We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles. The drive towards miniaturization in technology is demanding for increasingly thinner components, raising new mechanical challenges [1]. Thin films are, however, unstable to boundary or substrate-induced compressive loads: moderate compression results in regular wrinkling [2][3][4][5][6] while further confinement can lead to crumpling [7,8]. Regions of stress focusing can be a hindrance, acting as nucleation points for mechanical failure. Conversely, these deformations can be exploited constructively for tunable thin structures. For example, singular points of deformation dramatically affect the electronic properties of graphene [9].Here, we show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles, from strained suspended graphene to ordinary hanging curtains. We develop a formalism based on wrinklons, a localized transition zone in the merging of two wrinkles, as building blocks to describe these wrinkled patterns.To illustrate this hierarchical pattern, in Fig. 1(a), we show a wrinkled graphene sheet along with an ordinary hanged curtain. These patterns are also similar to the selfsimilar circular patterns first reported by Argon et al. for the blistering of thin films adhering on a thick substrate [10]. The diversity and complexity of those systems, characterized by various chemical and physical conditions, could suggest, a priori, that the underlying mechanisms governing the formation of these patterns are unrelated. However, these systems can be depicted, independently from the details of the experiments, as a thin sheet constrained at one edge while the others are free to adapt their morphology. These constraints can take the form of an imposed wavelength at one edge or just the requirement that it should remain flat.

The ability to create a 3D tissue structure from individual cells and then to stimulate it at will is a major goal for both the biophysics and regenerative medicine communities. Here we show an integrated set of magnetic techniques that meet this challenge using embryonic stem cells (ESCs). We assessed the impact of magnetic nanoparticles internalization on ESCs viability, proliferation, pluripotency and differentiation profiles. We developed magnetic attractors capable of aggregating the cells remotely into a 3D embryoid body. This magnetic approach to embryoid body formation has no discernible impact on ESC differentiation pathways, as compared to the hanging drop method. It is also the base of the final magnetic device, composed of opposing magnetic attractors in order to form embryoid bodies in situ, then stretch them, and mechanically stimulate them at will. These stretched and cyclic purely mechanical stimulations were sufficient to drive ESCs differentiation towards the mesodermal cardiac pathway.