We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain dragged at one end. First we consider an ideal chain with harmonic springs and no excluded volume between the monomers. The Rouse model of polymers is generalized to the case of self-propelled monomers and solved analytically. The swelling, as characterized by the spatial extension of the chain, scales with the monomer number defining a Flory exponent ν which is ν = 1/2, 0, 1 in the three different situations. As a result, we find that activity does not change the Flory exponent but affects the prefactor of the scaling law. This can be quantitatively understood by mapping the system onto an equilibrium chain with a higher effective temperature such that the chain swells under an increase of the self-propulsion strength. We then use computer simulations to study the effect of self-avoidance on active polymer swelling. In the three different situations, the Flory exponent is now ν = 3/4, 1/4, 1 and again unchanged under self-propulsion. However, the chain extension behaves non-monotonic in the self-propulsion strength.

In analogy to nanoscopic molecules that are composed of individual atoms, we consider an active "microswimmer molecule". It is built up from three individual magnetic colloidal microswimmers that are connected by harmonic springs and hydrodynamically interact with each other. In the ground state, they form a linear straight molecule. We analyze the relaxation dynamics for perturbations of this straight configuration. As a central result, with increasing self-propulsion, we observe an oscillatory instability in accord with a subcritical Hopf bifurcation scenario. It is accompanied by a corkscrew-like swimming trajectory of increasing radius. Our results can be tested experimentally, using for instance magnetic self-propelled Janus particles, supposably linked by DNA molecules.

Typically, in the description of active Brownian particles, a constant effective propulsion force is assumed, which is then subjected to fluctuations in orientation and translation, leading to a persistent random walk with an enlarged longtime diffusion coefficient. Here, we generalize previous results for the swimming path statistics to a time-dependent, and thus in many situations more realistic, propulsion which is a prescribed input. We analytically calculate both the noise-free and the noiseaveraged trajectories for time-periodic propulsion under the action of an additional torque. In the deterministic case, such an oscillatory microswimmer moves on closed paths that can be highly more complicated than the commonly observed straight lines and circles. When exposed to random fluctuations, the mean trajectories turn out to be self-similar curves which bear the characteristics of their noise-free counterparts. Furthermore, we consider a propulsion force which scales in time t as ∝ t α (with α = 0, 1, 2, . . .) and analyze the resulting superdiffusive behavior. Our predictions are verifiable for diffusiophoretic artificial microswimmers with prescribed propulsion protocols.

The article explores the ion flux response of a capacitor configuration to an alternating voltage. The model system comprises a symmetric binary electrolyte confined between plan-parallel capacitor plates. The AC response is investigated for the sparsely studied albeit practically important case of a large amplitude voltage applied across a narrow device, with the distance between the two plates amounting to a few ion diameters. Dynamic density functional theory is employed to solve for the spatiotemporal ion density distribution as well as the transient ion flux and complex impedance of the system. The analysis of these properties reveals a hitherto hidden impedance resonance. A single ion analogue of the capacitor, which is equivalent to neglecting all interactions between the ions, is employed for a physical interpretation of this phenomenon. It explains the resonance as a consequence of field-induced ion condensation at the capacitor plates and coherent motion of condensed ions in response to the field variation.