Jamming Transition Research Articles

Dynamics of a Supercooled Disordered Sphere-Forming Diblock Copolymer as Determined by X-ray Photon Correlation and Dynamic Mechanical Spectroscopies.

We report the dynamic behavior of a sphere-forming poly(styrene)-block-poly(1,4-butadiene) (PS-PB) diblock copolymer comprising 20 vol % PB below the order-disorder transition temperature (TODT = 153 °C) using dynamic mechanical spectroscopy (DMS) and X-ray photon correlation spectroscopy (XPCS). A time-temperature transformation diagram was constructed by monitoring the elasticity of the sample as a function of time following rapid quenches of the disordered melt to various temperatures T < TODT. Isothermal frequency spectra acquired prior to nucleation of the ordered BCC phase were time-temperature superposed, and the shift factors were fit using the Williams-Landel-Ferry (WLF) equation. For comparison, XPCS measurements were used to extract relaxation times from the supercooled liquid as a function of the quench temperature. Alignment of the temperature dependence of the XPCS-based relaxation times with that of the WLF shift factors in the range T = 125-140 °C indicates that both techniques probe the fluctuating mesomorphic micelle dynamics mediated by the relaxation modes of individual chains, including interparticle chain exchange. For deeper quench temperatures, TODT - T ≥ 28 °C, departure of the XPCS time constant from WLF behavior is consistent with a jamming transition, analogous to that encountered in concentrated colloidal systems. We postulate that the dominant relaxation mode in the supercooled disordered liquid transitions from ergodic dynamics governed by chain exchange to a nonergodic regime dominated by local rearrangement of micellar particles at T ≈ Terg, where Terg denotes the ergodicity temperature.

Effect of temperature on flow properties of magnetofluidized beds at low consolidations

In this work we investigate the fluidization behavior and mechanical properties of granular beds of fine magnetite beads as affected by an increase of temperature and the application of a magnetic field. In the range of temperatures tested (up to 200°C) the cohesiveness of the bed is decreased with temperature whereas it is enhanced by the magnetic field as revealed by measurements of the gas velocity at the fluid to solid (jamming) transition and the tensile yield stress of the bed settled under low consolidation stresses. The opposed effects of temperature and the magnetic field are independent in the range of temperatures tested. The increase of cohesiveness induced by the magnetic field, as reported in previous studies, can be explained from the enhancement of interparticle attractive forces due to particle magnetization. On the other hand, the observed decrease of cohesiveness with temperature, which can be of great relevance in many practical applications, is in contrast with reported results from previous works using other materials. This suggests that the effect of temperature on the cohesiveness of granular materials is material dependent. The physical mechanism by which interparticle attractive forces are affected by an increase of temperature remains as a relevant subject for future work.

Sticky Matters: Jamming and Rigid Cluster Statistics with Attractive Particle Interactions.

While the large majority of theoretical and numerical studies of the jamming transition consider athermal packings of purely repulsive spheres, real complex fluids and soft solids generically display attraction between particles. By studying the statistics of rigid clusters in simulations of soft particles with an attractive shell, we present evidence for two distinct jamming scenarios. Strongly attractive systems undergo a continuous transition in which rigid clusters grow and ultimately diverge in size at a critical packing fraction. Purely repulsive and weakly attractive systems jam via a first-order transition, with no growing cluster size. We further show that the weakly attractive scenario is a finite size effect, so that for any nonzero attraction strength, a sufficiently large system will fall in the strongly attractive universality class. We therefore expect attractive jamming to be generic in the laboratory and in nature.

Universality of jamming of nonspherical particles

Amorphous packings of nonspherical particles such as ellipsoids and spherocylinders are known to be hypostatic: The number of mechanical contacts between particles is smaller than the number of degrees of freedom, thus violating Maxwell's mechanical stability criterion. In this work, we propose a general theory of hypostatic amorphous packings and the associated jamming transition. First, we show that many systems fall into a same universality class. As an example, we explicitly map ellipsoids into a system of "breathing" particles. We show by using a marginal stability argument that in both cases jammed packings are hypostatic and that the critical exponents related to the contact number and the vibrational density of states are the same. Furthermore, we introduce a generalized perceptron model which can be solved analytically by the replica method. The analytical solution predicts critical exponents in the same hypostatic jamming universality class. Our analysis further reveals that the force and gap distributions of hypostatic jamming do not show power-law behavior, in marked contrast to the isostatic jamming of spherical particles. Finally, we confirm our theoretical predictions by numerical simulations.

The jamming transition is a k-core percolation transition

We explain the structural origin of the jamming transition in jammed matter as the sudden appearance of k-cores at precise coordination numbers which are related not to the isostatic point, but to the emergence of the giant 3- and 4-cores as given by k-core percolation theory. At the transition, the k-core variables freeze and the k-core dominates the appearance of rigidity. Surprisingly, the 3-D simulation results can be explained with the result of mean-field k-core percolation in the Erdös–Rényi network. That is, the finite-dimensional transition seems to be explained by the infinite-dimensional k-core, implying that the structure of the jammed pack is compatible with a fully random network.

Burgers and mKdV equation for car-following model considering drivers’ characteristics on a gradient highway

In this paper, we propose a new car-following model considering driver’s timid and aggressive characteristics on a gradient highway. Based on the control theory, the linear stability analysis of the model was conducted. It shows that the stability of traffic flow on the gradient highway varies with the drivers’ characteristics and the slope. Adopting nonlinear stability analysis, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are derived to describe the triangular shock waves and kink–antikink waves, respectively. The theoretical and numerical results show that aggressive drivers tend to stabilize traffic flow but timid drivers tend to destabilize traffic flow on a gradient highway both on an uphill situation and on a downhill situation. Moreover, the slope of the road also plays an important role in traffic jamming transition.

Two-Species Active Transport along Cylindrical Biofilaments is Limited by Emergent Topological Hindrance

Active motion of molecules along filamentous structures is a crucial feature of cell biology and is often modeled with the paradigmatic asymmetric simple exclusion process. Motivated by recent experimental studies that have addressed the stepping behavior of kinesins on microtubules, we investigate a lattice gas model for simultaneous transport of two species of active particles on a cylinder. The species are distinguished by their different gaits: While the first species moves straight ahead, the second follows a helical path. We show that the collective properties of such systems critically differ from those of one-species transport in a way that cannot be accounted for by standard models. This is most evident in a jamming transition far below full occupation, as well as in non-equilibrium pattern formation. The altered behavior arises because - unlike the case in single-species transport - any given position may be targeted by two particles from different directions at the same time. However, a particle can leave a given position only in one direction. This simple change in connectivity significantly amplifies the impact of steric interactions and thus becomes a key determinant of mixed species transport. We computationally characterize this type of hindrance and develop a comprehensive theory for collective two-species transport along a cylinder. Our observations show high robustness against model extensions that account for additional biomolecular features and demonstrate that even small fractions of a second species can significantly alter transport. This suggests that our analysis is also relevant in a biological context.

Two Diverging Length Scales in the Structure of Jammed Packings.

At densities higher than the jamming transition for athermal, frictionless repulsive spheres we find two distinct length scales, both of which diverge as a power law as the transition is approached. The first, ξ_{Z}, is associated with the two-point correlation function for the number of contacts on two particles as a function of the particle separation. The second, ξ_{f}, is associated with contact-number fluctuations in subsystems of different sizes. On scales below ξ_{f}, the fluctuations are highly suppressed, similar to the phenomenon of hyperuniformity usually associated with density fluctuations. The exponents for the divergence of ξ_{Z} and ξ_{f} are different and appear to be different in two and three dimensions.

A fluid-to-solid jamming transition underlies vertebrate body axis elongation.

Just as in clay molding or glass blowing, sculpting biological structures requires the constituent material to locally flow like a fluid while maintaining overall mechanical integrity like a solid. Disordered soft materials, such as foams, emulsions and colloidal suspensions, switch from fluid-like to solid-like behaviors at a jamming transition1–4. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D5,6 and jamming in cultured epithelial monolayers7,8, behaviors recently predicted theoretically9–11 and proposed to influence asthma pathobiology8 and tumor progression12. However, it is unknown if these seemingly universal behaviors occur in vivo and, specifically, if they play any functional role during embryonic morphogenesis. By combining direct in vivo measurements of tissue mechanics with analysis of cellular dynamics, we show that during vertebrate body axis elongation, posterior tissues undergo a jamming transition from a fluid-like behavior at the extending end, the mesodermal progenitor zone (MPZ), to a solid-like behavior in the presomitic mesoderm (PSM). We uncover an anteroposterior, N-cadherin-dependent gradient in yield stress that provides increasing mechanical integrity to the PSM, consistent with the tissue transiting from a wetter to a dryer foam-like architecture. Our results show that cell-scale stresses fluctuate rapidly (~1 min), enabling cell rearrangements and effectively ‘melting’ the tissue at the growing end. Persistent (>0.5 h) stresses at supracellular scales, rather than cell-scale stresses, guide morphogenetic flows in fluid-like tissue regions. Unidirectional axis extension is sustained by the reported PSM rigidification, which mechanically supports posterior, fluid-like tissues during remodeling prior to their maturation. The spatiotemporal control of fluid-like and solid-like tissue states may represent a generic physical mechanism of embryonic morphogenesis.

Theory for Swap Acceleration near the Glass and Jamming Transitions for Continuously Polydisperse Particles

Swap algorithms have provided recent insights into how liquids solidify into glass, but why they work is unknown. A new analysis shows that the answer lies in an effective potential that describes the size and interactions of particles.

Rheology of dense granular suspensions

Suspensions are composed of mixtures of particles and fluid and are omnipresent in natural phenomena and in industrial processes. The present paper addresses the rheology of concentrated suspensions of non-colloidal particles. While hydrodynamic interactions or lubrication forces between the particles are important in the dilute regime, they become of lesser significance when the concentration is increased, and direct particle contacts become dominant in the rheological response of concentrated suspensions, particularly those close to the maximum volume fraction where the suspension ceases to flow. The rheology of these dense suspensions can be approached via a diversity of approaches that the paper introduces successively. The mixture of particles and fluid can be seen as a fluid with effective rheological properties but also as a two-phase system wherein the fluid and particles can experience relative motion. Rheometry can be undertaken at an imposed volume fraction but also at imposed values of particle normal stress, which is particularly suited to yield examination of the rheology close to the jamming transition. The response of suspensions to unsteady or transient flows provides access to different features of the suspension rheology. Finally, beyond the problem of suspension of rigid, non-colloidal spheres in a Newtonian fluid, there are a great variety of complex mixtures of particles and fluid that remain relatively unexplored.

Scaling of flow curves: Comparison between experiments and simulations

Yield-stress materials form an interesting class of materials that behave like solids at small stresses, but start to flow once a critical stress is exceeded. It has already been reported both in experimental and simulation work that flow curves of different yield-stress materials can be scaled with the distance to jamming or with the confining pressure. However, different scaling exponents are found between experiments and simulations. In this paper we identify sources of this discrepancy. We numerically relate the volume fraction with the confining pressure and discuss the similarities and differences between rotational and oscillatory measurements. Whereas simulations are performed in the elastic response regime close to the jamming transition and with very small amplitudes to calculate the scaling exponents, these conditions are hardly possible to achieve experimentally. Measurements are often performed far away from the critical volume fraction and at large amplitudes. We show that these differences are the underlying reason for the different exponents for rescaling flow curves.

Solution of jamming transition problem using adomian decomposition method

PurposeThe purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM).Design/methodology/approachIn this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time.FindingsA highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method.Originality/valueThis is the first study to apply ADM to JTP.

Coarsening and mechanics in the bubble model for wet foams.

Aqueous foams are an important model system that displays coarsening dynamics. Coarsening in dispersions and foams is well understood in the dilute and dry limits, where the gas fraction tends to zero and one, respectively. However, foams are known to undergo a jamming transition from a fluidlike to a solidlike state at an intermediate gas fraction ϕ_{c}. Much less is known about coarsening dynamics in wet foams near jamming, and the link to mechanical response, if any, remains poorly understood. Here we probe coarsening and mechanical response using numerical simulations of a variant of the Durian bubble model for wet foams. As in other coarsening systems we find a steady state scaling regime with an associated particle size distribution. We relate the time rate of evolution of the coarsening process to the wetness of the foam and identify a characteristic coarsening time that diverges approaching jamming. We further probe mechanical response of the system to strain while undergoing coarsening. There are two competing timescales, namely the coarsening time and the mechanical relaxation time. We relate these to the evolution of the elastic response and the mechanical structure.

Analyses of lattice hydrodynamic model using delayed feedback control with passing

Delayed feedback control method is used for one dimensional lattice model by incorporating the effect of passing. In order to check the stability of system under control theory Hurwitz criteria is used and H∞ norm of transfer functions are obtained. The efficiency of control signal in minimizing the jamming transitions due to passing, is shown through Bode plot. The results show that the control parameter helps in reducing congestion and makes the flow stable even at higher rate of passing. Simulations are carried out and are found in good agreement with theoretical results.

Robustness of mean field theory for hard sphere models.

In very recent work the mean field theory of the jamming transition in infinite-dimensional hard sphere models was presented. Surprisingly, this theory predicts quantitatively the numerically determined characteristics of jamming in two and three dimensions. This is a rare and unusual finding. Here we argue that this agreement is nongeneric: only for hard sphere models does it happen that sufficiently close to the jamming density (at any temperature) the effective interactions are binary, in agreement with mean field theory, justifying the truncation of many-body interactions (which is the exact protocol in infinite dimensions). Any softening of the bare hard sphere interactions results in many-body effective interactions that are not mean field at any density, making the d=∞ results not applicable.

Microscale Descriptors for Particle-Void Distribution and Jamming Transition in Pre- and Post-Liquefaction of Granular Soils

AbstractMicromechanical modeling provides significant insight into the fundamental mechanism of soil liquefaction. In this study, a series of undrained cyclic simple shear simulations were conducte...

Strain rate and temperature effect on Zr50Cu50 metallic glass under pure shear

We present a molecular dynamics study of the mechanical properties of Zr50Cu50 glass under pure shear. The samples have 145.200 atoms with dimensions of 40 × 20 × 2 nm in the x, y and z directions, respectively. After quenching, we obtain 3 different systems at temperatures of 10, 50, 300 K. All systems were then subjected to dynamic pure shear at constant shear rates of 2.5×108 s−1, 5×108 s−1 and 2.5×109 s−1. We investigate the changes of mechanical properties as a function of temperature and shear rate, and find that the shear modulus is not sensitive to the changes of the shear rate, but decreases as the temperature rises. Ultimate strength is enhanced at higher shear rates and decreases with temperature. A study of the atomic structure reveals that the low values of ultimate strength are associated with high values of local atomic shear strain. These results are reminiscent of what happens at the jamming transition.

Jamming of packings of frictionless particles with and without shear**Project supported by the National Natural Science Foundation of China (Grant Nos. 11702289, 11734014, and 11574278) and the Anhui Provincial Natural Science Foundation (Grant No. 1708085QA07).

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 macrofriction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixed pressure.

Structural organisation and dynamics in king penguin colonies

During breeding, king penguins do not build nests, however they show strong territorial behaviour and keep a pecking distance to neighbouring penguins. Penguin positions in breeding colonies are highly stable over weeks and appear regularly spaced, but thus far no quantitative analysis of the structural order inside a colony has been performed. In this study, we use the radial distribution function to analyse the spatial coordinates of penguin positions. Coordinates are obtained from aerial images of two colonies that were observed for several years. Our data demonstrate that the structural order in king penguin colonies resembles a 2D liquid of particles with a Lennard-Jones-type interaction potential. We verify this using a molecular dynamics simulation with thermally driven particles, whereby temperature corresponds to penguin movements, the energy well depth ϵ of the attractive potential corresponds to the strength of the colony-forming behaviour, and the repulsive zone corresponds to the pecking radius. We can recapitulate the liquid disorder of the colony, as measured by the radial distribution function, when the particles have a temperature of several (1.4–10) and a normally distributed repulsive radius. To account for the observation that penguin positions are stable over the entire breeding period, we hypothesize that the liquid disorder is quenched during the colony formation process. Quenching requires the temperature to fall considerably below 1 , which corresponds to a glass transition, or the repulsion radius to exceed the distance between neighbouring penguins, which corresponds to a jamming transition. Video recordings of a breeding colony together with simulations suggest that quenching is achieved by a behavioural motility arrest akin to a glass transition. We suggest that a liquid disordered colony structure provides an ideal compromise between high density and high flexibility to respond to external disturbances that require a repositioning of penguins.