Shaping liquid drops by vibration

We present and analyze a minimal hydrodynamic model of a vertically vibrated liquid drop that undergoes dynamic shape transformations. In agreement with experiments, a circular lens-shaped drop is unstable above a critical vibration amplitude, spontaneously elongating in horizontal direction. Smaller drops elongate into localized states that oscillate with half of the vibration frequency. Larger drops evolve by transforming into a snake-like structure with gradually increasing length. The worm state is long-lasting with a potential to fragmentat into smaller drops

Rectification of self-propelled particles by symmetric barriers

The motion of self-propelled particles can be rectified by asymmetric or ratchet-like periodic patterns in space. Here we show that a non-zero average drift can already be induced in a periodic potential with symmetric barriers when the self-propulsion velocity is also symmetric and periodically modulated but phase-shifted against the potential. In the adiabatic limit of slow rotational diffusion we determine the mean drift analytically and discuss the influence of temperature. In the presence of asymmetric barriers modulating the self-propulsion can largely enhance the mean drift or even reverse it

Morphology changes in the evolution of liquid two-layer films

We consider two thin layers of immiscible liquids on a heated solid horizontal substrate. The free liquid-liquid and liquid-gas interfaces of such a two-layer (or bilayer) liquid film may be unstable due to effective molecular interactions or the Marangoni effect. Using a long wave approximation we derive coupled evolution equations for the interafce profiles for a general non-isothermal situation allowing for slip at the substrate. Linear and nonlinear analyses are performed for isothermal ultrathin layers below 100 nm thickness under the influence of destabilizing long-range and stabilizing short-range interactions. Flat films may be unstable to varicose, zigzag or mixed modes. During the long-time evolution the nonlinear mode type can change via switching between two different branches of stable stationary solutions or via coarsening along a single such branch.Comment: 14 eps figures and 1 tex fil

Coarsening modes of clusters of aggregating particles

There are two modes by which clusters of aggregating particles can coalesce: The clusters can merge either (i) by the Ostwald ripening process in which particles diffuse from one cluster to the other whilst the cluster centres remain stationary, or (ii) by means of a cluster translation mode, in which the clusters move towards each other and join. To understand in detail the interplay between these different modes, we study a model system of hard particles with an additional attraction between them. The particles diffuse along narrow channels with smooth or periodically corrugated walls, so that the system may be treated as one-dimensional. When the attraction between the particles is strong enough, they aggregate to form clusters. The channel potential influences whether clusters can move easily or not through the system and can prevent cluster motion. We use Dynamical Density Functional theory to study the dynamics of the aggregation process, focusing in particular on the coalescence of two equal size clusters. As long as the particle hard-core diameter is non-zero, we find that the coalescence process can be halted by a sufficiently strong corrugation potential. The period of the potential determines the size of the final stable clusters. For the case of smooth channel walls, we demonstrate that there is a cross-over in the dominance of the two different coarsening modes, that depends on the strength of the attraction between particles, the cluster sizes and the separation distance between clusters

Excitable systems with noise and delay with applications to control: renewal theory approach

We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after [Pyragas 1992] as a difference between the current system state and its state "tau" time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term