Emergent states in dense systems of active rods: from swarming to turbulence

Dense suspensions of self-propelled rod-like particles exhibit a fascinating variety of non-equilibrium phenomena. By means of computer simulations of a minimal model for rigid self-propelled colloidal rods with variable shape we explore the generic diagram of emerging states over a large range of rod densities and aspect ratios. The dynamics is studied using a simple numerical scheme for the overdamped noiseless frictional dynamics of a many-body system in which steric forces are dominant over hydrodynamic ones. The different emergent states are identified by various characteristic correlation functions and suitable order parameter fields. At low density and aspect ratio, a disordered phase with no coherent motion precedes a highly-cooperative swarming state at large aspect ratio. Conversely, at high densities weakly anisometric particles show a distinct jamming transition whereas slender particles form dynamic laning patterns. In between there is a large window corresponding to strongly vortical, turbulent flow. The different dynamical states should be verifiable in systems of swimming bacteria and artificial rod-like micro-swimmers.Comment: 14 pages, 8 figure

Dynamical density functional theory for the diffusion of injected Brownian particles

While the theory of diffusion of a single Brownian particle in confined geometries is well-established by now, we discuss here the theoretical framework necessary to generalize the theory of diffusion to dense suspensions of strongly interacting Brownian particles. Dynamical density functional theory (DDFT) for classical Brownian particles represents an ideal tool for this purpose. After outlining the basic ingredients to DDFT we show that it can be readily applied to flowing suspensions with time-dependent particle sources. Particle interactions lead to considerable layering in the mean density profiles, a feature that is absent in the trivial case of noninteracting, freely diffusing particles. If the particle injection rate varies periodically in time with a suitable frequency, a resonance in the layering of the mean particle density profile is predicted

Modelling chemotaxis of microswimmers: from individual to collective behavior

We discuss recent progress in the theoretical description of chemotaxis by coupling the diffusion equation of a chemical species to equations describing the motion of sensing microorganisms. In particular, we discuss models for autochemotaxis of a single microorganism which senses its own secretion leading to phenomena such as self-localization and self-avoidance. For two heterogeneous particles, chemotactic coupling can lead to predator-prey behavior including chase and escape phenomena, and to the formation of active molecules, where motility spontaneously emerges when the particles approach each other. We close this review with some remarks on the collective behavior of many particles where chemotactic coupling induces patterns involving clusters, spirals or traveling waves.Comment: to appear as a contribution to the book "Chemical kinetics beyond the textbook

Structure factors for the simplest solvable model of polydisperse colloidal fluids with surface adhesion

Closed analytical expressions for scattering intensity and other global structure factors are derived for a new solvable model of polydisperse sticky hard spheres. The starting point is the exact solution of the ``mean spherical approximation'' for hard core plus Yukawa potentials, in the limit of infinite amplitude and vanishing range of the attractive tail, with their product remaining constant. The choice of factorizable coupling (stickiness) parameters in the Yukawa term yields a simpler ``dyadic structure'' in the Fourier transform of the Baxter factor correlation function $q_{ij}(r)$, with a remarkable simplification in all structure functions with respect to previous works. The effect of size and stickiness polydispersity is analyzed and numerical results are presented for two particular versions of the model: i) when all polydisperse particles have a single, size-independent, stickiness parameter, and ii) when the stickiness parameters are proportional to the diameters. The existence of two different regimes for the average structure factor, respectively above and below a generalized Boyle temperature which depends on size polydispersity, is recognized and discussed. Because of its analycity and simplicity, the model may be useful in the interpretation of small-angle scattering experimental data for polydisperse colloidal fluids of neutral particles with surface adhesion.Comment: 32 pages, 7 figures, RevTex style, to appear in J. Chem. Phys. 1 December 200

Liquid pair correlations in four spatial dimensions: Theory versus simulation

Using liquid integral equation theory, we calculate the pair correlations of particles that interact via a smooth repulsive pair potential in d = 4 spatial dimensions. We discuss the performance of different closures for the Ornstein-Zernike equation, by comparing the results to computer simulation data. Our results are of relevance to understand crystal and glass formation in high-dimensional systems