When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex and obtaining a detailed physical understanding often requires case-by-case considerations. In order to facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

We analyse liquid-crystalline ordering in vertically vibrated monolayers of cylinders confined in a circular cavity. Short cylinders form tetratic arrangements with C 4 symmetry. This symmetry, which is incompatible with the geometry of the cavity, is restored by the presence of four point defects with total topological charge +4. Equilibrium Monte Carlo simulations predict the same structure. A new method to measure the elastic properties of the tetratic medium is developed which exploits the clear similarities between the vibrated dissipative system and the thermal equilibrium system. Our observations open up a new avenue to investigate the formation of defects in response to boundary conditions, an issue which is very difficult to realise in colloidal or molecular systems.

No abstract

No abstract

We introduce a method to sample the orientational distribution function in computer simulations. The method is based on the exact torque balance equation for classical many-body systems of interacting anisotropic particles in equilibrium. Instead of the traditional counting of events, we reconstruct the orientational distribution function via an orientational integral of the torque acting on the particles. We test the torque sampling method in two- and three-dimensions, using both Langevin dynamics and overdamped Brownian dynamics, and with two interparticle interaction potentials. In all cases the torque sampling method produces profiles of the orientational distribution function with better accuracy than those obtained with the traditional counting method. The accuracy of the torque sampling method is independent of the bin size, and hence it is possible to resolve the orientational distribution function with arbitrarily small angular resolutions.