Abstract: Small drops impinging obliquely on thin flowing soap films frequently demonstrate the rare emergence of bulk elastic effects working in-tandem with the more commonplace hydrodynamic interactions. Three collision regimes are observable: (a) drop piercing through the film, (b) it coalescing with the flow, and (c) it bouncing off the film surface. During impact, the drop deforms along with a bulk elastic deformation of the film. For impacts that are close-to-tangential, the bounce-off regime predominates. We outline a reduced order analytical framework assuming a deformable drop and a deformable three-dimensional film, and the idealization invokes a phase-based parametric study. Angular inclination of the film and the ratio of post and pre-impact drop sizes entail the phase parameters. We also perform experiments with vertically descending droplets (constituted from deionized water) impacting against an inclined soap film, flowing under constant pressure head. Model-predicted phase domain for bounce-off compares well to our experimental findings. Additionally, the experiments exhibit momentum transfer to the film in the form of shed vortex dipoles, along with propagation of free surface waves. On consulting prior published work, we note that for locomotion of water-walking insects using an impulsive action, the momentum distribution to the shed vortices and waves are both significant, taking up respectively 2/3 and 1/3 of the imparted streamwise momentum. Considering the visually similar impulse actions, this theory, despite its assumption of a quiescent liquid bath of infinite depth, is applied to the drop bounce-off experiments, and the resultant shed vortex dipole momenta are compared to the momenta of the coherent vortex structures computed from particle imaging velocimetry data. The magnitudes reveal identical order (10(-7) N s), suggesting that notwithstanding the disparities, the bounce-off regime may be tapped as a toy analog for impulse-based interfacial biolocomotion.

Abstract: Nonlinear systems that model physical experiments often have many equilibrium configurations, and the number of these static solutions grows with the number of degrees of freedom and the presence of symmetries. It is impossible to know a priori how many equilibria exist and which ones are stable or relevant, therefore from the modeler's perspective, an exhaustive search and symmetry classification in the space of solutions are necessary. With this purpose in mind, the method of deflation (introduced by Farrell as a modification of the classic Newton iterative method) offers a systematic way of finding every possible solution of a set of equations. In this contribution we apply deflated Newton and deflated continuation methods to a model of macroscopic magnetic rotors, and find hundreds of new equilibria that can be classified according to their symmetry. We assess the benefits and limitations of the method for finding branches of solutions in the presence of a symmetry group, and explore the high -dimensional basins of attraction of the method in selected 2 -dimensional sections, illustrating the effect of deflation on the convergence.

Abstract: Macroscopic magnets can easily be manipulated and positioned so that interactions between themselves and with external fields induce interesting dynamics and equilibrium configurations. In this work, we use rotating magnets positioned in a line or at the vertices of a regular polygon. The rotation planes of the magnets can be modified at will. The rich structure of stable and unstable configurations is dictated by symmetry and the side of the polygon. We show that both symmetric solutions and their symmetry-breaking bifurcations can be explained with group theory. Our results suggest that the predicted magnetic textures should emerge at any length scale as long as the interaction is polar, and the system is endowed with the same symmetries.

Abstract: The rapid squirt of a proteinaceous slime jet endows velvet worms (Onychophora) with a unique mechanism for defence from predators and for capturing prey by entangling them in a disordered web that immobilizes their target. However, to date, neither qualitative nor quantitative descriptions have been provided for this unique adaptation. Here we investigate the fast oscillatory motion of the oral papillae and the exiting liquid jet that oscillates with frequencies f similar to 30-60 Hz. Using anatomical images, high-speed videography, theoretical analysis and a physical simulacrum, we show that this fast oscillatory motion is the result of an elastohydrodynamic instability driven by the interplay between the elasticity of oral papillae and the fast unsteady flow during squirting. Our results demonstrate how passive strategies can be cleverly harnessed by organisms, while suggesting future oscillating microfluidic devices, as well as novel ways for micro and nanofibre production using bioinspired strategies.

Abstract: We combine the anisotropy of magnetic interactions and the point symmetry of finite solids in the study of dipolar clusters as new basic units for multiferroics metamaterials. The Hamiltonian of magnetic dipoles with an easy axis at the vertices of polygons and polyhedra, maps exactly into a Hamiltonian with symmetric and antisymmetric exchange couplings. The last one gives rise to a Dzyaloshinskii-Moriya contribution responsible for the magnetic modes of the systems and their symmetry groups, which coincide with those of a particle in a crystal field with spin-orbit interaction. We find that the clusters carry spin current and that they manifest the magnetoelectric effect. We expect our results to pave the way for the rational design of magnetoelectric devices at room temperature

Abstract: During the past decades magnetic materials and structures that span several length scales have been of interest mainly due to their application in data storage and processing, flexible electronics, medicine, between others. From a microscopic point of view, these systems are typically studied using the Landau-Lifshitz equation (LLE), while approaches such as the dumbbell model are used to study macroscopic magnetic structures. In this work we use both the LLE and the dumbbell model to study spin chains of various lengths under the effect of a time dependent-magnetic field, allowing us to compare qualitatively the results obtained by both approaches. This has allowed us to identify and describe in detail several frequency modes that appear, with additional modes arising as the chain length increases. Moreover, we find that high frequency modes tend to be absorbed by lower frequency ones as the amplitude of the field increases. The results obtained in this work are of interest not only to better understand the behavior of the macroscopic spins chains, but also expands the available tools for qualitative studies of both macroscopic and microscopic versions of the studied system, or more complex structures such as junctions or lattices. This would allow to study the qualitative behavior of microscopic systems (e.g. nanoparticles) using macroscopic arrays of magnets, and vice versa.