Search

A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, $N_c$, and their radius of gyration, $R_G$. We show that $N_c\propto R_G^{d_f}$, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, $d_f$, that is observed to increase with packing fraction $\phi$. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., $\phi\to\phi_c$. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor $S_4(q,t)$ and the dynamical susceptibility $\chi_4(t)$. $S_4(q,t)$ is shown to obey scaling in the full range of packing fractions, $0.6\leq\phi\leq 0.805$, and to become increasingly long-ranged as $\phi\to\phi_c$. Finite size scaling of $\chi_4(t)$ provides a consistency check for the previously analyzed divergences of $\chi_4(t)\propto (\phi-\phi_c)^{-\gamma_{\chi}}$ and the correlation length $\xi\propto (\phi-\phi_c)^{-\gamma_{\xi}}$. We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for $\phi\to\phi_c$ suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution., Comment: 14 pages, 25 figures

Considering a granular fluid of inelastic smooth hard spheres we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress $\sigma$ to the shear rate $\dot\gamma$, and predictions of the yield stress complete our discussion of granular rheology derived from first principles., Comment: 7 pages, minor fixes and extended appendix

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (\textsc{itt}) formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory---based on the physical picture, that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signalled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $\varepsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity., Comment: 37 pages, 7 figures

A theory for the non-local shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time $\tau$ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length $\xi\propto\tau$ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow to connect to fluidity and elasto-plastic models., Comment: 5 pages plus 1 page SI

Density-wave fronts in a vibrofluidized wet granular layer undergoing a gas-liquid-like transition are investigated experimentally. The threshold of the instability is governed by the amplitude of the vertical vibrations. Fronts, which are curved into a spiral shape, propagate coherently along the circular rim of the container with leading edges. They are stable beyond a critical distance from the container center. Based on an analysis of the emerging time and length scales, we propose a model for the pattern formation by considering the competition between the time scale for the condensation of wet granular particles from a gas-like state and that of the energy injection resisting this process., Comment: 11 pages, 5 figures

We study the self-propulsion of spherical droplets as simplified hydrodynamic models of swimming microorganisms or artificial microswimmers. In contrast to approaches, which start from active velocity fields produced by the system, we consider active surface force or body force densities or active stresses as the origin of autonomous swimming. For negligible Reynolds number and given activity we first calculate the external and the internal ow fields as well as the center of mass velocity and an angular velocity of the droplet at fixed time. To construct trajectories from single time snapshots, the evolution of active forces or stresses must be determined in the laboratory frame. Here, we consider the case of active matter, which is carried by a continuously distributed, rigid but sparse (cyto)-sceleton that is immersed in the droplet's interior. We calculate examples of trajectories of a droplet and its sceleton from force densities or stresses, which may be explicitely time dependent in a frame fixed within the sceleton

We develop a microscopic picture of shear thickening in dense suspensions which emphasizes the role of frictional forces, coupling rotational and translational degrees of freedom. Simulations with contact forces and viscous drag only, reveal pronounced shear thickening with a simultaneous increase in contact number and energy dissipation by frictional forces. At high densities, when the translational motion is severely constrained, we observe liquid-like gear-states with pronounced relative rotations of the particles coexisting with solid-like regions which rotate as a whole. The latter are stabilised by frustrated loops which become more numerous and persistent with increasing pressure, giving rise to an increasing lengthscale of this mosaique-like structure and a corresponding increase in viscosity., Comment: 7 pages, 12 figures, accepted in EPL

We analyze the stretching elasticity of a wormlike chain with a tension discontinuity resulting from a Hookean spring connecting its backbone to a fixed point. The elasticity of isolated semiflexible filaments has been the subject in a significant body of literature, primarily because of its relevance to the mechanics of biological matter. In real systems, however, these filaments are usually part of supramolecular structures involving cross-linkers or molecular motors which cause tension discontinuities. Our model is intended as a minimal structural element incorporating such a discontinuity. We obtain analytical results in the weakly bending limit of the filament, concerning its force-extension relation and the response of the two parts in which the filament is divided by the spring. For a small tension discontinuity, the linear response of the filament extension to this discontinuity strongly depends on the external tension. For large external tension $f$, the spring force contributes a subdominant correction $\sim 1/f^{3/2}$ to the well known $\sim 1/\sqrt{f}$ dependence of the end-to-end extension.

A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, $\sigma$, chosen in the unstable region of s-shaped flow curves. Stress controlled simulations reveal a phase diagram with reentrant stationary flow for small and large stress $\sigma$. In between no steady flow state can be reached, instead the system either jams or displays time dependent heterogeneous strain rates $\dot\gamma({\bf r},t)$. The results of simulations are in agreement with the stability analysis of a simple hydrodynamic model, coupling stress and microstructure which we tentatively associate with the frictional contact network.

Cells moving on a two dimensional substrate generate motion by polymerizing actin filament networks inside a flat membrane protrusion. New filaments are generated by branching off existing ones, giving rise to branched network structures. We investigate the force-extension relation of branched filaments, grafted on an elastic structure at one end and pushing with the free ends against the leading edge cell membrane. Single filaments are modeled as worm-like chains, whose thermal bending fluctuations are restricted by the leading edge cell membrane, resulting in an effective force. Branching can increase the stiffness considerably; however the effect depends on branch point position and filament orientation, being most pronounced for intermediate tilt angles and intermediate branch point positions. We describe filament networks without cross-linkers to focus on the effect of branching. We use randomly positioned branch points, as generated in the process of treadmilling, and orientation distributions as measured in lamellipodia. These networks reproduce both the weak and strong force response of lamellipodia as measured in force-velocity experiments. We compare properties of branched and unbranched networks. The ratio of the network average of the force per branched filament to the average force per unbranched filament depends on the orientation distribution of the filaments. The ratio exhibits compression dependence and may go up to about 4.5 in networks with a narrow orientation distribution. With orientation distributions measured in lamellipodia, it is about two and essentially independent from network compression, graft elasticity and filament persistence length.

We study analytically the intricate phase behavior of cross-linked $AB$ diblock copolymer melts, which can undergo two main phase transitions due to quenched random constraints: Gelation, i.e., spatially random localization of polymers forming a system-spanning cluster, is driven by increasing the number parameter $\mu$ of irreversible, type-selective cross-links between random pairs of $A$ blocks. Self-assembly into a periodic pattern of $A$/$B$-rich microdomains (microphase separation) is controlled by the $AB$ incompatibility $\chi$ inversely proportional to temperature. Our model aims to capture the system's essential microscopic features, including an ensemble of random networks that reflects spatial correlations at the instant of cross-linking. We identify suitable order parameters and derive a free-energy functional in the spirit of Landau theory that allows us to trace a phase diagram in the plane of $\mu$ and $\chi$. Selective cross-links promote microphase separation at higher critical temperatures than in uncross-linked diblock copolymer melts. Microphase separation in the liquid state facilitates gelation, giving rise to a novel gel state whose chemical composition density mirrors the periodic $AB$ pattern., Comment: 10 pages, 4 figures

We investigate theoretically the effect of polymer tension on the collective behavior of reversibly binding cross-links. For this purpose, we employ a model of two weakly bending wormlike chains aligned in parallel by a tensile force, with a sequence of inter-chain binding sites regularly spaced along the contours. Reversible cross-links attach and detach at the sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy of the system and find the emergence of a free-energy barrier which controls the reversible (un)binding. The tension affects the conformational entropy of the chains which competes with the binding energy of the cross-links. This competition gives rise to a sudden increase in the fraction of bound sites as the tension increases. We show that this transition is related to the cross-over between weak and strong localization of a directed polymer in a pinning potential. The cross-over to the strongly bound state can be interpreted as a mechanism for force-stiffening of cross-linked polymers -- beyond the elasticity of a single wormlike chain., Comment: 7 pages, 7 figures; accepted for publication in New J. Phys

We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate $N=\mathcal{O}(10^6)$ particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after a sudden change in flow rate giving rise to a change in stationary packing fraction and determine the timescale to reach a stationary state.

When pulling a particle in a driven granular fluid with constant force $F_{ex}$, the probe particle approaches a steady-state average velocity $v$. This velocity and the corresponding friction coefficient of the probe $\zeta=F_{ex}/v$ are obtained within a schematic model of mode-coupling theory and compared to results from event-driven simulations. For small and moderate drag forces, the model describes the simulation results successfully for both the linear as well as the nonlinear region: The linear response regime (constant friction) for small drag forces is followed by shear thinning (decreasing friction) for moderate forces. For large forces, the model demonstrates a subsequent increasing friction in qualitative agreement with the data. The square-root increase of the friction with force found in [Fiege et al., Granular Matter $\boldsymbol{14}$, 247 (2012)] is explained by a simple kinetic theory., Comment: 5 pages, 4 figures

Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\varepsilon=1$) as well as inelastic ($\varepsilon < 1$) collisions, are studied. As the fluid approaches structural arrest, i.e. for packing fractions in the range $0.6 \le \phi \le 0.805$, scaling is shown to hold: $S_4(q,t)/\chi_4(t)=s(q\xi(t))$. Both the dynamic susceptibility, $\chi_4(\tau_{\alpha})$, as well as the dynamic correlation length, $\xi(\tau_{\alpha})$, evaluated at the $\alpha$ relaxation time, $\tau_{\alpha}$, can be fitted to a power law divergence at a critical packing fraction. The measured $\xi(\tau_{\alpha})$ widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, $\chi_4(\tau_{\alpha}) \approx\xi^{d-p}(\tau_{\alpha})$, with an exponent $d-p\approx 1.6$. This scaling is remarkably independent of $\varepsilon$, even though the strength of the dynamical heterogeneity increases dramatically as $\varepsilon$ grows., Comment: 5 pages, 6 figures