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Spontaneous emulsification, resulting from the assembly and accumulation of surfactants at liquid–liquid interfaces, is an interfacial instability where microdroplets are generated and diffusively spread from the interface until complete emulsification. Here, it is shown that an external magnetic field can modulate the assembly of paramagnetic nanoparticle surfactants (NPSs) at liquid–liquid interfaces to trigger an oversaturation in the areal density of the NPSs at the interface, as evidenced by a marked reduction in the interfacial tension, γ, and corroborated with a magnetostatic continuum theory. Despite the significant reduction in γ, the presence of the magnetic field does not cause stable interfaces to become unstable. Upon rapid removal of the field, however, an explosive ejection of a plume of microdroplets from the surface occurs, a dynamical interfacial instability which is termed explosive emulsification. This explosive event rapidly reduces the areal density of the NPSs to its pre-field level, stabilizing the interface. The ability to externally suppress or trigger the explosive emulsification and controlled generation of tens of thousands of microdroplets, uncovers an efficient energy storage and release process, that has potential applications for controlled and directed delivery of chemicals and remotely controlled soft microrobots, taking advantage of the ferromagnetic nature of themore »microdroplets.« less

Archetypal analysis (AA) is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of AA in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided data are approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of AA. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of AA. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets.