Jamming Transition Research Articles

Discontinuous Shear Thickening in Biological Tissue Rheology.

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

Motion Evaluation of Variable-Stiffness Link Based on Shape-Memory Alloy and Jamming Transition Phenomenon

In rapidly aging societies, the application of robots has spread from industry to nursing and social welfare. As the designs of industrial and non-industrial robots are different, numerous robot components with various shapes and stiffness are required for different tasks. In this study, we attached a variable-stiffness link based on a shape-memory alloy (SMA) and the jamming transition phenomenon to a robot arm and evaluated its pick-and-place motion for various objects with different shapes and weights. The link can be fixed in an arbitrary shape and then restored to its initial shape via the shape memory effect. The objects were picked up and moved by a prototype link, which consisted of four SMA wires inserted in the jamming mechanism. We compared two states of the link, namely with and without deformation of the link into a shape (the centerline and the cross section) to suit the target object using a mold. Experiments confirmed that changing and fixing the link shape to suit the target object increased both positioning accuracy and weight capacity.

Schramm-Loewner Evolution in 2D Rigidity Percolation.

Amorphous solids may resist external deformation such as shear or compression, while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter, we exploit this finding to characterize the universality class of central-force rigidity percolation (RP), using Schramm-Loewner evolution (SLE) theory. We provide numerical evidence that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE_{κ}, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant κ, we obtain the estimation κ∼2.9 for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension D_{f} and correlation length exponent ν, providing new, nontrivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.

Understanding slow compression of frictional granular particles by network analysis.

We consider frictional granular packings exposed to quasi-static compression rates, with a focus on systems above the jamming transition. For frictionless packings, earlier work (S. Luding et al., Soft Matter, 2022, 18(9), 1868-1884) has uncovered that the system evolution/response involves smooth evolution phases, interrupted by fast transitions (events). The general finding is that the force networks' static quantities correlate closely with the pressure, while their evolution resembles the kinetic energy for both frictionless and frictional packings. The former represents reversible (elastic) particle deformations with affine and non-affine components, whereas the latter also involves much stronger, irreversible (plastic) rearrangements of the packings. Events are associated with jumps in the overall kinetic energy as well as dramatic changes in the force networks describing the particle micro-structure. The frictional nature of particle interactions affects both their frequency and the relevant time scale magnitude. For intermediate friction, events are often followed by an unexpected slow-down during which the kinetic energy drops below its average value. We find that these slow-downs are associated with a significant decrease in the non-affine dynamics of the particles, and are strongly influenced by friction. Friction modifies the structure of the networks, both through the typical number of contacts of a particle, and by influencing topological features of the resulting networks. Furthermore, friction modifies the dynamics of the networks, with larger values of friction leading to smaller changes of the more stable networks.

Exceptionally dense and resilient critically jammed polydisperse disk packings.

Understanding the way disordered particle packings transition between jammed (rigid) and unjammed (fluid) states is of both great practical importance and strong fundamental interest. The values of critical packing fraction (and other state variables) at the jamming transition are protocol dependent. Here, we demonstrate that this variability can be systematically traced to structural measures of packing, as well as to energy measures inside the jammed regime. A novel generalized simultaneous particle swap algorithm constructs overjammed states of desired energy, which upon decompression lead to predictable critical packing fractions. Thus, for a given set of particle sizes, states with extraordinarily high critical packing fractions can be found efficiently, which sustain substantial shear strain and preserve their special structure over the entire jammed domain. The close relation revealed here between the energy landscape of overjammed soft-particle packings and the behavior near the jamming transition points towards new ways of understanding and constructing disordered materials with exceptional properties.

Fabric-based jamming phase diagram for frictional granular materials.

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

Effect of R-phase on shape recovery speed of Ti-Ni shape memory alloy wire for variable-stiffness mechanism using jamming transition phenomenon

Effect of R-phase on shape recovery speed of Ti-Ni shape memory alloy wire for variable-stiffness mechanism using jamming transition phenomenon

Abnormal blockage of water flow in valveless nanopumps

In the narrow orifice of a cone-shaped channel, blockage can occur for granular matter. However, water molecules can enter into and even permeate through carbon nanotubes of diameters down to 0.8 nm at ultrafast rates. Here we demonstrate by molecular dynamics simulations that clogging can also emerge unexpectedly in the water flowing through a nanoscale valve-less pump. The designed pump features two truncated carbon nanocones, with the narrowest region having a diameter of 1.2 nm (larger than that of (6, 6) carbon nanotube), linked to a fluid cavity volume, and is powered by the vibration of a graphene sheet. In the low frequency range, water molecules can be driven through the nanocones effectively by the vibration of the graphene sheet. The maximum flux reaches 83 ns<sup>–1</sup>, which is approximately 20 times the measured value of (3.9 ± 0.6) ns<sup>–1</sup> for aquaporin-1. However, at higher frequencies, water molecules suffer blockage at the narrow exits. Much unlike granular matter, high-frequency vibration cannot restore water flow. The key to this phenomenon is that in the narrow exits of two nanocones acting as diffuser/nozzle, the number density of water molecules rapidly increases with frequency increasing, the tight hydrogen-bonding network is formed, and the mean lifetime of hydrogen bonds increases dramatically under high-frequency vibrations. High frequency fluctuations in the middle chamber make H-bond network between water molecules in the narrow exits more stable. The probability density distribution of water exhibits a non-equilibrium transition from a disordered state to ordered state. This work reveals a new mechanism of water flowing/blocking in a nanoscale valve-less pump based on two asymmetrical nanocones, offers valuable insights into understanding nonequilibrium jamming transition in nanoscale fluid.

From flow to jamming: Lattice Gas Automaton simulations in granular materials

We introduce the first extension of a Lattice Gas Automaton (LGA) model to accurately replicate observed emergent phenomena in granular materials with a special focus on previously unexplored jamming transitions by incorporating gravitational effects, energy dissipation in particle collisions, and wall friction. We successfully reproduce flow rate evolution, density wave formation, and jamming transition observed in experiments. We also explore the critical density at which jamming becomes probable. This research advances our understanding of granular dynamics and offers insights into the jamming behavior of granular materials.

Non-Destructive Evaluation of White-Flesh Dragon Fruit Decay with a Robot

Dragon fruit is a tropical fruit with significant potential for consumers and producers. The quality assurance of this high-value product is crucial to satisfy consumer expectations. The quality of imported dragon fruit after storage may deteriorate due to inappropriate storage conditions. The firmness of dragon fruit is an essential parameter to estimate its conditions, and it is usually measured by destructive testing. The objective of the present study is to develop and test a non-destructive robotic sensor for assessing dragon fruit quality related to texture deterioration. Sixty white-fresh dragon fruits obtained from a store were divided in two sets of thirty fruits and stored 48 h at different conditions (cold and room storage) to produce deteriorated and consumer-acceptable fruits. First, the fruit samples were assessed non-destructive with the force sensor of a collaborative robot while they were touched. The robot tool is a pad capable of adapting and copying fruit shapes while controlling its hardness with the jamming transition of its internal granular fill. Second, the fruits were evaluated with destructive tests such as fruit firmness, flesh firmness, and soluble solid content. The procedure followed to produce deteriorated and acceptable fruits were confirmed. A discriminant analysis was carried out to segregate the fruit between the two categories according to the non-destructive variables extracted from the sensor. The variables obtained from the robotic first slope (S1) and the difference between the maximum value and the first overshoot (Os) were significant predictors for the separation in the two quality categories. Promising results were obtained with 77.50% of well classified fruit from the model data set, and 84.21% from the validation data set. The use of the robot could be an efficient tool in evaluating the quality of dragon fruit. This process may lead to substantial savings, particularly considering the elevated cost associated with the importation of tropical fruits into the European market.

Chaotic jam and phase transitions in heterogeneous lattice model integrating the delay characteristics difference with passing effect under autonomous and human-driven vehicles environment

In heterogeneous traffic flow, the response delay of different types' vehicles varies. Accordingly, a heterogeneous lattice model is created for the mixed traffic flows including autonomous vehicles and human-driven vehicles accounting for the delay difference characteristics with the passing effect. The neutral stability condition is acquired from the linear stability analysis, which shows that the stability region of the system significantly decreases with the increase of the passing effect, the proportion of regular vehicles and the reaction time coefficient. The kink-antikink solution of the modified Korteweg-de Vries equation is inferred via nonlinear analysis. The jamming transitions occur between the kink jam and no jam regions with lower passing effect. When the passing effect increases to a critical value, a chaotic jam region appears between the kink jam and no jam regions. And the chaotic jam region further expands with higher passing effect. Moreover, simulation experiments indicate that traffic stability gets better with the delayed time falling down in heterogeneous traffic flow. Also, the impact factors of chaos phenomenon, including the passing effect, the delayed time and proportion of regular vehicles, are investigated in heterogeneous lattice model through Poincaré phase diagram and Lyapunov exponent.

Local Rotational Jamming and Multi-Stage Hyperuniformities in an Active Spinner System

An active system consisting of many self-spinning dimers is simulated, and a distinct local rotational jamming transition is observed as the density increases. In the low density regime, the system stays in an absorbing state, in which each dimer rotates independently subject to the applied torque; while in the high density regime, a fraction of the dimers become rotationally jammed into local clusters, and the system exhibits microphase-separation like two-phase morphologies. For high enough densities, the system becomes completely jammed in both rotational and translational degrees of freedom. Such a simple system is found to exhibit rich and multiscale disordered hyperuniformities among the above phases: the absorbing state shows a critical hyperuniformity of the strongest class and subcritically preserves the vanishing density fluctuation scaling up to some length scale; the locally jammed state shows a two-phase hyperuniformity conversely beyond some length scale with respect to the phase cluster sizes; the totally jammed state appears to be a monomer crystal, but intrinsically loses large-scale hyperuniformity. These results are inspiring for designing novel phase-separation and disordered hyperuniform systems through dynamical organization.

Topological damping in an ultrafast giant cell

Cellular systems are known to exhibit some of the fastest movements in biology, but little is known as to how single cells can dissipate this energy rapidly and adapt to such large accelerations without disrupting internal architecture. To address this, we investigate Spirostomum ambiguum-a giant cell (1-4 mm in length) well-known to exhibit ultrafast contractions (50% of body length) within 5 ms with a peak acceleration of 15[Formula: see text]. Utilizing transmitted electron microscopy and confocal imaging, we identify an association of rough endoplasmic reticulum (RER) and vacuoles throughout the cell-forming a contiguous fenestrated membrane architecture that topologically entangles these two organelles. A nearly uniform interorganelle spacing of 60 nm is observed between RER and vacuoles, closely packing the entire cell. Inspired by the entangled organelle structure, we study the mechanical properties of entangled deformable particles using a vertex-based model, with all simulation parameters matching 10 dimensionless numbers to ensure dynamic similarity. We demonstrate how entangled deformable particles respond to external loads by an increased viscosity against squeezing and help preserve spatial relationships. Because this enhanced damping arises from the entanglement of two networks incurring a strain-induced jamming transition at subcritical volume fractions, which is demonstrated through the spatial correlation of velocity direction, we term this phenomenon "topological damping." Our findings suggest a mechanical role of RER-vacuolar meshwork as a metamaterial capable of damping an ultrafast contraction event.

Theoretical and experimental investigation on nonlinear dynamic of grain-beam system

We experimentally investigated the system of a simply supported beam immersed in a granular medium, which displays jump and new peaks in its amplitude-frequency curve under harmonic excitation. The relationship between the macroscopic nonlinear response and microscopic state of the granular medium was studied using the discrete element method. Using the dynamic modulus and vibrational density of states as indicators, we show that the granular medium changes from a solid-like to liquid-like state when the frequency increases to approach the jumping point. Considering the similarity between this system and acoustic metamaterial beams, an equivalent theoretical model was established for the former. Numerical results of the theoretical model were consistent with the experimental ones. It was revealed that the new peak and jump phenomena were caused by negative equivalent mass, negative equivalent stiffness of the granular medium and abrupt change in the additional stiffness cause by the jamming transition. This theoretical model is useful for studying the nonlinear dynamic characteristics of this coupled grain-beam system.

Corrigendum to “Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles” [Physica A 623 (2023) 128903

Corrigendum to “Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles” [Physica A 623 (2023) 128903

Slow and fast particles in shear-driven jamming: Critical behavior.

We do extensive simulations of a simple model of shear-driven jamming in two dimensions to determine and analyze the velocity distribution at different densities ϕ around the jamming density ϕ_{J} and at different low shear strain rates, γ[over ̇]. We then find that the velocity distribution is made up of two parts which are related to two different physical processes which we call the slow process and the fast process as they are dominated by the slower and the faster particles, respectively. Earlier scaling analyses have shown that the shear viscosity η, which diverges as the jamming density is approached from below, consists of two different terms, and we present strong evidence that these terms are related to the two different processes: the leading divergence is due to the fast process, whereas the correction-to-scaling term is due to the slow process. The analysis of the slow process is possible thanks to the observation that the velocity distribution for different γ[over ̇] and ϕ at and around the shear-driven jamming transition has a peak at low velocities and that the distribution has a constant shape up to and slightly above this peak. We then find that it is possible to express the contribution to the shear viscosity due to the slow process in terms of height and position of the peak in the velocity distribution and find that this contribution matches the correction-to-scaling term, determined through a standard critical scaling analysis. A further observation is that the collective particle motion is dominated by the slow process. In contrast to the usual picture in critical phenomena with a direct link between the diverging correlation length and a diverging order parameter, we find that correlations and shear viscosity decouple since they are controlled by different sets of particles and that shear-driven jamming is thus an unusual kind of critical phenomenon.

Single and two-cells shape analysis from energy functionals for three-dimensional vertex models.

Vertex models have been extensively used for simulating the evolution of multicellular systems, and have given rise to important global properties concerning their macroscopic rheology or jamming transitions. These models are based on the definition of an energy functional, which fully determines the cellular response and conclusions. While two-dimensional vertex models have been widely employed, three-dimensional models are far more scarce, mainly due to the large amount of configurations that they may adopt and the complex geometrical transitions they undergo. We here investigate the shape of single and two-cells configurations as a function of the energy terms, and we study the dependence of the final shape on the model parameters: namely the exponent of the term penalising cell-cell adhesion and surface contractility. In single cell analysis, we deduce analytically the radius and limit values of the contractility for linear and quadratic surface energy terms, in 2D and 3D. In two-cells systems, symmetrical and asymmetrical, we deduce the evolution of the aspect ratio and the relative radius. While in functionals with linear surface terms yield the same aspect ratio in 2D and 3D, the configurations when using quadratic surface terms are distinct. We relate our results with well-known solutions from capillarity theory, and verify our analytical findings with a three-dimensional vertex model.

Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles

As communication and perception technologies develop, connected vehicles (CVs) advance rapidly. In the process of popularization of CVs, it is bound to lead to the coexistence of CVs and human-driven vehicles (HDVs) on the road network for some time to come, and the previous study assumes that road vehicle is homogeneous, which could not quantify the difference between mixed vehicular flow, based on this, we consider the differences between CAVs and CVs in the way of information acquisition, a heterogeneous lattice hydrodynamics model mixing the HDVs and CVs are presented. Subsequently, by using the small perturbation method, we analyze the linear stability of the proposed model and derive the corresponding stability criteria; when the above stability norm does not hold, in order to investigate the nonlinear phenomenon, nonlinear stability analysis is performed and a modified Korteweg–de Vries equation (mKdV) corresponding to the proposed model is derived. By solving the mKdV equation, we obtain the kink - antikink solitary wave solution which can be used to explain how traffic jams form and propagate. At last, several numerical simulations were conducted to test the impact of the penetration rate of CVs and the bi-directional visual field for both forward-looking and backward-looking on the heterogeneous traffic flow stability, i.e., the first two are positive, while the last is negligible, this conclusion is consistent with the conclusion of theoretical derivation.

Numerical investigation of drag force on a spherical intruder by granular material

Insertions of large objects or intruders into granular material are common both in nature and in industrial applications. The intruder experiences resistance or granular drag force (analogy from fluid) during penetration into granular material due to the formation of inter-particle force chains. The main aim of this article is to study the drag force on an intruder during penetration in granular material and explain the underlying physics. For this study, numerical simulations are performed using the discrete element method (DEM). It is observed by studying various characteristics of granular material that particles undergo jamming transition below the intruder, and the region of jammed particles increases with the depth of intrusion, which is the main reason for the increase in the granular drag force with the depth of intrusion.

Dynamic Gardner cross-over in a simple glass.

The criticality of the jamming transition responsible for amorphous solidification has been theoretically linked to the marginal stability of a thermodynamic Gardner phase. While the critical exponents of jamming appear independent of the preparation history, the pertinence of Gardner physics far from equilibrium is an open question. To fill this gap, we numerically study the nonequilibrium dynamics of hard disks compressed toward the jamming transition using a broad variety of protocols. We show that dynamic signatures of Gardner physics can be disentangled from the aging relaxation dynamics. We thus define a generic dynamic Gardner cross-over regardless of the history. Our results show that the jamming transition is always accessed by exploring increasingly complex landscape, resulting in anomalous microscopic relaxation dynamics that remains to be understood theoretically.