The equations of motion of active systems can be modeled in terms of Ornstein-Uhlenbeck processes (OUPs) with appropriate correlators. For further theoretical studies, these should be approximated to yield a Markovian picture for the dynamics and a simplified steady-state condition. We perform a comparative study of the Unified Colored Noise Approximation (UCNA) and the approximation scheme by Fox recently employed within this context. We review the approximations necessary to define effective interaction potentials in the low-density limit and study the conditions for which these represent the behavior observed in two-body simulations for the OUPs model and Active Brownian particles. The demonstrated limitations of the theory for potentials with a negative slope or curvature can be qualitatively corrected by a new empirical modification. In general, we find that in the presence of translational white noise the Fox approach is more accurate. Finally, we examine an alternative way to define a force-balance condition in the limit of small activity. CONTENTS

The classical dynamical density functional theory (DDFT) provides an approximate extension of equilibrium DFT to treat nonequilibrium systems subject to Brownian dynamics. However, the method fails when applied to driven systems, such as sheared colloidal dispersions. The breakdown of DDFT can be traced back to an inadequate treatment of the flowinduced distortion of the pair correlation functions. By considering the distortion of the pair correlations to second order in the flow-rate we show how to systematically correct the DDFT for driven systems. As an application of our approach we consider Poiseuille flow. The theory predicts that the particles will accumulate in spatial regions where the local shear rate is small, an effect known as shear-induced migration. We compare these predictions to Brownian dynamics simulations with generally good agreement.

We investigate the mean first passage time of an active Brownian particle in one dimension using numerical simulations. The activity in one dimension is modelled as a two state model; the particle moves with a constant propulsion strength but its orientation switches from one state to other as in a random telegraphic process. We study the influence of a finite resetting rate r on the mean first passage time to a fixed target of a single free Active Brownian Particle and map this result using an effective diffusion process. As in the case of a passive Brownian particle, we can find an optimal resetting rate r * for an active Brownian particle for which the target is found with the minimum average time. In the case of the presence of an external potential, we find good agreement between the theory and numerical simulations using an effective potential approach.

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by nonaffine particle motion arising from interparticle interactions. Starting from a DDFT which incorporates the nonaffine motion, we perform a linear stability analysis that enables identification of the regions of parameter space where lanes form. We illustrate our general approach by applying it to a simple one-component fluid of soft penetrable particles.

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Using a strategy that may be applied in theory or in experiments, we identify the regime in which a model binary soft matter mixture forms quasicrystals. The system is described using classical density functional theory combined with integral equation theory. Quasicrystal formation requires particle ordering with two characteristic length scales in certain particular ratios. How the length scales are related to the form of the pair interactions is reasonably well understood for one-component systems, but less is known for mixtures. In our model mixture of big and small colloids confined to an interface, the two length scales stem from the range of the interactions between pairs of big particles and from the cross big-small interactions, respectively. The small-small length scale is not significant. Our strategy for finding quasicrystals involves tuning locations of maxima in the dispersion relation, or equivalently in the liquid state partial static structure factors.

We investigate the microstructural and microrheological response to a tracer particle of a two-dimensional colloidal suspension under thermodynamic conditions close to a liquid-gas phase boundary. On the liquid side of the binodal, increasing the velocity of the (repulsive) tracer leads to the development of a pronounced cavitation bubble, within which the concentration of colloidal particles is strongly depleted. The tendency of the liquid to cavitate is characterized by a dimensionless "colloidal cavitation" number. On the gas side of the binodal, a pulled (attractive) tracer leaves behind it an extended trail of colloidal liquid, arising from downstream advection of a wetting layer on its surface. For both situations the velocity dependent friction is calculated.

Phase transitions have an essential role in the assembly of nature’s protein-based materials into hierarchically organized structures, yet many of the underlying mechanisms and interactions remain to be resolved. A central question for designing proteins for materials is how the protein architecture and sequence affects the nature of the phase transitions and resulting assembly. In this work, we produced 82 kDa (1×), 143 kDa (2×), and 204 kDa (3×) silk-mimicking proteins by taking advantage of protein ligation by SpyCatcher/Tag protein-peptide pair. We show that the three silk proteins all undergo a phase transition from homogeneous solution to assembly formation. In the assembly phase, a length- and concentration-dependent transition between two distinct assembly morphologies, one forming aggregates and another coacervates, exists. The coacervates showed properties that were dependent on the protein size. Computational modeling of the proteins by a bead-spring model supports the experimental results and provides us a possible mechanistic origin for the assembly transitions based on architectures and interactions.