Synchronization of driven oscillators is a key aspect of flow generation in artificial and biological filaments such as cilia. Previous theoretical and numerical studies have considered the "rotor" model of a cilium in which the filament is coarse grained into a colloidal sphere driven with a given force law along a predefined trajectory to represent the oscillating motion of the cilium. These studies pointed to the importance of two factors in the emergence of synchronization: the modulation of the driving force around the orbit and the deformability of the trajectory. In this work it is shown via experiments, supported by numerical simulations and theory, that both of these factors are important and can be combined to produce strong synchronization (within a few cycles) even in the presence of thermal noise.

Motile cilia are highly conserved structures in the evolution of organisms, generating the transport of fluid by periodic beating, through remarkably organized behavior in space and time. It is not known how these spatiotemporal patterns emerge and what sets their properties. Individual cilia are nonequilibrium systems with many degrees of freedom. However, their description can be represented by simpler effective force laws that drive oscillations, and paralleled with nonlinear phase oscillators studied in physics. Here a synthetic model of two phase oscillators, where colloidal particles are driven by optical traps, proves the role of the average force profile in establishing the type and strength of synchronization. We find that highly curved potentials are required for synchronization in the presence of noise. The applicability of this approach to biological data is also illustrated by successfully mapping the behavior of cilia in the alga Chlamydomonas onto the coarse-grained model.

Surface tension is a macroscopic manifestation of the cohesion of matter, and its value σ_{∞} is readily measured for a flat liquid-vapor interface. For interfaces with a small radius of curvature R, the surface tension might differ from σ_{∞}. The Tolman equation, σ(R)=σ_{∞}/(1+2δ/R), with δ a constant length, is commonly used to describe nanoscale phenomena such as nucleation. Here we report experiments on nucleation of bubbles in ethanol and n-heptane, and their analysis in combination with their counterparts for the nucleation of droplets in supersaturated vapors, and with water data. We show that neither a constant surface tension nor the Tolman equation can consistently describe the data. We also investigate a model including 1/R and 1/R^{2} terms in σ(R). We describe a general procedure to obtain the coefficients of these terms from detailed nucleation experiments. This work explains the conflicting values obtained for the Tolman length in previous analyses, and suggests directions for future work.