-Self-organization in statistical physics PACS 64.75.Xc -Phase separation and segregation in colloids Abstract -Using Brownian Dynamics (BD) simulations we investigate the non-equilibrium structure formation of a two-dimensional (2D) binary system of dipolar colloids propelling in opposite directions. Despite of a pronounced tendency for chain formation, the system displays a transition towards a laned state reminiscent of lane formation in systems with isotropic repulsive interactions. However, the anisotropic dipolar interactions induce novel features: First, the lanes have themselves a complex internal structure characterized by chains or clusters. Second, laning occurs only in a window of interaction strengths. We interprete our findings by a phase separation process and simple force balance arguments.Introduction. -Lane formation is a protoype of a non-equilibrium self-organization process, where an originally homogenous mixture of particles (or other types of "agents") moving in opposite directions segregates into macroscopic lanes composed of different species. This ubiquitous phenomenon occurs, e.g., in driven binary mixtures of colloidal particles [1-3] and migrating macroions [4], in binary plasmas [5,6], but also in "selfpropelling" systems with aligned velocities such as bacteria in channels [7] and humans in pedestrian zones [8]. In particular, studies of charged colloids have revealed many fundamental aspects of laning such as the impact of density [9], the role of hydrodyamics [10], the accompanying microscopic dynamics (particularly, the so-called dynamical locking) [2], and the impact of anisotropic friction [11].

We investigate non-equilibrium lane formation in a generic model of a fluid with attractive interactions, that is, a two-dimensional Lennard-Jones (LJ) fluid composed of two particle species driven in opposite directions. Performing Brownian Dynamics (BD) simulations for a wide range of parameters, supplemented by a stability analysis based on dynamical density functional theory (DDFT), we identify generic features of lane formation in presence of attraction, including structural properties. In fact, we find a variety of states (as compared to purely repulsive systems), as well as a close relation between laning and long wavelength instabilities of the homogeneous phase such as demixing and condensation.

a Dipolar interactions between nano-and micron sized colloids lead to their assembly into domains with well-defined local order. The particles with a single dipole induced by an external field assemble into linear chains and clusters. However, to achieve the formation of multidirectionally organized nano-or microassemblies with tunable physical characteristics, more sophisticated interaction tools are needed.Here we demonstrate that such complex interactions can be introduced in the form of two independent, non-interacting dipoles (double-dipoles) within a microparticle. We show how this can be achieved by the simultaneous application of alternating current (AC)-electric field and uniform magnetic field to dispersions of superparamagnetic microspheres. Depending on their timing and intensity, concurrent electric and magnetic fields lead to the formation of bidirectional particle chains, colloidal networks, and discrete crystals. We investigate the mechanistic details of the assembly process, and identify and classify the non-equilibrium states formed. The morphologies of different experimental states are in excellent correlation with our theoretical predictions based on Brownian dynamics simulations combined with a structural analysis based on local energy parameters. This novel methodology of introducing and interpreting double-dipolar particle interactions may assist in the assembly of colloidal coatings, dynamically reconfigurable particle networks, and bidirectional active structures.

a Based on Brownian Dynamics computer simulations in two dimensions we investigate aggregation scenarios of colloidal particles with directional interactions induced by multiple external fields. To this end we propose a model which allows continuous change in the particle interactions from point-dipole-like to patchy-like (with four patches). We show that, as a result of this change, the non-equilibrium aggregation occurring at low densities and temperatures transforms from conventional diffusion-limited cluster aggregation (DLCA) to slippery DLCA involving rotating bonds; this is accompanied by a pronounced change of the underlying lattice structure of the aggregates from square-like to hexagonal ordering.Increasing the temperature we find a transformation to a fluid phase, consistent with results of a simple mean-field density functional theory.

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