Long-range interactions in randomly driven granular fluids

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Asymmetric and long range interactions in shaken granular media

We use a computational model to investigate the emergence of interaction forces between pairs of intruders in a horizontally vibrated granular fluid. The time evolution of a pair of particles shows a maximum of the likelihood to find the pair at contact in the direction of shaking. This relative interaction is further studied by fixing the intruders in the simulation box where we identify effective mechanical forces and torques between particles and quantify an emergent long range attractive force as a function of the shaking relative angle, the amplitude, and the packing density of grains. We determine the local density and kinetic energy profiles of granular particles along the axis of the dimer to find no gradients in the density fields and additive gradients in the kinetic energies.

Heat flux of driven granular mixtures at low density: Stability analysis of the homogeneous steady state

The Navier-Stokes order hydrodynamic equations for a low-density driven granular mixture obtained previously [Khalil and Garzó, Phys. Rev. E 88, 052201 (2013)PLEEE81539-375510.1103/PhysRevE.88.052201] from the Chapman-Enskog solution to the Boltzmann equation are considered further. The four transport coefficients associated with the heat flux are obtained in terms of the mass ratio, the size ratio, composition, coefficients of restitution, and the driven parameters of the model. Their quantitative variation on the control parameters of the system is demonstrated by considering the leading terms in a Sonine polynomial expansion to solve the exact integral equations. As an application of these results, the stability of the homogeneous steady state is studied. In contrast to the results obtained in undriven granular mixtures, the stability analysis of the linearized Navier-Stokes hydrodynamic equations shows that the transversal and longitudinal modes are (linearly) stable with respect to long enough wavelength excitations. This conclusion agrees with a previous analysis made for single granular gases.

Persistent-random-walk approach to anomalous transport of self-propelled particles

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Transport coefficients for driven granular mixtures at low density

The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the Chapman-Enskog method for states near homogeneous steady states. The mass, momentum, and heat fluxes are determined to first order in the spatial gradients of the hydrodynamic fields, and the associated transport coefficients are identified. They are given in terms of the solutions of a set of coupled linear integral equations. As in the monocomponent case, since the collisional cooling cannot be compensated for locally by the heat produced by the external driving, the reference distributions (zeroth-order approximations) f(i)((0)) (i=1,2) for each species depend on time through their dependence on the pressure and the temperature. Explicit forms for the diffusion transport coefficients and the shear viscosity coefficient are obtained by assuming the steady-state conditions and by considering the leading terms in a Sonine polynomial expansion. A comparison with previous results obtained for granular Brownian motion and by using a (local) stochastic thermostat is also carried out. The present work extends previous theoretical results derived for monocomponent dense gases [Garzó, Chamorro, and Vega Reyes, Phys. Rev. E 87, 032201 (2013)] to granular mixtures at low density.