Liquid-crystal-based topological photonics.

Liquid crystals are complex fluids that allow exquisite control of light propagation thanks to their orientational order and optical anisotropy. Inspired by recent advances in liquid-crystal photo-patterning technology, we propose a soft-matter platform for assembling topological photonic materials that holds promise for protected unidirectional waveguides, sensors, and lasers. Crucial to our approach is to use spatial variations in the orientation of the nematic liquid-crystal molecules to emulate the time modulations needed in a so-called Floquet topological insulator.

Model for the scaling of stresses and fluctuations in flows near jamming.

We probe flows of soft, viscous spheres near the jamming point, which acts as a critical point for static soft spheres. Starting from energy considerations, we find nontrivial scaling of velocity fluctuations with strain rate. Combining this scaling with insights from jamming, we arrive at an analytical model that predicts four distinct regimes of flow, each characterized by rational-valued scaling exponents.

Low-frequency vibrations of soft colloidal glasses.

We conduct experiments on two-dimensional packings of colloidal thermosensitive hydrogel particles whose packing fraction can be tuned above the jamming transition by varying the temperature. By measuring displacement correlations between particles, we extract the vibrational properties of a corresponding "shadow" system with the same configuration and interactions, but for which the dynamics of the particles are undamped. The vibrational properties are very similar to those predicted for zero-temperature sphere packings and found in atomic and molecular glasses; there is a boson peak at low frequency that shifts to higher frequency as the system is compressed above the jamming transition.

Jammed frictionless disks: Connecting local and global response.

By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale l* up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Deltaz , where Deltaz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes.

Coherent structures in dissipative particle dynamics simulations of the transition to turbulence in compressible shear flows.

We present simulations of coherent structures in compressible flows near the transition to turbulence using the dissipative particle dynamics method. The structures we find are remarkably consistent with experimental observations and direct numerical simulations (DNS) simulations of incompressible flows, despite a difference in Mach number of several orders of magnitude. The bifurcation from the laminar flow is bistable and shifts to higher Reynolds numbers when the fluid becomes more compressible.

Soft glassy rheology of supercooled molecular liquids.

We probe the mechanical response of two supercooled liquids, glycerol and ortho-terphenyl, by conducting rheological experiments at very weak stresses. We find a complex fluid behavior suggesting the gradual emergence of an extended, delicate solid-like network in both materials in the supercooled state-i.e.

Critical and noncritical jamming of frictional grains.

We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient mu. The density of vibrational states exhibits a crossover from a plateau at frequencies omega > or similar to omega*(p,mu) to a linear growth for omega < or similar to omega*(p,mu). We show that omega* is proportional to Deltaz, the excess number of contacts per grain relative to the minimally allowed, isostatic value.

Force mobilization and generalized isostaticity in jammed packings of frictional grains.

We show that in slowly generated two-dimensional packings of frictional spheres, a significant fraction of the friction forces lie at the Coulomb threshold-for small pressure p and friction coefficient mu , about half of the contacts. Interpreting these contacts as constrained leads to a generalized concept of isostaticity, which relates the maximal fraction of fully mobilized contacts and contact number. For p-->0 , our frictional packings approximately satisfy this relation over the full range of mu .

Critical scaling in linear response of frictionless granular packings near jamming.

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition.

Mechanism of polymer drag reduction using a low-dimensional model.

Using a retarded-motion expansion to describe the polymer stress, we derive a low-dimensional model to understand the effects of polymer elasticity on the self-sustaining process that maintains the coherent wavy streamwise vortical structures underlying wall-bounded turbulence. Our analysis shows that at small Weissenberg numbers, Wi, elasticity enhances the coherent structures. At higher Wi, however, polymer stresses suppress the streamwise vortices (rolls) by calming down the instability of the streaks that regenerates the rolls.

Continuum approach to wide shear zones in quasistatic granular matter.

Slow and dense granular flows often exhibit narrow shear bands, making them ill suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field.

Elastic wave propagation in confined granular systems.

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wave front followed by random oscillations made of multiply scattered waves. We find that the coherent wave front is insensitive to details of the packing: force chains do not play an important role in determining this wave front.

Subcritical finite-amplitude solutions for plane Couette flow of viscoelastic fluids.

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation is sufficient to create a secondary flow, and the threshold value for the amplitude of the perturbation decreases as the Weissenberg number increases.

Rod-climbing effect in Newtonian fluids.

When a rotating rod is brought into a polymer melt or concentrated polymer solution, the meniscus climbs the rod. This spectacular rod climbing is due to the normal stresses present in the polymer fluid and is thus a purely non-Newtonian effect. A similar rod climbing of an interface between two fluids has therefore been taken as a signature that one of the fluids exhibits normal stress effects.

Dynamics and stability of vortex-antivortex fronts in type-II superconductors.

The dynamics of vortices in type-II superconductors exhibit a variety of patterns whose origin is poorly understood. This is partly due to the nonlinearity of the vortex mobility, which gives rise to singular behavior in the vortex densities. Such singular behavior complicates the application of standard linear stability analysis.

Packing geometry and statistics of force networks in granular media.

The relation between packing geometry and force network statistics is studied for granular media. Based on simulations of two-dimensional packings of Hertzian spheres, we develop a geometrical framework relating the distribution of interparticle forces P(f) to the weight distribution P(w), which is measured in experiments. We apply this framework to reinterpret recent experimental data on strongly deformed packings and suggest that the observed changes of P(w) are dominated by changes in contact network while P(f) remains relatively unaltered.

Force network ensemble: a new approach to static granular matter.

An ensemble approach for force distributions in static granular packings is developed. This framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. We show how the formalism yields realistic results, both for disordered and regular triangular "snooker ball" configurations, and obtain a shear-induced unjamming transition of the type proposed recently for athermal media.

Front propagation and diffusion in the A left arrow over right arrow A+A hard-core reaction on a chain.

We study front propagation and diffusion in the reaction-diffusion system A left arrow over right arrow A+A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact.

Sources and holes in a one-dimensional traveling-wave convection experiment.

We study dynamical behavior of local structures, such as sources and holes, in traveling-wave patterns in a very long (2 m) heated wire convection experiment. The sources undergo a transition from stable coherent behavior to erratic behavior when the driving parameter epsilon is decreased. This transition, as well as the scaling of the average source width in the erratic regime are both qualitatively and quantitatively in accord with earlier theoretical predictions.

Force and weight distributions in granular media: effects of contact geometry.

The influence of the local contact network on interparticle forces and effective particle weights is studied in simulations of two-dimensional packings of frictionless, Hertzian spheres. The weight distribution P(w) changes qualitatively when approaching a boundary and differs for regular and irregular packings, while the interparticle force distribution P(f) is robust. We provide examples where P(w) at the boundary, which is the quantity probed experimentally, deviates substantially from P(f) in the bulk.

Experimental evidence for an intrinsic route to polymer melt fracture phenomena: a nonlinear instability of viscoelastic Poiseuille flow.

The production rate of polymer fibers by extrusion is usually limited by the appearance of a series of instabilities ("melt fracture") that lead to unwanted undulations of the surface. We present both qualitative and quantitative experimental evidence that-in addition to previously known polymer-specific scenarios-there is an intrinsic route towards melt fracture type phenomena: a nonlinear ("subcritical") instability of viscoelastic Poiseuille flow.

Intrinsic route to melt fracture in polymer extrusion: a weakly nonlinear subcritical instability of viscoelastic poiseuille flow.

As is well known, the extrusion rate of polymers from a cylindrical tube or slit (a "die") is in practice limited by the appearance of "melt fracture" instabilities which give rise to unwanted distortions or even fracture of the extrudate. We present the results of a weakly nonlinear analysis which gives evidence for an intrinsic generic route to melt fracture via a weakly nonlinear subcritical instability of viscoelastic Poiseuille flow. This instability and the onset of associated melt fracture phenomena appear at a well-defined ratio of the elastic stresses to viscous stresses of the polymer solution.

Fluctuating pulled fronts: The origin and the effects of a finite particle cutoff.

Recently, it has been shown that when an equation that allows the so-called pulled fronts in the mean-field limit is modeled with a stochastic model with a finite number N of particles per correlation volume, the convergence to the speed v(*) for N--> infinity is extremely slow-going only as ln(-2)N. Pulled fronts are fronts that propagate into an unstable state, and the asymptotic front speed is equal to the linear spreading speed v(*) of small linear perturbations about the unstable state. In this paper, we study the front propagation in a simple stochastic lattice model.

Fronts with a growth cutoff but with speed higher than the linear spreading speed.

Fronts, propagating into an unstable state phi=0, whose asymptotic speed v(as) is equal to the linear spreading speed v* of infinitesimal perturbations about that state (so-called pulled fronts), are very sensitive to changes in the growth rate f(phi) for phi<<1. It was recently found that with a small cutoff, f(phi)=0 for phi< epsilon, v(as) converges to v* very slowly from below, as ln(-2) epsilon. Here we show that with such a cutoff and a small enhancement of the growth rate for small phi behind it, one can have v(as)>v*, even in the limit epsilon -->0.

Morphological instability and dynamics of fronts in bacterial growth models with nonlinear diffusion.

Depending on the growth condition, bacterial colonies can exhibit different morphologies. As argued by Ben-Jacob et al. there is biological and modeling evidence that a nonlinear diffusion coefficient of the type D(b)=D(0)b(k) is a basic mechanism that underlies almost all of the patterns and generates a long-wavelength instability.