Jamming Transition Research Articles

Push both ways to avoid a jam

Materials Science When subject to shear flow, dense solutions of particles can jam together, dramatically increasing their viscosity. This can be helpful, such as in traction control systems, or it can be harmful, such as when a pipe becomes blocked during industrial processing. During flow, when the stress exceeds a critical value, particle interactions transform from lubricated to frictional, leading to transient force chains. Lin et al. show that this particle jamming transition is not fixed by the suspension formulation, but rather can be dynamically tuned: The trick is to introduce perturbations in an orthogonal direction to break up the force chains before they fully form. This enables control of the thickening viscosity over two orders of magnitude. Proc. Nat. Acad. Sci. 10.1073/pnas.1608348113 (2016).

Nonlinear analysis of a new car-following model accounting for the global average optimal velocity difference

In this paper, a new car-following model is proposed by considering the global average optimal velocity difference effect on the basis of the full velocity difference (FVD) model. We investigate the influence of the global average optimal velocity difference on the stability of traffic flow by making use of linear stability analysis. It indicates that the stable region will be enlarged by taking the global average optimal velocity difference effect into account. Subsequently, the mKdV equation near the critical point and its kink–antikink soliton solution, which can describe the traffic jam transition, is derived from nonlinear analysis. Furthermore, numerical simulations confirm that the effect of the global average optimal velocity difference can efficiently improve the stability of traffic flow, which show that our new consideration should be taken into account to suppress the traffic congestion for car-following theory.

Protocol-dependent shear modulus of amorphous solids

We investigate the linear elastic response of amorphous solids to a shear strain at zero temperature. We find that the response is characterized by at least two distinct shear moduli. The first one, , is associated with the linear response of a single energy minimum. The second, , is related to sampling, through plastic events, an ensemble of distinct energy minima. We provide examples of protocols that allow one to measure both shear moduli. In agreement with a theoretical prediction based on the exact solution in infinite spatial dimensions, the ratio is found to vanish proportionally to the square root of pressure at the jamming transition. Our results establish that amorphous solids are characterized by a rugged energy landscape, which has a deep impact on their elastic response, as suggested by the infinite-dimensional solution.

Bursts of activity in collective cell migration

Dense monolayers of living cells display intriguing relaxation dynamics, reminiscent of soft and glassy materials close to the jamming transition, and migrate collectively when space is available, as in wound healing or in cancer invasion. Here we show that collective cell migration occurs in bursts that are similar to those recorded in the propagation of cracks, fluid fronts in porous media, and ferromagnetic domain walls. In analogy with these systems, the distribution of activity bursts displays scaling laws that are universal in different cell types and for cells moving on different substrates. The main features of the invasion dynamics are quantitatively captured by a model of interacting active particles moving in a disordered landscape. Our results illustrate that collective motion of living cells is analogous to the corresponding dynamics in driven, but inanimate, systems.

The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential

We present a parallel derivation of the Thouless–Anderson–Palmer (TAP) equations and of an effective thermodynamic potential for the negative perceptron and soft sphere models in high dimension. Both models are continuous constrained satisfaction problems with a critical jamming transition characterized by the same exponents. Our analysis reveals that a power expansion of the potential up to the second order constitutes a successful framework to approach the jamming points from the SAT phase (the region of the phase diagram where at least one configuration verifies all the constraints), where the ground-state energy is zero. An interesting outcome is that approaching the jamming line the effective thermodynamic potential has a logarithmic contribution, which turns out to be dominant in a proper scaling regime. Our approach is quite general and can be directly applied to other interesting models. Finally we study the spectrum of small harmonic fluctuations in the SAT phase recovering the typical scaling below the cutoff frequency but a different behavior characterized by a non-trivial exponent above it.

Geometric aspects of shear jamming induced by deformation of frictionless sphere packings

It has recently been demonstrated that shear deformation of frictionless sphere packings leads to structures that will undergo jamming in the presence of friction, at densities well below the isotropic jamming point , and at high enough strains. Here, we show that the geometric features induced by strain are robust with respect to finite size effects, and include the feature of hyperuniformity, previously studied in the context of jamming, and more recently in driven systems. We study the approach to jamming as strain is increased, by evolving frictionless sheared configurations through frictional dynamics, and thereby identify a critical, or jamming, strain for each density, for a chosen value of the coefficient of friction. In the presence of friction above a certain strain value the sheared frictionless packings begin to develop finite stresses, which marks the onset of shear jamming. At a higher strain value, the shear stress reaches a saturation value after rising rapidly above the onset of shear jamming, which permits identification of the shear jamming transition. The onset of shear jamming and shear jamming are found to occur when the coordination number Z reaches values of Z = 3 and Z = 4 respectively. By considering percolation probabilities for the contact network, clusters of four coordinated and six coordinated spheres, we show that the percolation of four coordinated spheres corresponds to the onset of shear jamming behaviour, whereas the percolation of six coordinated spheres corresponds to shear jamming, for the chosen friction coefficients. At the onset of shear jamming, the force distribution begins to develop a peak at finite value and the force network is anisotropic and heterogeneous. And at the shear jamming transition, the force distribution has a well defined peak close to and the force network is less anisotropic and homogeneous. We briefly discuss mechanical aspects of the jamming behaviour by performing normal mode analysis and computing shear modulus.

Modeling and analyses of driver’s characteristics in a traffic system with passing

This paper investigates the effect of aggressive or timid characteristics of driver’s behavior with passing by means of lattice hydrodynamic traffic flow model. The effect of driver’s characteristic on the stability of traffic flow is examined through linear stability analysis. It is shown that for both the cases of passing or without passing the stability region significantly enlarges (reduces) as the proportion of aggressive (timid) drivers increases. To describe the propagation behavior of a density wave near the critical point, nonlinear analysis is conducted and mKdV equation representing kink–antikink soliton is derived. It is observed that jamming transition occurs between uniform flow and kink jam phase with increase in aggressive driver’s characteristics for smaller values of passing. When passing constant is greater than a critical value, jamming transitions occur among uniform traffic flow and kink-Bando traffic wave through chaotic phase. Numerical simulation is carried out to validate the theoretical findings which confirm that traffic jam can be suppressed efficiently by considering the driver’s characteristics in a single-lane traffic system with or without passing.

Scaling ansatz for the jamming transition

We propose a Widom-like scaling ansatz for the critical jamming transition. Our ansatz for the elastic energy shows that the scaling of the energy, compressive strain, shear strain, system size, pressure, shear stress, bulk modulus, and shear modulus are all related to each other via scaling relations, with only three independent scaling exponents. We extract the values of these exponents from already known numerical or theoretical results, and we numerically verify the resulting predictions of the scaling theory for the energy and residual shear stress. We also derive a scaling relation between pressure and residual shear stress that yields insight into why the shear and bulk moduli scale differently. Our theory shows that the jamming transition exhibits an emergent scale invariance, setting the stage for the potential development of a renormalization group theory for jamming.

Effect of particle collisions in dense suspension flows.

We study nonlocal effects associated with particle collisions in dense suspension flows, in the context of the Affine Solvent Model, known to capture various aspects of the jamming transition. We show that an individual collision changes significantly the velocity field on a characteristic volume Ω_{c}∼1/δz that diverges as jamming is approached, where δz is the deficit in coordination number required to jam the system. Such an event also affects the contact forces between particles on that same volume Ω_{c}, but this change is modest in relative terms, of order f_{coll}∼f[over ¯]^{0.8}, where f[over ¯] is the typical contact force scale. We then show that the requirement that coordination is stationary (such that a collision has a finite probability to open one contact elsewhere in the system) yields the scaling of the viscosity (or equivalently the viscous number) with coordination deficit δz. The same scaling result was derived [E. DeGiuli, G. Düring, E. Lerner, and M. Wyart, Phys. Rev. E 91, 062206 (2015)PLEEE81539-375510.1103/PhysRevE.91.062206] via different arguments making an additional assumption. The present approach gives a mechanistic justification as to why the correct finite size scaling volume behaves as 1/δz and can be used to recover a marginality condition known to characterize the distributions of contact forces and gaps in jammed packings.

Universal Non-Debye Scaling in the Density of States of Amorphous Solids.

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher packing fractions remains, however, unclear. One might expect to find a simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field in nature, however, these solutions are only strictly valid in the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, away from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio evolves as dimension increases.

Phase diagram for inertial granular flows.

Flows of hard granular materials depend strongly on the interparticle friction coefficient μ_{p} and on the inertial number I, which characterizes proximity to the jamming transition where flow stops. Guided by numerical simulations, we derive the phase diagram of dense inertial flow of spherical particles, finding three regimes for 10^{-4}≲I≲10^{-1}: frictionless, frictional sliding, and rolling. These are distinguished by the dominant means of energy dissipation, changing from collisional to sliding friction, and back to collisional, as μ_{p} increases from zero at constant I. The three regimes differ in their kinetics and rheology; in particular, the velocity fluctuations and the stress ratio both display nonmonotonic behavior with μ_{p}, corresponding to transitions between the three regimes of flow. We rationalize the phase boundaries between these regimes, show that energy balance yields scaling relations between microscopic properties in each of them, and derive the strain scale at which particles lose memory of their velocity. For the frictional sliding regime most relevant experimentally, we find for I≥10^{-2.5} that the growth of the macroscopic friction μ(I) with I is induced by an increase of collisional dissipation. This implies in that range that μ(I)-μ(0)∼I^{1-2b}, where b≈0.2 is an exponent that characterizes both the dimensionless velocity fluctuations L∼I^{-b} and the density of sliding contacts χ∼I^{b}.

Micro origins for macro behavior in granular media

We report the latest advances in understanding, characterization and modeling of key micro mechanisms and origins underpinning the interesting and complex macroscopic behavior of granular matter. Included in this Topical Collection are novel theories, innovative experimental tools and new numerical approaches, focusing primarily on three subtopics governing important multiscale properties of granular media: (a) the jamming transition from fluid- to solid-like behavior, critical state flow and wave propagation, (b) the signature of fabric and its evolution for granular media under general loading conditions, and (c) mechanisms like rotation, breakage, failure and aggregation. The significance of these contributions and exploratory future directions pertaining to cross-scale understanding of granular matter are discussed

Elastic moduli and vibrational modes in jammed particulate packings.

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, nonaffine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus M, it is therefore necessary to take into account not only the affine modulus M_{A}, but also the nonaffine modulus M_{N} that arises from the nonaffine deformation. In the present work, we study the bulk (M=K) and shear (M=G) moduli in static jammed particulate packings over a range of packing fractions φ. The affine M_{A} is determined essentially by the static structural arrangement of particles, whereas the nonaffine M_{N} is related to the vibrational eigenmodes. We elucidate the contribution of each vibrational mode to the nonaffine M_{N} through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition φ_{c}, the vibrational density of states g(ω) shows a plateau in the intermediate-frequency regime above a characteristic frequency ω^{*}. We illustrate that this unusual feature apparent in g(ω) is reflected in the behavior of M_{N}: As φ→φ_{c}, where ω^{*}→0, those modes for ω<ω^{*} contribute less and less, while contributions from those for ω>ω^{*} approach a constant value which results in M_{N} to approach a critical value M_{Nc}, as M_{N}-M_{Nc}∼ω^{*}. At φ_{c} itself, the bulk modulus attains a finite value K_{c}=K_{Ac}-K_{Nc}>0, such that K_{Nc} has a value that remains below K_{Ac}. In contrast, for the critical shear modulus G_{c},G_{Nc} and G_{Ac} approach the same value so that the total value becomes exactly zero, G_{c}=G_{Ac}-G_{Nc}=0. We explore what features of the configurational and vibrational properties cause such a distinction between K and G, allowing us to validate analytical expressions for their critical values.

The role of passing in a two-dimensional network

The phenomenon of passing on a two-dimensional network has been studied through lattice hydrodynamic approach. Near the critical point, the effect of passing is investigated theoretically and numerically. The modified Korteweg–de Vries equation near the critical point is derived using the reduction perturbation method through nonlinear analysis. Analytically, it is shown that for all possible configurations of vehicle, the stable region significantly reduces with an increase in the passing rate. It is shown that the jamming transition occurs among no jam to chaotic jam for any configuration of vehicles for larger rate of passing constant, while for smaller rate of passing, the jamming transitions occur from no jam to chaotic jam through kink jam for any configuration of vehicles. The results show that the modified model is able to explain the complex phenomena of traffic flow at a better level of accuracy than the most of the existing models. Simulation results are found consistent with the theoretical findings, which confirm that the passing plays a significant role in a two-dimensional traffic system.

Lattice hydrodynamic model based traffic control: A transportation cyber–physical system approach

Abstract Lattice hydrodynamic model is a typical continuum traffic flow model, which describes the jamming transition of traffic flow properly. Previous studies in lattice hydrodynamic model have shown that the use of control method has the potential to improve traffic conditions. In this paper, a new control method is applied in lattice hydrodynamic model from a transportation cyber–physical system approach, in which only one lattice site needs to be controlled in this control scheme. The simulation verifies the feasibility and validity of this method, which can ensure the efficient and smooth operation of the traffic flow.

Pinning Susceptibility: The Effect of Dilute, Quenched Disorder on Jamming.

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}∝|ϕ-ϕ_{c}^{∞}|^{-γ_{p}} where ϕ_{c}^{∞} 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±0.026(0.291) in d=2 and γ_{p}=1.534±0.120(0.822) in d=3. Logarithmic corrections raise the exponent in d=2 to close to the d=3 value, although the systematic errors are very large.

Equilibrium Sampling of Hard Spheres up to the Jamming Density and Beyond.

We implement and optimize a particle-swap MonteCarlo algorithm that allows us to thermalize a polydisperse system of hard spheres up to unprecedentedly large volume fractions, where previous algorithms and experiments fail to equilibrate. We show that no glass singularity intervenes before the jamming density, which we independently determine through two distinct nonequilibrium protocols. We demonstrate that equilibrium fluid and nonequilibrium jammed states can have the same density, showing that the jamming transition cannot be the end point of the fluid branch.

Critical scaling of Bagnold rheology at the jamming transition of frictionless two-dimensional disks.

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 discuss in detail the critical scaling ansatz for the shear-driven jamming transition and carry out a detailed scaling analysis of our resulting data for pressure p and shear stress σ. Our analysis determines the critical exponent β that describes the algebraic divergence of the Bagnold transport coefficients lim_{γ[over ̇]→0}p/γ[over ̇]^{2},σ/γ[over ̇]^{2}∼(ϕ_{J}-ϕ)^{-β} as the jamming transition ϕ_{J} is approached from below. For the low strain rates considered in this work, we show that it is still necessary to consider the leading correction-to-scaling term in order to achieve a self-consistent analysis of our data, in which the critical parameters become independent of the size of the window of data used in the analysis. We compare our resulting value β≈5.0±0.4 against previous numerical results and competing theoretical models. Our results confirm that the shear-driven jamming transition in Bagnoldian systems is well described by a critical scaling theory and we relate this scaling theory to the phenomenological constituent laws for dilatancy and friction.

Finite-size effects in the Nagel-Schreckenberg traffic model

We examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. We show that the low-density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, we observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed V_{max} is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on V_{max}. The jamming transition at large V_{max} can be viewed as the nucleation of jams in a background of freely flowing vehicles. For small V_{max} no such clean separation into jammed and free vehicles is possible.

Single DNA molecule jamming and history-dependent dynamics during motor-driven viral packaging.

In many viruses molecular motors forcibly pack single DNA molecules to near-crystalline density into ~50–100 nm prohead shells1, 2. Unexpectedly, we found that packaging frequently stalls in conditions that induce net attractive DNA-DNA interactions3. Here, we present findings suggesting that this stalling occurs because the DNA undergoes a nonequilibrium jamming transition analogous to that observed in many soft-matter systems, such as colloidal and granular systems4–8. Experiments in which conditions are changed during packaging to switch DNA-DNA interactions between purely repulsive and net attractive reveal strongly history-dependent dynamics. An abrupt deceleration is usually observed before stalling, indicating that a transition in DNA conformation causes an abrupt increase in resistance. Our findings suggest that the concept of jamming can be extended to a single polymer molecule. However, compared with macroscopic samples of colloidal particles5 we find that single DNA molecules jam over a much larger range of densities. We attribute this difference to the nanoscale system size, consistent with theoretical predictions for jamming of attractive athermal particles.9, 10