rheological laws obtained for different layer thicknesses can be collapsed into a unique master curve, supporting that non-loca…
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 …
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 use numerical simulations to study the flow of a bidisperse mixture of athermal, frictionless, soft-core two dimensional spherocylinders driven in uniform steady state shear. Energy dissipation is via a viscous drag with respect to a uniformly sheared host fluid, giving a model for a non-Brownian suspension with a Newtonian rheology. We study pressure $p$ and deviatoric shear stress $σ$ as a function of packing fraction $ϕ$, strain rate $\dotγ$, and a parameter $α$ that measures the asphericity of the particles. We consider the anisotropy of the stress tensor, the macroscopic friction $μ=σ/…
We perform numerical simulations to determine the shear stress and pressure of steady-state shear flow in a soft-disk model in two dimensions at zero temperature in the vicinity of the jamming transition ϕ_J. We use critical point scaling analyses to determine the critical behavior at jamming, and we find that it is crucial to include corrections to scaling for a reliable analysis. We find that the relative size of these corrections are much smaller for pressure than for shear stress. We furthermore find a superlinear behavior for pressure and shear stress above ϕ_J, both from the scaling anal…
We carry our numerical simulations of athermally sheared, bidisperse, frictionless disks in two dimensions. From an appropriately defined velocity correlation function, we determine that there are two diverging length scales, $ξ$ and $\ell$, as the jamming transition is approached. We analyze our results using a critical scaling ansatz for the correlation function, and argue that the more divergent length $\ell$ is a consequence of a dangerous irrelevant scaling variable, and that it is $ξ$ which is the correlation length that determines the divergence of the system viscosity as jamming is app…
We simulate numerically the compression driven jamming of athermal, frictionless, soft-core spherocylinders in two dimensions, for a range of particle aspect ratios $α$. We find the critical packing fraction $ϕ_J(α)$ for the jamming transition, and the average number of contacts per particle $z_J(α)$ at jamming. We find that both are nonmonotonic, with a peak at $α\approx 1$. We find that configurations at the compression driven jamming point are always hypostatic for all $α$, with $z_J<z_\mathrm{iso}=2d_f=6$ the isostatic value. We show that, for moderately elongated spherocylinders, there is…
A new method is introduced to simulate jamming of polyhedral grains under controlled stress that incorporates global degrees of freedom through the metric tensor of a periodic cell containing grains. Jamming under hydrostatic/isotropic stress and athermal conditions leads to a precise definition of the ideal jamming point at zero shear stress. The structures of tetrahedra jammed hydrostatically exhibit less translational order and lower jamming-point density than previously described `maximally random jammed' hard tetrahedra. Under the same conditions, cubes jam with negligible nematic order. …
We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via purely repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol. However, the probability to obtain a particular jammed packing depends on the packing-generation protocol. We predict the average shear strain required to induce jamming in initially unjammed packings from th…
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…
Amorphous packings of spheres have been intensely investigated in order to understand the mechanical and flow behaviour of dense granular matter, and to explore universal aspects of the transition from fluid to structurally arrested or jammed states. Considerable attention has recently been focussed on anisotropic packings of frictional grains generated by shear deformation leading to shear jamming, which occurs below the jamming density for isotropic packings of frictionless grains. With the aim of disentangling the role of shear deformation induced structures and friction in generating shear…
We review the physics of jamming from the theoretical, experimental and numerical perspectives. We summarize the mean-field theory of jamming and the marginally stable solid phase, with particular emphasis on the connection with the Replica Symmetry Breaking theory of glasses. We report validations of the mean-field theory of jamming from experimental and numerical studies of critical behaviors near the transition. In particular, we describe the physics of jamming of frictionless, spherical particles, as well as more recent work on jamming of frictionless, non-spherical particles and frictiona…
We study the structural and mechanical properties of jammed ellipse packings, and find that the nature of the jamming transition in these systems is fundamentally different from that for spherical particles. Ellipse packings are generically hypostatic with more degrees of freedom than constraints. The spectra of low energy excitations possess two gaps and three distinct branches over a range of aspect ratios. In the zero compression limit, the energy of the modes in the lowest branch increases {\it quartically} with deformation amplitude, and the density of states possesses a $δ$-function at z…
We numerically study a three dimensional system of athermal, overdamped, frictionless spheres, using a simplified model for a non-Brownian suspension. We compute the bulk viscosity under both uniaxial and isotropic compression as a means to address the question of whether stress-anisotropic and stress-isotropic jamming are in the same critical universality class. Carrying out a critical scaling analysis of the system pressure $p$, shear stress $σ$, and macroscopic friction $μ=σ/p$, as functions of particle packing fraction $ϕ$ and compression rate $\dotε$, we find good agreement for all critic…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we review a theoretical framework that gives a scaling description of stationary flows of frictionless particles. Our analysis applies both to suspensions and inertial flows of hard particles. We report numerical results in support of the theory, and show the phase diagram that results wh…
Due to significant computational expense, discrete element method simulations of jammed packings of size-dispersed spheres with size ratios greater than 1:10 have remained elusive, limiting the correspondence between simulations and real-world granular materials with large size dispersity. Invoking a recently developed neighbor binning algorithm, we generate mechanically-stable jammed packings of frictionless spheres with power-law size distributions containing up to nearly four million particles with size ratios up to 1:100. By systematically varying the width and exponent of the underlying p…
We numerically study the distributions of global pressure that are found in ensembles of statically jammed and quasistatically sheared systems of bidisperse, frictionless, disks at fixed packing fraction $ϕ$ in two dimensions. We use these distributions to address the question of how pressure increases as $ϕ$ increases above the jamming point $ϕ_J$, $p\sim |ϕ- ϕ_J|^y$. For statically jammed ensembles, our results are consistent with the exponent $y$ being simply related to the power law of the interparticle soft-core interaction. For sheared systems, however, the value of $y$ is consistent wit…
The formation of self-organised structures that resist shear deformation have been discussed in the context of shear jamming and thickening[1-3], with frictional forces playing a key role. However, shear induces geometric features necessary for jamming even in frictionless packings[4]. We analyse conditions for jamming in such assemblies by solving force and torque balance conditions for their contact geometry. We demonstrate, and validate with frictional simulations, that the isostatic condition for mean contact number Z = D + 1 (for spatial dimension D = 2, 3) holds at jamming for both finit…
We propose a phase diagram for the shear flow of dry granular particles in two dimensions based on simulations and a phenomenological Landau-theory for a nonequilibrium first order phase transition. Our approach incorporates both frictional as well as frictionless particles. The most important feature of the frictional phase diagram is re-entrant flow and a critical jamming point at finite stress. In the frictionless limit the regime of re-entrance vanishes and the jamming transition is continuous with a critical point at zero stress. The jamming phase diagrams derived from the model agree wit…
A mechanically-based structural optimization method is utilized to explore the phenomena of jamming for assemblies of frictionless Platonic solids. Systems of these regular convex polyhedra exhibit mechanically stable phases with density substantially less than optimal for a given shape, revealing that thermal motion is necessary to access high density phases. We confirm that the large system jamming threshold of $0.623 \pm 0.003$ for tetrahedra is consistent with experiments on tetrahedral dice. Also, the extremely short-ranged translational correlations of packed tetrahedra observed in exper…
While frictionless spheres at jamming are isostatic, frictional spheres at jamming are not. As a result, frictional spheres near jamming do not necessarily exhibit an excess of soft modes. However, a generalized form of isostaticity can be introduced if fully mobilized contacts at the Coulomb friction threshold are considered as slipping contacts. We show here that, in this framework, the vibrational density of states (DOS) of frictional discs exhibits a plateau when the generalized isostaticity line is approached. The crossover frequency to elastic behavior scales linearly with the distance f…
We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $ϕ$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $ϕ$ all the way up to $ϕ_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $ϕ_m$, which is largest for shear flows. Trouto…
We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter $α\to 0$ and particles approach spherical. We find that the nematic order parameter $S_2$ is non-monotonic in the packing fraction $ϕ$, and that as $α\to 0$ $S_{2}$ stays finite at jamming and above. The approach to spherical particles thus appears to be singular. We also find that sheared particles continue to rotate above jamming, and that particle contacts p…
Using molecular dynamics simulations, we study the steady shear flow of dense assemblies of anisotropic spherocylindrical particles of varying aspect ratios. Comparing frictionless and frictional particles we discuss the specific role of frictional inter-particle forces for the rheological properties of the system. In the frictional system we evidence a shear-thickening regime, similar to that for spherical particles. Furthermore, friction suppresses alignment of the spherocylinders along the flow direction. Finally, the jamming density in frictional systems is rather insensitive to variations…
Geometrical properties of two-dimensional mixtures near the jamming transition point are numerically investigated using harmonic particles under mechanical training. The configurations generated by the quasi-static compression and oscillatory shear deformations exhibit anomalous suppression of the density fluctuations, known as hyperuniformity, below and above the jamming transition. For the jammed system trained by compression above the transition point, the hyperuniformity exponent increases. For the system below the transition point under oscillatory shear, the hyperuniformity exponent also…
We study random packings of frictionless particles at T=0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows and its peak approaches random close-packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.
The average number of constraints per particle $< C_{total} >$ in mechanically stable systems of Platonic solids (except cubes) approaches the isostatic limit at the jamming point ($< C_{total} > \rightarrow 12$), though average number of contacts are hypostatic. By introducing angular alignment metrics to classify the degree of constraint imposed by each contact, constraints are shown to arise as a direct result of local orientational order reflected in edge-face and face-face alignment angle distributions. With approximately one face-face contact per particle at jamming chain-like face-face …
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…
Collections of bidisperse frictionless particles at zero temperature in three dimensions are simulated with a shear-driven dynamics with the aim to compare with behavior in two dimensions. Contrary to the prevailing picture, and in contrast to results from isotropic jamming from compression or quench, we find that the critical exponents in three dimensions are different from those in two dimensions and conclude that shear-driven jamming in two and three dimensions belong to different universality classes.
We use numerical simulations to study the shear-driven steady-state flow of athermal, frictionless, overdamped, two dimensional cross-shaped particles of varying aspect ratios, and make comparison with the behavior of rod-shaped and staple-shaped particles. We find that the extent of non-convexity of the particle shape plays an important role in determining both the value of the jamming packing fraction as well as the rotational motion and orientational ordering of the particles.
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…
Rheological properties of dense flows of hard particles are singular as one approaches the jamming threshold where flow ceases, both for aerial granular flows dominated by inertia, and for over-damped suspensions. Concomitantly, the lengthscale characterizing velocity correlations appears to diverge at jamming. Here we introduce a theoretical framework that proposes a tentative, but potentially complete scaling description of stationary flows. Our analysis, which focuses on frictionless particles, applies {\it both} to suspensions and inertial flows of hard particles. We compare our prediction…
We carry out constant volume simulations of steady-state, shear driven flow in a simple model of athermal, bidisperse, soft-core, frictionless disks in two dimensions, using a dissipation law that gives rise to Bagnoldian rheology. Focusing on the small strain rate limit, we map out the rheological behavior as a function of particle packing fraction $ϕ$ and a parameter $Q$ that measures the elasticity of binary particle collisions. We find a $Q^*(ϕ)$ that marks the clear crossover from a region characteristic of strongly inelastic collisions, $Q<Q^*$, to a region characteristic of weakly inela…
Particles suspended in a Newtonian fluid raise the viscosity and also generally give rise to a shear-rate dependent rheology. In particular, pronounced shear thickening may be observed at large solid volume fractions. In a recent article (R. Seto, R. Mari, J. F. Morris, and M. M. Denn., Phys. Rev. Lett., 111:218301, 2013) we have considered the minimum set of components to reproduce the experimentally observed shear thickening behavior, including Discontinuous Shear Thickening (DST). We have found frictional contact forces to be essential, and were able to reproduce the experimental behavior b…
We study the nature of the frictional jamming transition within the framework of rigidity percolation theory. Slowly sheared frictional packings are decomposed into rigid clusters and floppy regions with a generalization of the pebble game including frictional contacts. We discover a second-order transition controlled by the emergence of a system-spanning rigid cluster accompanied by a critical cluster size distribution. Rigid clusters also correlate with common measures of rigidity. We contrast this result with frictionless jamming, where the rigid cluster size distribution is noncritical.
We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of inter-particle contacts until a force-equilibrated state is reached. For different particle aspect ratios $α=10\ldots 40$, we calculate contacts $z$, pressure as well as bulk and shear modulus. Most important is the fraction $f_0$ of spherocylinders with contacts at both ends as it governs the jamming threshold $z_c(f_0)=8+2f_0$. These results highlight the important role o…
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…
We investigate energy dissipation and the distribution of particle velocities at the jamming transition for overdamped shear-driven frictionless disks in two dimensions at zero temperature. We find that the dissipation is caused by the fastest particles and that the fraction of particles responsible for the dissipation decreases towards zero as jamming is approached. These particles belong to an algebraic tail of the velocity distribution that approaches $\sim v^{-3}$ as jamming is approached. We further find that different measures of the velocity diverge differently, which means that concept…
A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponen…
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…
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…
Rheological properties of a dense granular material consisting of frictionless spheres are investigated. It is found that the shear stress, the pressure, and the kinetic temperature obey critical scaling near the jamming transition point, which is considered as a critical point. These scaling laws have some peculiar properties in view of conventional critical phenomena because the exponents depend on the interparticle force models so that they are not universal. It is also found that these scaling laws imply the relation between the exponents that describe the growing correlation length.
