Peeling from a patterned thin elastic film

Inspired by the observation that many naturally occurring adhesives arise as textured thin films, we consider the displacement controlled peeling of a flexible plate from an incision-patterned thin adhesive elastic layer. We find that crack initiation from an incision on the film occurs at a load much higher than that required to propagate it on a smooth adhesive surface; multiple incisions thus cause the crack to propagate intermittently. Microscopically, this mode of crack initiation and propagation in geometrically confined thin adhesive films is related to the nucleation of cavitation bubbles behind the incision which must grow and coalesce before a viable crack propagates. Our theoretical analysis allows us to rationalize these experimental observations qualitatively and quantitatively and suggests a simple design criterion for increasing the interfacial fracture toughness of adhesive films.Comment: 8 pages, To appear in Proceedings of Royal Society London, Ser.

Network Structure, Topology and Dynamics in Generalized Models of Synchronization

We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state, interconnected oscillators synchronize in stages, revealing network's underlying community structure. Traditional models of synchronization assume that interactions between nodes are mediated by a conservative process, such as diffusion. However, social and biological processes are often non-conservative. We propose a new model of synchronization in a network of oscillators coupled via non-conservative processes. We study dynamics of synchronization of a synthetic and real-world networks and show that different synchronization models reveal different structures within the same network

Interference measurements of non-Abelian e/4 & Abelian e/2 quasiparticle braiding

The quantum Hall states at filling factors $\nu=5/2$ and $7/2$ are expected to have Abelian charge $e/2$ quasiparticles and non-Abelian charge $e/4$ quasiparticles. For the first time we report experimental evidence for the non-Abelian nature of excitations at $\nu=7/2$ and examine the fermion parity, a topological quantum number of an even number of non-Abelian quasiparticles, by measuring resistance oscillations as a function of magnetic field in Fabry-P\'erot interferometers using new high purity heterostructures. The phase of observed $e/4$ oscillations is reproducible and stable over long times (hours) near $\nu=5/2$ and $7/2$, indicating stability of the fermion parity. When phase fluctuations are observed, they are predominantly $\pi$ phase flips, consistent with fermion parity change. We also examine lower-frequency oscillations attributable to Abelian interference processes in both states. Taken together, these results constitute new evidence for the non-Abelian nature of $e/4$ quasiparticles; the observed life-time of their combined fermion parity further strengthens the case for their utility for topological quantum computation.Comment: A significantly revised version; 54 double-column pages containing 14 pages of main text + Supplementary Materials. The figures, which include a number of new figures, are now incorporated into the tex