Jamming Transition Research Articles

Taming macroscopic jamming in transportation networks

In transportation networks, a spontaneous jamming transition is often observed, e.g. in urban road networks and airport networks. Because of this instability, flow distribution is significantly imbalanced on a macroscopic level. To mitigate the congestion, we consider a simple control method, in which congested nodes are closed temporarily, and investigate how it influences the overall system. Depending on the timing of the node closure and opening, and congestion level of a network, the system displays three different phases: free-flow phase, controlled phase, and deadlock phase. We show that when the system is in the controlled phase, the average flow is significantly improved, whereas when in the deadlock phase, the flow drops to zero. We study how the control method increases the network flow and obtain their transition boundary analytically.

Evaluation of the exfoliation and stability of Na-montmorillonite in aqueous dispersions

In aqueous dispersion, Na-montmorillonite swells due to absorption of water and exfoliate into smaller entities, known as tactoids, with electric double layers on their surfaces. The exfoliation rate of such tactoids in aqueous Laponite dispersion was seen to be greatly reduced at the jamming transition and was reported by this group in a recent article [Langmuir, 2013, 29, 12663–12669]. The work reported here uses ultrasound attenuation spectroscopy experiments on Na-montmorillonite dispersions and shows that the complete exfoliation of tactoids is not achieved even below the jamming concentration. This behavior indicates that screened Coulomb repulsions between and within tactoids, as well as the osmotic pressure of hydrated Na+ ions, play very important roles in the exfoliation kinetics of tactoids. In this work, the phenomenon of tactoid exfoliation is studied systematically by changing clay mineral concentration, ionic conditions and the ages of the dispersions. A signature of an irreversible process of tactoid reformation under certain ionic conditions is also observed. Finally, electroacoustic measurements and rheometry are used to assess the influence of tactoid exfoliation on the stability and viscoelasticity of the arrested phases formed under different ionic conditions.

Nonmonotonic flow curves of shear thickening suspensions.

The discontinuous shear thickening (DST) of dense suspensions is a remarkable phenomenon in which the viscosity can increase by several orders of magnitude at a critical shear rate. It has the appearance of a first-order phase transition between two hypothetical "states" that we have recently identified as Stokes flows with lubricated or frictional contacts, respectively. Here we extend the analogy further by means of stress-controlled simulations and show the existence of a nonmonotonic steady-state flow curve analogous to a nonmonotonic equation of state. While we associate DST with an S-shaped flow curve, at volume fractions above the shear jamming transition the frictional state loses flowability and the flow curve reduces to an arch, permitting the system to flow only at small stresses. Whereas a thermodynamic transition leads to phase separation in the coexistence region, we observe a uniform shear flow all along the thickening transition. A stability analysis suggests that uniform shear may be mechanically stable for the small Reynolds numbers and system sizes in a rheometer.

Jamming and unjamming transition of oil-in-water emulsions under continuous temperature change

To analyze the jamming and unjamming transition of oil-in-water emulsions under continuous temperature change, we simulated an emulsion system whose critical volume fraction was 0.3, which was validated with experimental results under oscillatory shear stress. In addition, we calculated the elastic modulus using the phase lag between strain and stress. Through heating and cooling, the emulsion experienced unjamming and jamming. A phenomenon-which is when the elastic modulus does not reach the expected value at the isothermal system-occurred when the emulsion system was cooled. We determined that this phenomenon was caused by the frequency being faster than the relaxation of the deformed droplets. We justified the relation between the frequency and relaxation by simulating the frequency dependency of the difference between the elastic modulus when cooled and the expected value at the same temperature.

Effect of particle size polydispersity on the yield stress of magnetofluidized beds as depending on the magnetic field orientation

This work analyzes the influence of particle size polydispersity and shape, as well as orientation and strength of an externally imposed magnetic field, on the rheology of gas-fluidized beds of fine magnetizable particles. Samples consisted of nearly spherical magnetite beads and irregularly shaped steel particles of same average mean diameter but different particle size distributions and magnetization properties. The application of an external magnetic field to the unstable bubbling bed confers it a solid-plastic behavior suppressing the growth of large bubbles. The yield stress, the permeability to gas flow and the gas velocity at the jamming transition of the stabilized magnetofluidized beds (MFBs) have been measured. Steel MFBs have significantly larger values of the yield stress than magnetite MFBs particularly when the gas flow and magnetic field directions were parallel (co-flow configuration). Visual observations and permeability data shows that polydispersed steel particles arrange into more porous and expanded structures than magnetite beads by the application of co-flow magnetic fields. In the cross-flow configuration (when the external magnetic field is perpendicular to the vertical gas flow), it is observed just a moderate enhancement of the magnetic yield stress of steel MFBs as compared to magnetite, which is explained by a larger misalignment between the steel chained particles and the horizontal magnetic field. Finally, a theoretical model has been used to reproduce the observed trends of the magnetic yield stress by taking into account details on the interparticle magnetic forces and the microstructure arrangement.

Analysis of a new two-lane lattice hydrodynamic model with consideration of the global average flux

A new two-lane traffic lattice hydrodynamic model is proposed with the consideration of the global average-and-optimal flux difference effect based on the local relative flux two-lane lattice model. First, the influence of the global average-and-optimal flux difference on the stability of traffic flow is investigated through linear stability theory. The results reveal that the unstable region will be shrunk by taking the global average-and-optimal flux difference effect into account. Additionally, by using the reductive perturbation method, the mKdV equation near the critical point is derived and traffic jam transition can be described by its kink–antikink soliton solution. The good agreement between the numerical simulations and the analytical results shows that traffic congestion can be suppressed efficiently by considering the global average-and-optimal flux difference and the local relative flux effects in two-lane traffic system and the local relative flux is more important than the global average-and-optimal flux difference in stabilizing traffic flow.

Theory of the jamming transition at finite temperature.

A theory for the microscopic structure and the vibrational properties of soft sphere glass at finite temperature is presented. With an effective potential, derived here, the phase diagram and vibrational properties are worked out around the Maxwell critical point at zero temperature T and pressure p. Variational arguments and effective medium theory identically predict a non-trivial temperature scale T(∗) ∼ p((2-a)/(1-a)) with a ≈ 0.17 such that low-energy vibrational properties are hard-sphere like for T ≳ T(∗) and zero-temperature soft-sphere like otherwise. However, due to crossovers in the equation of state relating T, p, and the packing fraction ϕ, these two regimes lead to four regions where scaling behaviors differ when expressed in terms of T and ϕ. Scaling predictions are presented for the mean-squared displacement, characteristic frequency, shear modulus, and characteristic elastic length in all regions of the phase diagram.

Maturation of the human bronchial epithelial cell (HBEC) layer causes a jamming transition, but compression of the layer, as in bronchospasm, causes unjamming

In asthma, bronchospasm is one of major characteristics. In HBE cells in air-liquid interface (ALI) culture, compressive stress, as in bronchospasm, induces airway remodeling. Here, we investigated the physical behavior of HBE cells from normal or asthmatic donors in ALI culture. To determine an existence of jamming phase, we captured time-lapse images of HBE cells. As days progress in ALI culture, a phase transition occurred from a mobile, unjammed phase to a quiescent, jammed phase; days 6-8 in normal vs. delayed until day 14 in asthmatic cells (Fig 1). In cell lysates, the existence of vimentin was temporally well correlated with the onset of the jamming transition. In asthmatic cells during ALI days, treatment with SB431542, a TGF receptor inhibitor, promoted a jamming transition and disappearance of vimentin. Compression caused the unjamming transition of jammed cells (Fig 2), but pretreatment with SB431542 attenuated the compression-induced unjamming transition. Along with the unjamming transition, compression induced Hic-5, a LIM protein. Taken together, maturation of the HBEC layer causes a jamming transition, but compression of the layer, as in bronchospasm, causes unjamming. Importantly, TGFbeta controls this jamming transition along with vimentin and Hic-5 expression. Our findings suggest that the jamming-unjamming phase transition is a novel physical feature that captures injury-repair process and differentiates normal from asthmatic cells.

Jamming Criticality Revealed by Removing Localized Buckling Excitations

Recent theoretical advances offer an exact, first-principles 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 interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

Active microrheology in active matter systems: Mobility, intermittency, and avalanches

We examine the mobility and velocity fluctuations of a driven particle moving through an active matter bath of self-mobile disks for varied density or area coverage and varied activity. We show that the driven particle mobility can exhibit nonmonotonic behavior that is correlated with distinct changes in the spatiotemporal structures that arise in the active media. We demonstrate that the probe particle velocity distributions exhibit specific features in the different dynamic regimes and identify an activity-induced uniform crystallization that occurs for moderate activity levels and is distinct from the previously observed higher activity cluster phase. The velocity distribution in the cluster phase has telegraph noise characteristics produced when the probe particle moves alternately through high-mobility areas that are in the gas state and low-mobility areas that are in the dense phase. For higher densities and large activities, the system enters what we characterize as an active jamming regime. Here the probe particle moves in intermittent jumps or avalanches that have power-law-distributed sizes that are similar to the avalanche distributions observed for nonactive disk systems near the jamming transition.

Analysis of average density difference effect in a new two-lane lattice model

A new lattice model is proposed by taking the average density difference effect into account for two-lane traffic system according to Transportation Cyber-physical Systems. The influence of average density difference effect on the stability of traffic flow is investigated through linear stability theory and nonlinear reductive perturbation method. The linear analysis results reveal that the unstable region would be reduced by considering the average density difference effect. The nonlinear kink–antikink soliton solution derived from the mKdV equation is analyzed to describe the properties of traffic jamming transition near the critical point. Numerical simulations confirm the analytical results showing that traffic jam can be suppressed efficiently by considering the average density difference effect for two-lane traffic system.

Analysis of anticipation driving effect in traffic lattice hydrodynamic model with on-ramp

A new traffic lattice hydrodynamic model with on-ramp is proposed with consideration of driver’s anticipation effect according to transportation cyber physical systems. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region on the phase diagram will be enlarged by considering driver’s anticipation effect but shrunk with the consideration of on-ramp effect. In order to depict traffic jamming transition, the modified Korteweg-de Vries (mKdV) equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density wave can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results, and all the results confirm that both driver’s anticipation effect and on-ramp effect affect the traffic stability of the main road importantly.

The car following model considering traffic jerk

Based on optimal velocity car following model, a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway. Traffic jerk means the sudden braking and acceleration of vehicles, which has a significant impact on traffic movement. The nature of the model is researched by using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow. The time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived to describe the traffic flow near the critical point and the traffic jam. In addition, the connection between the TDGL and the mKdV equations are also given.

Random matrix theory approach to vibrations near the jamming transition

It has been shown that the dynamical matrix M describing harmonic oscillations in granular media can be represented in the form M = AA T, where the rows of the matrix A correspond to the degrees of freedom of individual granules and its columns correspond to elastic contacts between granules. Such a representation of the dynamical matrix makes it possible to estimate the density of vibrational states with the use of the random matrix theory. The found density of vibrational states is approximately constant in a wide frequency range ω− < ω < ω+, which is determined by the ratio of the number of degrees of freedom to the total number of contacts in the system, which is in good agreement with the results of the numerical experiments.

A random matrix definition of the boson peak

The density of vibrational states for glasses and jammed solids exhibits universal features, including an excess of modes above the Debye prediction known as the boson peak located at a frequency . We show that the eigenvector statistics for boson peak modes are universal, and develop a new definition of the boson peak based on this universality that displays the previously observed characteristic scaling . We identify a large new class of random matrices that obey a generalized global tranlational invariance constraint and demonstrate that members of this class also have a boson peak with precisely the same universal eigenvector statistics. We denote this class as boson peak random matrices, and conjecture it comprises a new universality class. We characterize the eigenvector statistics as a function of coordination number, and find that one member of this new class reproduces the scaling of with coordination number that is observed near the jamming transition.

Spatiotemporal chaotic unjamming and jamming in granular avalanches.

We have investigated the spatiotemporal chaotic dynamics of unjamming and jamming of particles in a model experiment – a rotating drum partially filled with bidisperse disks to create avalanches. The magnitudes of the first Lyapunov vector δu(t) and velocity v(t) of particles are directly measured for the first time to yield insights into their spatial correlation Cδu,v, which is on statistical average slightly larger near the unjamming than the value near the jamming transition. These results are consistent with the recent work of Banigan et al (Nature Phys. 2013), and it is for the first time to validate their theoretical models in a real scenario. v(t) shows rich dynamics: it grows exponentially for unstable particles and keeps increasing despite stochastic interactions; after the maximum, it decays with large fluctuations. Hence the spatiotemporal chaotic dynamics of avalanche particles are entangled, causing temporal correlations of macroscopic quantities of the system. We propose a simple model for these observations.

Effect of multi-phase optimal velocity function on jamming transition in a lattice hydrodynamic model with passing

In this paper, we study the effect of multi-phase optimal velocity function on a density difference lattice model with passing. The effect of reaction coefficient is examined through linear stability analysis and shown that it can significantly enlarge the stability region on the phase diagram for any rate of passing. Using nonlinear stability analysis, the critical value of passing constant is obtained and found independent of reaction coefficient. Below this critical value for which kink soliton solution of mKdV equation exists. By varying the density, multiple phase transitions are analyzed, which highly depend on the sensitivity, reaction coefficient and passing constant. It is observed that the number of stages in multi-phase transitions closely related to the number of the turning points in the optimal velocity function. The theoretical findings are verified using numerical simulation, which confirm that phase diagrams of multi-phase traffic in the case of passing highly depend on the choice of optimal velocity function as well as on other parameters such as sensitivity, reaction coefficient and rate of passing.

Diverging viscosity and soft granular rheology in non-Brownian suspensions.

We use large scale computer simulations and finite-size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size and carefully study the asymptotic limits of large system sizes and infinitely hard particle repulsion. We first focus on the asymptotic behavior of the shear viscosity in the hard particle limit. By measuring the viscosity increase over about 5 orders of magnitude, we are able to confirm its asymptotic power law divergence close to the jamming transition. However, a precise determination of the critical density and critical exponent is difficult due to the "multiscaling" behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. Finally, we study the effect of particle softness and propose a natural extension of the standard granular rheology, which we test against our simulation data. Close to the jamming transition, this "soft granular rheology" offers a detailed description of the nonlinear rheology of soft particles, which differs from earlier empirical scaling forms.

Disordered solids without well-defined transverse phonons: the nature of hard-sphere glasses.

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by calculating the dynamical structure factors. The Ioffe-Regel limit (frequency) is reached when the phonon wavelength is comparable to the mean free path, beyond which phonons are no longer well defined. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamminglike transition and glass transition, respectively. As a consequence, glasses between the glass transition and the jamminglike transition, which are hard-sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamminglike transition.

Compression- and shear-driven jamming of U-shaped particles in two dimensions

We carry out numerical simulations of soft, U-shaped, frictionless particles in $d=2$ dimensions in order to explore the effects of complex particle shape on the jamming transition. We consider both cases of uniform compression-driven and shear-driven jamming as packing fraction $\phi$ and compression or shear rate is varied. Upon slow compression, jamming is found to occur when the isostatic condition is satisfied. Under driven steady state shearing, jamming occurs at a higher packing fraction $\phi_J$ than observed in compression. A growing relaxation time and translational correlation length is found as $\phi$ increases towards $\phi_J$. We consider the orientational ordering and rotation of particles induced by the shear flow. Both nematic and tetratic ordering are found, but these decrease as $\phi$ increases to $\phi_J$. At the jamming transition, the nematic ordering further decreases, while the tetratic ordering increases, but the orientational correlation lengths remain small throughout. The average angular velocity of the particles is found to increase as $\phi$ increases, saturating to a plateau just below $\phi_J$, but then increasing again as $\phi$ increases above $\phi_J$.