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We present and analyze a theoretical model for the dynamics and interactions of "capillary surfers," which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. In our companion paper [1], we reported the results of an experimental investigation of the surfer system, which showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers' positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good quantitative agreement with experimental data. Moreover, a linear stability analysis shows that the bound states are quantized on the capillary wavelength, with stable branches of equilibria separated by unstable ones. Generally, our work shows that self-propelling objects coupled by interfacial flows constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.

The problem of the restitution of motion in the artistic images from classical antiquity is explored through the philosophical and anthropological conceptions of the movement in Greek thought. The concepts of σχῆμα and ῥυθμός are fundamental to clarify the dialectical relationship between movement and stasis in relation to μίμηεσις, both in dance, the “mimetic” art par excellence, and in the visual arts. A painted or sculpted figure is an ἠρεμία, an isolated punctum temporis, which nevertheless potentially contains the flow of movement, which the observer can mentally recreate by imagining what precedes and follows it. The views of the Ancients on this topic are compared with those of some modern thinkers (Lessing, Bergson, Deleuze) and the visual anthropology of Aby Warburg is reconsidered in the light of recent acquisitions of cognitive psychology and neuroesthetics. On examine le problème de la restitution du mouvement dans les images de l’art de l’antiquité classique, en partant de la conception philosophique et anthropologique du mouvement des penseurs grecs. Les concepts de σχῆμα et ῥυθμός sont fondamentaux pour clarifier la relation dialectique entre mouvement et stase en relation avec la μίμηεσις, à la fois dans la danse, l’art ‘mimétique’ par excellence, et dans les arts visuels. Une figure peinte ou sculptée est une ἠρεμία, un punctum temporis isolé, qui contient néanmoins potentiellement le flux du mouvement, que l’observateur peut récréer mentalement en imaginant les mouvances qui la précèdent et celles qui la suivent. On compare les vues des Anciens en matière avec celles des certains penseur modernes (Lessing, Bergson, Deleuze) et on termine en revisitant l’anthropologie visuelle fondée par Warburg à la lumière des récentes acquisitions de la psychologie cognitive et de la neuroesthétique.

We present an experimental study of capillary surfers, a new fluid-mediated active system that bridges the gap between dissipation- and inertia-dominated regimes. Surfers are wave-driven particles that self-propel and interact on a fluid interface via an extended field of surface waves. A surfer's speed and interaction with its environment can be tuned broadly through the particle, fluid, and vibration parameters. The wave nature of interactions among surfers allows for multistability of interaction modes and promises a number of novel collective behaviors., Comment: 6 pages, 4 figures