On the convergence of the usual perturbative expansions

The study of the convergence of power series expansions of energy eigenvalues for anharmonic oscillators in quantum mechanics differs from general understanding, in the case of quasi-exactly solvable potentials. They provide examples of expansions with finite radius and suggest techniques useful to analyze more generic potentials.Comment: 11 pages, Latex (1 EPS figure included

Realizing the physics of motile cilia synchronization with driven colloids

Cilia and flagella in biological systems often show large scale cooperative behaviors such as the synchronization of their beats in "metachronal waves". These are beautiful examples of emergent dynamics in biology, and are essential for life, allowing diverse processes from the motility of eukaryotic microorganisms, to nutrient transport and clearance of pathogens from mammalian airways. How these collective states arise is not fully understood, but it is clear that individual cilia interact mechanically,and that a strong and long ranged component of the coupling is mediated by the viscous fluid. We review here the work by ourselves and others aimed at understanding the behavior of hydrodynamically coupled systems, and particularly a set of results that have been obtained both experimentally and theoretically by studying actively driven colloidal systems. In these controlled scenarios, it is possible to selectively test aspects of the living motile cilia, such as the geometrical arrangement, the effects of the driving profile and the distance to no-slip boundaries. We outline and give examples of how it is possible to link model systems to observations on living systems, which can be made on microorganisms, on cell cultures or on tissue sections. This area of research has clear clinical application in the long term, as severe pathologies are associated with compromised cilia function in humans.Comment: 31 pages, to appear in Annual Review of Condensed Matter Physic

Universality of the Tearing Phase in Matrix Models

The spontaneous symmetry breaking associated to the tearing of a random surface, where large dynamical holes fill the surface, was recently analized obtaining a non-universal critical exponent on a border phase. Here the issue of universality is explained by an independent analysis. The one hole sector of the model is useful to manifest the origin of the (limited) non-universal behaviour, that is the existence of two inequivalent critical points.Comment: 9 pages, 1 figure non include

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, \emph{multivalent interactions} mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.Comment: 63 pages, revie