Modeling the Transition between Localized and Extended Deposition in Flow Networks through Packings of Glass Beads.

We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal particles in pressure-driven systems of packed beads have shown that at lower pressure drop, particles deposit locally at the inlet, while at higher pressure drop, they deposit uniformly along the direction of flow. We develop a mathematical model and use agent-based simulations to capture these essential qualitative features observed in experiments.

Stress-stress correlations reveal force chains in gels.

We investigate the spatial correlations of microscopic stresses in soft particulate gels using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space.

Tensor electromagnetism and emergent elasticity in jammed solids.

The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how nonperiodic networks-apparently indistinguishable from a snapshot of a fluid-sustain shear. We present a stress-only theory of emergent elasticity for a nonthermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent U(1) tensor electromagnetism, which then accounts for the mechanical response of such solids.

Dilatancy, shear jamming, and a generalized jamming phase diagram of frictionless sphere packings.

Granular packings display the remarkable phenomenon of dilatancy, wherein their volume increases upon shear deformation. Conventional wisdom and previous results suggest that dilatancy, also being the related phenomenon of shear-induced jamming, requires frictional interactions. Here, we show that the occurrence of isotropic jamming densities φ above the minimal density (or the J-point density) φ leads both to the emergence of shear-induced jamming and dilatancy in frictionless packings.

Emergent Elasticity in Amorphous Solids.

The mechanical response of naturally abundant amorphous solids such as gels, jammed grains, and biological tissues are not described by the conventional paradigm of broken symmetry that defines crystalline elasticity. In contrast, the response of such athermal solids are governed by local conditions of mechanical equilibrium, i.e.

Athermal Fluctuations in Disordered Crystals.

We analyze the fluctuations in particle positions and interparticle forces in disordered crystals composed of jammed soft particles in the limit of weak disorder. We demonstrate that such athermal systems are fundamentally different from their thermal counterparts, characterized by constrained fluctuations of forces perpendicular to the lattice directions. We develop a disorder perturbation expansion in polydispersity about the crystalline state, which we use to derive exact results to linear order.

Motion of active tracer in a lattice gas with cross-shaped particles.

We analyze the dynamics of an active tracer particle embedded in a thermal lattice gas. All particles are subject to exclusion up to third nearest neighbors on the square lattice, which leads to slow dynamics at high densities. For the case with no rotational diffusion of the tracer, we derive an analytical expression for the resulting drift velocity v of the tracer in terms of non-equilibrium density correlations involving the tracer particle and its neighbors, which we verify using numerical simulations.

Stress fluctuations in transient active networks.

Inspired by experiments on dynamic extensile gels of biofilaments and motors, we propose a model of a network of linear springs with kinetics consisting of growth at a prescribed rate, death after a lifetime drawn from a distribution, and birth at a randomly chosen node. The model captures features such as the build-up of self-stress, that are not easily incorporated into hydrodynamic theories. We study the model numerically and show that our observations can largely be understood through a stochastic effective-medium model.

Microscopic Origin of Frictional Rheology in Dense Suspensions: Correlations in Force Space.

We develop a statistical framework for the rheology of dense, non-Brownian suspensions, based on correlations in a space representing forces, which is dual to position space. Working with the ensemble of steady state configurations obtained from simulations of suspensions in two dimensions, we find that the anisotropy of the pair correlation function in force space changes with confining shear stress (σ_{xy}) and packing fraction (ϕ). Using these microscopic correlations, we build a statistical theory for the macroscopic friction coefficient: the anisotropy of the stress tensor, μ=σ_{xy}/P.

The physics of jamming for granular materials: a review.

Granular materials consist of macroscopic grains, interacting via contact forces, and unaffected by thermal fluctuations. They are one of a class systems that undergo jamming, i.e.

Ergodicity breaking dynamics of arch collapse.

Flows in hoppers and silos are susceptible to clogging due to the formation of arches at the exit. The failure of these arches is the key to reinitiation of flow, yet the physical mechanism of failure is not well understood. Experiments on vibrated hoppers exhibit a broad distribution of the duration of clogs.

Theory of microphase separation in bidisperse chiral membranes.

We present a Ginzburg-Landau theory of microphase separation in a bidisperse chiral membrane consisting of rods of opposite handedness. This model system undergoes a phase transition from an equilibrium state where the two components are completely phase separated to a state composed of microdomains of a finite size comparable to the twist penetration depth. Characterizing the phenomenology using linear stability analysis and numerical studies, we trace the origin of the discontinuous change in microdomain size that occurs during this phase transition to a competition between the cost of creating an interface and the gain in twist energy for small microdomains in which the twist penetrates deep into the center of the domain.

Gaps between avalanches in one-dimensional random-field Ising models.

We analyze the statistics of gaps (ΔH) between successive avalanches in one-dimensional random-field Ising models (RFIMs) in an external field H at zero temperature. In the first part of the paper we study the nearest-neighbor ferromagnetic RFIM. We map the sequence of avalanches in this system to a nonhomogeneous Poisson process with an H-dependent rate ρ(H).

Scaling Theory for the Frictionless Unjamming Transition.

We develop a scaling theory of the unjamming transition of soft frictionless disks in two dimensions by defining local areas, which can be uniquely assigned to each contact. These serve to define local order parameters, whose distribution exhibits divergences as the unjamming transition is approached. We derive scaling forms for these divergences from a mean-field approach that treats the local areas as noninteracting entities, and demonstrate that these results agree remarkably well with numerical simulations.

Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space.

Solids are distinguished from fluids by their ability to resist shear. In equilibrium systems, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern that is persistent, which in turn results from minimizing the free energy. In this work, we focus on a class of systems where this paradigm is challenged.

Protocol dependence of the jamming transition.

We propose a theoretical framework for predicting the protocol dependence of the jamming transition for frictionless spherical particles that interact via repulsive contact forces. We study isostatic jammed disk packings obtained via two protocols: isotropic compression and simple shear. We show that for frictionless systems, all jammed packings can be obtained via either protocol.

Synchronization patterns in geometrically frustrated rings of relaxation oscillators.

Diffusively coupled chemical oscillators can exhibit a wide variety of complex spatial patterns. In this paper, we show that a ring of relaxation oscillators diffusively coupled through the inhibitory species leads to remarkable spatiotemporal patterns in the regime where there is a large separation of time scales between the activator and the inhibitor dynamics. The origin of these complex patterns can be traced back to a preponderance of antiphase synchronized states in the space of attractors.

Shear-induced rigidity in athermal materials: A unified statistical framework.

Recent studies of athermal systems such as dry grains and dense, non-Brownian suspensions have shown that shear can lead to solidification through the process of shear jamming in grains and discontinuous shear thickening in suspensions. The similarities observed between these two distinct phenomena suggest that the physical processes leading to shear-induced rigidity in athermal materials are universal. We present a nonequilibrium statistical mechanics model, which exhibits the phenomenology of these shear-driven transitions, shear jamming and discontinuous shear thickening, in different regions of the predicted phase diagram.

Origin of rigidity in dry granular solids.

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a nonuniform density pattern. In this work, we focus on the emergence of shear rigidity in a class of solids where this paradigm is challenged.

Structural relaxation in dense liquids composed of anisotropic particles.

We perform extensive molecular dynamics simulations of dense liquids composed of bidisperse dimer- and ellipse-shaped particles in two dimensions that interact via purely repulsive contact forces. We measure the structural relaxation times obtained from the long-time α decay of the self part of the intermediate scattering function for the translational and rotational degrees of freedom (DOF) as a function of packing fraction φ, temperature T, and aspect ratio α. We are able to collapse the packing-fraction and temperature-dependent structural relaxation times for disks, and dimers and ellipses over a wide range of α, onto a universal scaling function F(±)(|φ-φ(0)|,T,α), which is similar to that employed in previous studies of dense liquids composed of purely repulsive spherical particles in three dimensions.

Segregation of polymers in confined spaces.

We investigate the motion of two overlapping polymers confined in a 2D box. A statistical model is constructed using blob-free-energy arguments. We find spontaneous segregation under the condition L > R([parallel]), and mixing under L < R([parallel]), where L is the length of the box and R([parallel]) is the polymer extension in an infinite slit.

Constraints and vibrations in static packings of ellipsoidal particles.

We numerically investigate the mechanical properties of static packings of frictionless ellipsoidal particles in two and three dimensions over a range of aspect ratio and compression Δφ. While amorphous packings of spherical particles at jamming onset (Δφ=0) are isostatic and possess the minimum contact number z_{iso} required for them to be collectively jammed, amorphous packings of ellipsoidal particles generally possess fewer contacts than expected for collective jamming (z View Article and Find Full Text PDF

Jamming by shear.

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu-Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort.

Prolonging assembly through dissociation: a self-assembly paradigm in microtubules.

We study a one-dimensional model of microtubule assembly and disassembly in which GTP bound to tubulins within the microtubule undergoes stochastic hydrolysis. In contrast to models that consider only a cap of GTP-bound tubulin, stochastic hydrolysis allows GTP-bound tubulin remnants to exist within the microtubule. We find that these buried GTP remnants enable an alternative mechanism of recovery from shrinkage and enhances fluctuations of filament lengths.

Phase and frequency entrainment in locally coupled phase oscillators with repulsive interactions.

Recent experiments in one- and two-dimensional microfluidic arrays of droplets containing Belousov-Zhabotinsky reactants show a rich variety of spatial patterns [M. Toiya et al., J.