Phase coexistence of active Brownian particles.

We investigate motility-induced phase separation of active Brownian particles, which are modeled as purely repulsive spheres that move due to a constant swim force with freely diffusing orientation. We develop on the basis of power functional concepts an analytical theory for nonequilibrium phase coexistence and interfacial structure. Theoretical predictions are validated against Brownian dynamics computer simulations. We show that the internal one-body force field has four nonequilibrium contributions: (i) isotropic drag and (ii) interfacial drag forces against the forward motion, (iii) a superadiabatic spherical pressure gradient, and (iv) the quiet life gradient force. The intrinsic spherical pressure is balanced by the swim pressure, which arises from the polarization of the free interface. The quiet life force opposes the adiabatic force, which is due to the inhomogeneous density distribution. The balance of quiet life and adiabatic forces determines bulk coexistence via equality of two bulk state functions, which are independent of interfacial contributions. The internal force fields are kinematic functionals which depend on density and current but are independent of external and swim forces, consistent with power functional theory. The phase transition originates from nonequilibrium repulsion, with the agile gas being more repulsive than the quiet liquid.

Power functional theory for active Brownian particles: General formulation and power sum rules.

We generalize power functional theory [Schmidt and Brader, J. Chem. Phys. 138, 214101 (2013)] to Brownian many-body systems with orientational degrees of freedom. The framework allows the study of active particles in general inhomogeneous and time-dependent nonequilibrium. We prove for steady states that the free power equals half the negative dissipated external work per time, and is hence trivially related to the average forward swim speed of the particles. The variational theory expresses the free power as a functional of the microscopic one-body density and current distribution. Both fields are time-, position- and orientation-dependent, and the total current consists of translational and rotational parts. Minimization of the free power functional with respect to the current(s) yields the physical dynamics of the system. We give a simple approximation for the superadiabatic (above adiabatic) contribution which describes excess dissipation in homogeneous bulk fluids due to drag. In steady states, we evaluate the free power using Brownian dynamics simulations for short-ranged soft repulsive spheres. We describe the necessary sampling strategies and show that the theory provides a good account of the simulation data.

Erratum: Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation [Phys. Rev. Lett. 117, 208003 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.117.208003.

Nonequilibrium Phase Behavior from Minimization of Free Power Dissipation.

We develop a general theory for describing phase coexistence between nonequilibrium steady states in Brownian systems, based on power functional theory [M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013)]. We apply the framework to the special case of fluid-fluid phase separation of active soft sphere swimmers. The central object of the theory, the dissipated free power, is calculated via computer simulations and compared to a simple analytical approximation. The theory describes well the simulation data and predicts motility-induced phase separation due to avoidance of dissipative clusters.

Minimal model for dynamic bonding in colloidal transient networks.

We investigate a model for colloidal network formation using Brownian dynamics computer simulations. Hysteretic springs establish transient bonds between particles with repulsive cores. If a bonded pair of particles is separated by a cutoff distance, the spring vanishes and reappears only if the two particles contact each other. We present results for the bond lifetime distribution and investigate the properties of the van Hove dynamical two-body correlation function. The model displays crossover from fluidlike dynamics, via transient network formation, to arrested quasistatic network behavior.

Order-disorder transition in swirled granular disks.

We study the order-disorder transition of horizontally swirled dry and wet granular disks by means of computer simulations. Our systematic investigation of the local order formation as a function of amplitude and period of the external driving force shows that a large cluster of hexagonally ordered particles forms for both dry and wet granular particles at intermediate driving energies. Disordered states are found at small and large driving energies. Wet granular particles reach a higher degree of local hexagonal order with respect to the dry case. For both cases we report a qualitative phase diagram showing the amount of local order at different state points. Furthermore, we find that the transition from hexagonal order to a disordered state is characterized by the appearance of particles with square local order.