Understanding the shear and intrusion rheological behavior of granular materials under reduced gravitational conditions is crucial for applications in planetary exploration and submarine earthquake engineering. To this end, it is important to understand whether gravity affects the drag forces on objects intruding granular media and, if so, quantify these effects. We have studied this issue experimentally in 1 g and 0 g conditions, the latter using the Beijing Drop Tower. Measuring the resistive forces on a cylinder moving at a constant speed through a granular bed, we find that gravity plays a significant role – the resistive forces increase significantly with cylinder speed in 0 g, while increasing much more slowly in 1 g. We use Coupled Eulerian-Lagrangian (CEL) simulations that support our results. We attribute this behavior to the increasingly dominant effect of pressure-sensitive frictional forces in microgravity with increasing fluidity in these conditions. Other than the significant implications for extraterrestrial exploration, our findings suggest that constitutive modeling of flow in microgravity should differ significantly from that in 1 g.

During quasistatic dynamics of granular systems, the stress and structure self-organize, but there is currently no quantitative measure or understanding of this phenomenon. Such an understanding is essential because local structural properties of the settled material are then correlated with the local stress, which calls into question existing linear theories of stress transmission in granular media. A method to quantify the local stress-structure correlations is necessary for addressing this issue and we present here such a method for planar systems. We then use it to analyze numerically several different systems, compressed quasistatically by two different procedures. We define cells, cell orders, cell orientations, and cell stresses and report the following results. (i) Cells orient along the local stress major principal axes. (ii) The mean ratio of cell principal stresses decreases with cell order and increases with friction. (iii) The ratio distributions collapse onto a single curve under a simple scaling, for all packing protocols and friction coefficients. (iv) A constructed model explains the correlations between the local cell and stress principal axis orientations. (v) The collapse of the stress ratios onto a Weibull distribution is modeled theoretically. Our results quantify the cooperative stress-structure self-organization and provide a way to relate quantitatively the stress-structure coupling to different process parameters and particle characteristics. Significantly, the strong stress-structure correlation, driven by structural reorganization upon application of external stress, suggests that current stress theories of granular matter need to be revisited.

The impact response of rubble-pile asteroids is essential for both elucidating their formation and evolution history and evaluating the efficacy of impact defense strategies. Although state-of-the-art numerical simulations have allowed for the replication of many macroscopic impact characteristics consistent with observations, the understanding of dynamics and response mechanisms within rubble-pile structures remains incomplete and requires further in-depth investigation. Such understanding is critical for assessing the effects and safety of impact defense missions. The loose structure of rubble-pile asteroids affects inhomogeneous internal stress propagation via inherent force chains, which may lead to structural fracturing. We demonstrate this phenomenon here, using a proof-of-principle two-dimensional model of granular aggregates. We find that the velocity response front to impact disturbances preferentially propagates along pre-existing force chains, with particles not in chains responding more slowly. The sites within the response zone where high dynamic stresses manifest are strongly correlated with these initial force chains, and the damages that result are predominantly located within areas enclosed by these chains. The strong correlation between pre-existing force chains and dynamic response is independent of the location, magnitude, direction of the disturbance velocity, or the aggregate's particle size distribution. All evidence suggests that the core reasons for this propagation preference lie in the structural heterogeneity of granular aggregates and the resulting differences in mechanical wave propagation. This investigation provides guidance for future research aimed at quantitatively assessing fragmentation risks based on the statistical properties of force chains.

Predicting theoretically the highest density, which a disordered packing of discs can achieve, has been a long-standing unresolved problem. Such predictions are hindered by two difficulties - the dependence of the density on the packing procedure and ensuring disorder. A theory that overcomes these difficulties has been developed recently for mono-disperse disc packing . However, to minimise order, experiments and numerical simulations often use two-size discs and a prediction of the highest possible packing fraction, ϕ_RCP, for these packings is arguably more useful. This problem is more complex because in such packings, ϕ_RCP is not a number but a function of the sizes ratio, D, and concentrations, p, of the disc types. A disorder-guaranteeing theory is formulated here to derive ϕ_RCP(p,D) under some assumptions, using the concept of the cell order distribution. Exact upper and lower bounds on the densest disordered packing fraction are also derived.

This study presents an analysis of granular cell, defined by the smallest loop of grains in contact, observed in 2D cohesive granular materials using Discrete Element simulations. The adopted particle interaction is the combination of non-contact DLVO force and linear contact repulsion. 9000 mono-sized disk particles were randomly generated in a double-periodic space with a very loose unjammed state, and then compressed isotropically to keep its uniformity by equilibrating the external isotropic compressive stress with agglomeration stress. The external stress was increased stepwise to reproduce the oedometer test in soil mechanics. Then we investigated the granular cell statistics for each loading step. What we found is the following: (1) Within the examined pressure range, the e − log p curve can be well approximated by a straight line, and the effect of interparticle friction appears to be negligible. However, the mean coordination number z shows a clear dependence on interparticle friction. (2) The distribution of cell volumes transitions from a power-law to an exponential form as the external load increases. This suggests that the larger cells are mechanically weaker and tend to collapse earlier. (3) The average cell shape becomes more circular with increasing external load, indicating that circular cells are more stable under compressive stress than elongated ones. Those results suggest that the granular cell approach is also applicable and effective for analysing cohesive granular systems.

The principle of detailed balance (DB) states that every kinetic transition in a system with many micro-states, µ , is balanced, on average, with the opposite transition, µ i (cid:11) µ j . Since its introduction by Boltzmann, this principle has been used by luminaries, such as Einstein, Eddington, Kramers, Pauli, Ehrenfest, Dirac, Onsager, and many others to derive significant results that underpin much of our scientific understanding. The current belief is that DB is satisfied only in equilibrium systems, while non-equilibrium steady states can only be balanced by cycles, such as A → B → C → A . We show here experimentally that DB can exist and is commonly and robustly satisfied in a family of quasi-statically cyclically sheared granular systems. We further study the approach to DB as a function of system size and time. Given the significant impact that this principle has had on equilibrium systems, we believe that this discovery paves the way for better models of the dynamics of non-equilibrium systems.

We argue that a suite of recent experimental and numerical observations are signatures of cooperative stress-structure self-organisation (SO) in granular dynamics. These observations include: a) detail-insensitive collapses of certain quantities; b) correlations between stress and structure and evidence of entropy-stability competition in settled packings, which cast doubt on most linear stress theories of granular materials; c) detailed balanced steady states, which seem contradictory to the common belief that only systems in thermal equilibrium satisfy detailed balance, but are not, as we explain. We then propose a new statistical mechanical formulation that takes into account the cooperative SO.

Recent studies of two-dimensional polydisperse disk systems have revealed a coordinated self-organization of cell stresses and shapes, with certain distributions collapsing onto a master form for many processes, size distributions, friction coefficients, and cell orders. Here we examine the effects of particle angularity on the indicators of self-organization, using simulations of bidisperse regular N polygons and varying N systematically. We find that the strong correlation between local cell stresses and orientations, as well as the collapses of the conditional distributions of scaled cell stress ratios to a master Weibull form for all cell orders k, is independent of angularity and friction coefficient. In contrast, increasing angularity makes the collapses of the conditional distributions sensitive to changes in the friction coefficient.

A basic problem in the science of realistic granular matter is the plethora of heuristic models of the stress field in the absence of a first-principles theory. Such a theory is formulated here, based on the idea that static granular assemblies can be regarded as two-phase composites. A thought experiment is described, demonstrating that the state of such materials can be varied continuously from marginal stability, via a two-phase granular assembly, then porous structure, and finally be made perfectly elastic. For completeness, I review briefly the condition for marginal stability in infinitely large assemblies. The general solution for the stress equations in d=2 is reviewed in detail and shown to be consistent with the two-phase idea. A method for identifying the phases of finite regions in larger systems is constructed, providing a stability parameter that quantifies the "proximity" to the marginally stable state. The difficulty involved in deriving stress fields in such composites is a unique constraint on the boundary between phases, and, to highlight it, a simple case of a stack of plates of alternating phase is solved explicitly. An effective medium approximation, which satisfies this constraint, is then developed and analyzed in detail. This approach forms a basis for the extension of the stress theory to general granular solids that are not marginally stable or at the yield threshold.

Introduction: Kinetic impact deflection is one of the strategies for addressing the threat of near-Earth small body impacts. The DART mission has confirmed the effectiveness of deflection and demonstrated the generation and morphological evolution of ejecta. However, what happens to the remaining asteroid shortly after the impact remains a blind spot for in-situ detection. The propagation of residual kinetic energy within the remaining rubble-pile asteroid, and the possible internal structural damage, are crucial for understanding the subsequent evolution of the remaining asteroid. Using a proof-of-principle numerical model, we simulated the response within rubble-pile asteroids to residual impacts and found that the propagation strongly depends on the inherent internal stress chains. Such chains occur in three- and two-dimensional aggregates and we mainly study this phenomenon in 2D.Methods: We first establish the 2D granular aggregate model and show the existence of initial stress chains based on the particle-scale stress tensor calculation1–3. Velocity perturbations are applied in the form of pulses to particles in strong stress chains or weak stress regions, and then we observe the propagation of particle speeds, normal and shear stresses, and contact failure events. The dependences of propagation patterns on the magnitude and direction of perturbation velocity, the location of perturbed particles, and the particle size distribution of aggregates are investigated. All the numerical simulations are employed using discrete element code DEMBody4–6.Results: In bi-disperse granular aggregates (Fig. 1a), we observed that particle speed response preferentially propagates along the initial (pre-impact) stress chains than in the direction of perturbation velocity (Fig. 1b). The dynamic normal and shear stresses propagate faster and are higher along the inherent stress chain structure (Fig.1c). According to the probability scatter map in Fig.1d, particles under high dynamic shear stress are highly likely to have initially high stress levels, which means that they belong to initial stress chain structures. The heterogeneity of the initial stress chain structure causes anisotropy in the propagation of impact responses, as demonstrated by the D (it characterizes the mean propagating distance of particle speed response) evolution in the 8 sectors around disturbed particle I (Fig. 2).Figure 1. (a) Initial stress distribution of the bi-disperse aggregate. Particles are colored by the trace of stress tensor Tr(σ0) and the negative sign means the compressed state. The redder the color, the larger the stress. Yellow circles and arrows denote the disturbed particles and directions of perturbation velocities respectively. (b) The particle speed (blue-red) at τ=6.6×10-4 superpose on the initial stress Tr(σ0) in grey. Particles with u≤0.01 are invisible. (c) The post-impact particle stress trace Tr(σ). (d) The bi-variate probability scatter map in the ε-ζ plane at τ=6.6×10-4. ε=Tr(σ0)-Tr(σ0)med and ζ=σ12-σ12med with (•)med denoting the median value. All the quantities are non-dimensional.Figure 2. (a) A zoom on Tr(σ0) around the location I, with the region divided into 8 sectors. (b) The evolution of D in the 8 sectors under impact perturbation b. All the quantities are presented in dimensionless form.We also noticed that sliding and rolling failure events frequently occur in weak stress particles that are in contact with particles in the initial stress chains (Fig. 3a and 3b). When the magnitude of the perturbation velocity is large, the preference for response propagation remains unchanged, but particles near the disturbed particle exhibit significant displacement, and the particles scattered by the impact (coordinate number = 0) are predominantly distributed in the cavities formed by the initial stress chain structure (Fig. 3c).Figure 3. Impact perturbation is applied on particle II along the direction d, as shown in Fig. 1a. (a) Particles that undergo sliding failure (yellow) superpose on the initial stress chains. uimpact=1.0, τ=6.6×10-3. (b) Particles that undergo rolling failure (green). The same condition and moment as panel (a). (c) Particles with coordinate number = 0 (red). uimpact=100.0, τ=6.6×10-3.Impact perturbation simulations conducted in bi-disperse aggregates with surface boulders and power-law-distribution aggregates exhibit the same response propagation patterns. All the quantities are presented in dimensionless form.Conclusion and Discussion: To conclude, the response to impact perturbations propagates preferentially along the initial stress chains, which bear the majority of the load induced by the residual impact kinetic energy. It suggests the impact disturbance may travel further than expected along these invisible paths, rather than dissipated uniformly in all directions from the impact crater. Particles in the weak stress regions enclosed by the initial stress chains are more easily scattered by impacts. Downstream of this work, we will focus on the extent and patterns of structural damage in the remaining rubble-pile asteroids and their dependency on impact perturbations.Acknowledgments: C.H. is grateful for the hospitality of Imperial College London, where this work was carried out. C.H. is supported by the international joint doctoral education fund of Beihang University. Y.Y. acknowledges the financial support provided by the National Natural Science Foundation of China Grants No. 12272018.Reference:1. Ball, R. C. & Blumenfeld, R. Stress Field in Granular Systems: Loop Forces and Potential Formulation. Phys. Rev. Lett. 88, 115505 (2002).2. Blumenfeld, R. Stresses in Isostatic Granular Systems and Emergence of Force Chains. Phys. Rev. Lett. 93, 108301 (2004).3. Nicot, F., Hadda, N., Guessasma, M., Fortin, J. & Millet, O. On the definition of the stress tensor in granular media. Int. J. Solids Struct. 50, 2508–2517 (2013).4. Cheng, B., Yu, Y. & Baoyin, H. Collision-based understanding of the force law in granular impact dynamics. Phys. Rev. E 98, 012901 (2018).5. Cheng, B., Yu, Y. & Baoyin, H. Numerical simulations of the controlled motion of a hopping asteroid lander on the regolith surface. Mon. Not. R. Astron. Soc. 485, 3088–3096 (2019).6. Cheng, B. et al. Reconstructing the formation history of top-shaped asteroids from the surface boulder distribution. Nat. Astron. 5, 134–138 (2021).

Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to self-organisation of the neighbour probability distribution. The emergence of detailed balance in non-equilibrium granular dynamics could constitute a major step toward better models of granular media, as well as provide more insight into non-equilibrium processes in general. We show analytically that DBSS emerges when a certain neighbour probability is uniform across the system. This condition leads to a conditional cell order distribution being independent of the condition. We then carry out rotational shear experiments, in which this condition is satisfied, and show that they give rise to robust detailed-balanced steady states. We also show that, when the unconditional cell order distribution maximises the entropy, it is determined by a single constant parameter that is characteristic of all cell transitions. These results illustrate the predictive power of recently proposed evolution equations, which pave the way to simpler models of the dynamics of planar granular systems.

Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse analytically and numerically the steady states of this theory in systems of arbitrary density and report the following. (1) We discover that all such dynamics almost certainly possess only one physical steady state, which may or may not satisfy detailed balance. (2) We show rigorously that, if a detailed balance solution is possible then it is unique. The above two results correct an erroneous conjecture in the literature. (3) We show rigorously that the detailed-balance solutions in very dense systems are globally stable, extending the local stability found for these solutions in the literature. (4) In view of recent experimental observations of robust detailed balance steady states in very dilute cyclically sheared systems, our results point to a self-organisation of process rates in dynamic granular systems.

We investigate the effect of a bevelled (or slanted) outlet on the discharge rate of mono-sized spheres from a quasi-two-dimensional silo, using the discrete element method. In contrast to hopper discharges, where the bevelling is across the entire base of the container, we study a bevelled opening that is significantly smaller than the silo width and in which the slanting is limited to half a sphere diameter at the boundary of the outlet. We show that the bevelling increases the flow rate comparably to the inclination in hopper walls. Using Beverloo's model, we relate this increase in rate to what we define as the 'effective opening' of the silo and analyse the velocity profiles associated with the discharges. We show that different openings, having effectively the same discharge rates, give rise to distinctly different internal dynamics in the silo. These results have the potential to aid industrial processes by fine-tuning and improving control of silo discharges, with a minimal impact on silo design, thus significantly reducing production and handling costs.

The method, proposed in \cite{Za22} to derive the densest packing fraction of random disc and sphere packings, is shown to yield in two dimensions too high a value that (i) violates the very assumption underlying the method and (ii) corresponds to a high degree of structural order. The claim that the obtained value is supported by a specific simulation is shown to be unfounded. One source of the error is pointed out.

Phase transitions are common in inanimate systems and have been studied extensively in natural sciences. Less explored are the rich transitions that take place at the micro- and nano-scales in biological systems. In conventional phase transitions, large-scale properties of the media change discontinuously in response to continuous changes in external conditions. Such changes play a significant role in the dynamic behaviours of organisms. In this review, we focus on some transitions in both free-living and biofilms of bacteria. Particular attention is paid to the transitions in the flagellar motors and filaments of free-living bacteria, in cellular gene expression during the biofilm growth, in the biofilm morphology transitions during biofilm expansion, and in the cell motion pattern transitions during the biofilm formation. We analyse the dynamic characteristics and biophysical mechanisms of these phase transition phenomena and point out the parallels between these transitions and conventional phase transitions. We also discuss the applications of some theoretical and numerical methods, established for conventional phase transitions in inanimate systems, in bacterial biofilms.

In development, lineage segregation is coordinated in time and space. An important example is the mammalian inner cell mass, in which the primitive endoderm (PrE, founder of the yolk sac) physically segregates from the epiblast (EPI, founder of the fetus). While the molecular requirements have been well studied, the physical mechanisms determining spatial segregation between EPI and PrE remain elusive. Here, we investigate the mechanical basis of EPI and PrE sorting. We find that rather than the differences in static cell surface mechanical parameters as in classical sorting models, it is the differences in surface fluctuations that robustly ensure physical lineage sorting. These differential surface fluctuations systematically correlate with differential cellular fluidity, which we propose together constitute a non-equilibrium sorting mechanism for EPI and PrE lineages. By combining experiments and modeling, we identify cell surface dynamics as a key factor orchestrating the correct spatial segregation of the founder embryonic lineages.

It is accepted that stress and structure self-organize cooperatively during quasi-static dynamics of granular systems, but the consequences of this self-organization are not fully understood. Such an understanding is essential because local structural properties of the settled material are then correlated with the local stress, which calls into question existing linear theories of stress transmission in granular media. A method to quantify the local stress-structure correlations is necessary for addressing this issue and we present here such a method for planar systems. We then use it to analyze numerically several different systems, compressed quasi-statically by two different procedures. We define cells, cell orders, cell orientations, and cell stresses and report the following. 1. The mean ratio of cell principal stresses decreases with cell order and increases with friction. 2. The ratio distributions collapse onto a single curve under a simple scaling, for all packing protocols and friction coefficients. 3. Cells orient along the local stress major principal axes. 4. A simple first-principles model explains the correlations between the local cell and stress principal axis orientations. Our results quantify the cooperative stress-structure self-organization and provide a way to relate quantitatively the stress-structure coupling to different process parameters and particle characteristics. Significantly, the strong stress-structure correlation, driven by structural re-organization upon application of external stress, suggests that current stress theories of granular matter need to be revisited.

Gravitational-collapse-based explanations of the cosmic web lead to problems in estimating the total mass in the universe. A first-principles several-scales model is developed here for the structural organisation of cosmic matter in a flat universe, showing that the web formation could be driven by inelastic collisions before gravity took hold, suggesting a possible way to resolve these problems. The following results are derived. (i) The diffusion rate in the particulate gas after recombination is sub-anomalous, with a rapid decay of particle velocities. (ii) The evolution of the particle velocity distribution is calculated explicitly. (iii) The gas density is shown to be unstable, leading to void formation and clusters nucleation. (iv) Rounded clusters are shown to be unstable and tend to elongate. (v) An equation is derived for the growth of long clusters into filaments and solved explicitly. The fast-growing clusters deplete the regions around them and generate large voids, potentially giving rise to the cosmic web before gravity dominated.

There is no agreement in the literature on the rate of diffusion of a particle in a cooling granular gas. Predictions and model assumptions range from the conventional to very exotic dependence of the mean square distance (MSD) on time. This problem is addressed here by calculating the MSD from first-principles. The calculation is based on random-walking and it circumvents the common use of continuum equations and equations of states, which involve approximations that erode at low gas particle densities. The MSD is found to increase logarithmically with time – slower than even in anomalous diffusion. This result is consistent with the well-established Haff's law for the decay of the kinetic energy, which is also derived along the way from the same first principles. This derivation also pins down Haff's time constant, alleviating the usual need for a fitting parameter. The diffusion theory is then used to calculate explicitly the time evolution of any initial particle velocity distribution, yielding an unusual functional form. The limitations of the theory are discussed and extensions to it are outlined.

Many reptiles, known as `sand swimmers’, adapt to their specific environments by vibrating or rotating their body. To understand these type of interactions of active objects with granular media, we study a simplified model of a self-excited spherical object (SO) immersed in the granular bed, using three-dimensional discrete element method (DEM) simulations. Modelling the vibration by an oscillatory motion, we simulate the longitudinal locomotion of the SO in three modes: transverse vibration, rotation around different axes, and a combination of both. We find that the mode of oscillation in y direction coupled with rotation around x-axis is optimal in the sense that the SO rises fastest, with periodic oscillations, in the z direction while remaining stable at the initial x position. We analyze the physical mechanisms governing the meandering up or down and show that the large oscillations are caused by an asynchronous changes between the directions of oscillation and rotation. We also observed that the SO’s rising rate is sensitive to three parameters: the oscillation amplitude, the oscillation frequency, f, and the rotation angular velocity, Ω. We report the following results. 1. When the frequencies of the rotation and transverse motion are synchronised, SO rises when Ω<0 and sinks when Ω>0; the average rising/sinking rate is proportional to |Ω|. 2. The rising rate increases linearly with the oscillation amplitude. 3. There exists a critical oscillation frequency, above and below which the rising mechanisms are different. Our study reveals the range of parameters that idealized `swimmers’ need to use to optimize performance in granular environments.