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We characterize a system of hard spheres with a simple collision rule that breaks time-reversal symmetry but conserves energy. The collisions lead to an achiral, isotropic, and homogeneous stationary state whose properties are determined in simulations and compared to an approximate theory originally developed for elastic hard spheres. In the nonequilibrium fluid state, velocities are correlated, a phenomenon known from other nonequilibrium stationary states. The correlations are long-ranged decaying like 1/r^{D} in D dimensions. Such correlations are expected on general grounds far from equilibrium and had previously been observed in driven or nonstationary systems.

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It has recently been reported that bacteria, such as Escherichia coli Bhattacharjee and Datta, Nat. Commun. 10, 2075 (2019).NCAOBW2041-172310.1038/s41467-019-10115-1 and Pseudomonas putida Alirezaeizanjani et al., Sci. Adv. 6, eaaz6153 (2020).SACDAF2375-254810.1126/sciadv.aaz6153, perform distinct modes of motion when placed in porous media as compared to dilute regions or free space. This has led us to suggest an efficient strategy for active particles in a disordered environment: reorientations are suppressed in locally dilute regions and intensified in locally dense ones. Thereby the local geometry determines the optimal path of the active agent and substantially accelerates the dynamics for up to 2 orders of magnitude. We observe a nonmonotonic behavior of the diffusion coefficient in dependence on the tumbling rate and identify a localization transition, either by increasing the density of obstacles or by decreasing the reorientation rate.

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We analyze the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a range of stress and strain rates where no stationary flow can exist. Whereas small systems were shown previously to exhibit hysteretic jumps between the low and high stress branches, large systems exhibit continuous shear thickening arising from averaging unsteady, spatially heterogeneous flows. The observed large scale patterns as well as their dynamics are found to depend on strain rate: At the lower end of the unstable region, force chains merge to form giant bands that span the system in the compressional direction and propagate in the dilational direction. At the upper end, we observe large scale clusters which extend along the dilational direction and propagate along the compressional direction. Both patterns, bands and clusters, come in with infinite correlation length similar to the sudden onset of system-spanning plugs in impact experiments.

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The motion of active polymers in a two-dimensional porous medium is shown to depend critically on flexibility, activity, and degree of polymerization. For a given Péclet number, we observe a transition from localization to diffusion as the stiffness of the chains is increased. Whereas stiff chains move almost unhindered through the porous medium, flexible ones spiral and get stuck. Their motion can be accounted for by the model of a continuous time random walk with a renewal process corresponding to unspiraling. The waiting time distribution is shown to develop heavy tails for decreasing stiffness, resulting in subdiffusive and ultimately caged behavior.

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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 σ to the shear rate γ[over ˙] and predictions of the yield stress complete our discussion of granular rheology derived from first principles.

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We develop a generalized hydrodynamic theory, which can account for the build-up of long-ranged and long-lived shear stress correlations in supercooled liquids as the glass transition is approached. Our theory is based on the decomposition of tensorial stress relaxation into fast microscopic processes and slow dynamics due to conservation laws. In the fluid, anisotropic shear stress correlations arise from the tensorial nature of stress. By approximating the fast microscopic processes by a single relaxation time in the spirit of Maxwell, we find viscoelastic precursors of the Eshelby-type correlations familiar in an elastic medium. The spatial extent of shear stress fluctuations is characterized by a correlation length ξ which grows like the viscosity η or time scale τ ∼ η, whose divergence signals the glass transition. In the solid, the correlation length is infinite and stress correlations decay algebraically as r-d in d dimensions.

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We suggest a simple model for reversible cross-links, binding, and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the time scale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest time scale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau value, which for irreversible cross-linkers extends all the way to the static limit. This additional relaxation mechanism can be controlled by the relative weight of reversible and irreversible linkers.

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A theory for the nonlocal 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 τ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length ξ∝τ 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 us to connect to fluidity and elastoplastic models.

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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 ∼1/f^{3/2} to the well-known ∼1/sqrt[f]-dependence of the end-to-end extension.

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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, Nc, and their radius of gyration, RG. We show that , providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, df, that is observed to increase with packing fraction ϕ. The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ→ϕc. Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S4(q,t) and the dynamical susceptibility χ4(t). S4(q,t) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ϕ≤ 0.805, and to become increasingly long-ranged as ϕ→ϕc. Finite size scaling of χ4(t) provides a consistency check for the previously analyzed divergences of χ4(t) ∝ (ϕ-ϕc)(-γχ) and the correlation length ξ∝ (ϕ-ϕc)(-γξ). We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ→ϕc suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.

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A two-dimensional dense fluid of frictional grains is shown to exhibit time-chaotic, spatially heterogeneous flow in a range of stress values, σ, 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 σ. In between, no steady flow state can be reached, instead the system either jams or displays time-dependent heterogeneous strain rates γ(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.

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The actin and microtubule networks form the dynamic cytoskeleton. Network dynamics is driven by molecular motors applying force onto the networks and the interactions between the networks. Here we assay the dynamics of centrosomes in the scale of seconds as a proxy for the movement of microtubule asters. With this assay we want to detect the role of specific motors and of network interaction. During interphase of syncytial embryos of Drosophila, cortical actin and the microtubule network depend on each other. Centrosomes induce cortical actin to form caps, whereas F-actin anchors microtubules to the cortex. In addition, lateral interactions between microtubule asters are assumed to be important for regular spatial organization of the syncytial embryo. The functional interaction between the microtubule asters and cortical actin has been largely analyzed in a static manner, so far. We recorded the movement of centrosomes at 1 Hz and analyzed their fluctuations for two processes­pair separation and individual movement. We found that F-actin is required for directional movements during initial centrosome pair separation, because separation proceeds in a diffusive manner in latrunculin-injected embryos. For assaying individual movement, we established a fluctuation parameter as the deviation from temporally and spatially slowly varying drift movements. By analysis of mutant and drug-injected embryos, we found that the fluctuations were suppressed by both cortical actin and microtubules. Surprisingly, the microtubule motor Kinesin-1 also suppressed fluctuations to a similar degree as F-actin. Kinesin-1 may mediate linkage of the microtubule (+)-ends to the actin cortex. Consistent with this model is our finding that Kinesin-1-GFP accumulates at the cortical actin caps.

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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.

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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 localisation of polymers forming a system-spanning cluster, is driven by increasing the number parameter µ 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 χ 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 µ and χ. 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.

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We propose a phase diagram for the shear flow of dry granular particles in two dimensions based on simulations and a phenomenological Landau theory for a nonequilibrium first-order phase transition. Our approach incorporates both frictional as well as frictionless particles. The most important feature of the frictional phase diagram is reentrant flow and a critical jamming point at finite stress. In the frictionless limit the regime of reentrance vanishes and the jamming transition is continuous with a critical point at zero stress. The jamming phase diagrams derived from the model agree with the experiments of Bi et al. [Nature (London) 480, 355 (2011)] and brings together previously conflicting numerical results.

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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 (ϵ=1) and inelastic (ϵ<1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6≤ϕ≤0.805, scaling is shown to hold: S(4)(q,t)/χ(4)(t)=s(qξ(t)). Both the dynamic susceptibility χ(4)(τ(α)) and the dynamic correlation length ξ(τ(α)) evaluated at the α relaxation time τ(α) can be fitted to a power law divergence at a critical packing fraction. The measured ξ(τ(α)) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ(4)(τ(α))≈ξ(d-p)(τ(α)), with an exponent d-p≈1.6. This scaling is remarkably independent of ϵ, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on ϵ.

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When pulling a particle in a driven granular fluid with constant force Fex, the probe particle approaches a steady-state average velocity v. This velocity and the corresponding friction coefficient of the probe ζ=Fex/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., Granul. Matter 14, 247 (2012)] is explained by a simple kinetic theory.

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We investigate the long time dynamics of a strong glass former, SiO(2), below the glass transition temperature by averaging single-particle trajectories over time windows which comprise roughly 100 particle oscillations. The structure on this coarse-grained time scale is very well defined in terms of coordination numbers, allowing us to identify ill-coordinated atoms, which are called defects in the following. The most numerous defects are O-O neighbors, whose lifetimes are comparable to the equilibration time at low temperature. On the other hand, SiO and OSi defects are very rare and short lived. The lifetime of defects is found to be strongly temperature dependent, consistent with activated processes. Single-particle jumps give rise to local structural rearrangements. We show that in SiO(2) these structural rearrangements are coupled to the creation or annihilation of defects, giving rise to very strong correlations of jumping atoms and defects.

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We explore the effect of an attractive interaction between parallel-aligned polymers which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with line tension ε and weakly bending chains with bending stiffness κ.

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Aiming at the mechanical properties of cross-linked biopolymers, we set up and analyze a model of two weakly bending wormlike chains subjected to a tensile force, with regularly spaced inter-chain bonds (cross-links) represented by harmonic springs. Within this model, we compute the force-extension curve and the differential stiffness exactly and discuss several limiting cases. Cross-links effectively stiffen the chain pair by reducing thermal fluctuations transverse to the force and alignment direction. The extra alignment due to cross-links increases both with growing number and with growing strength of the cross-links, and is most prominent for small force f. For large f, the additional, cross-link-induced extension is subdominant except for the case of linking the chains rigidly and continuously along their contour. In this combined limit, we recover asymptotically the elasticity of a weakly bending wormlike chain without constraints, stiffened by a factor of 4. The increase in differential stiffness can be as large as 100% for small f or large numbers of cross-links.

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