Learn More
Soon after the crowd streamed on to London's Millennium Bridge on the day it opened, the bridge started to sway from side to side: many pedestrians fell spontaneously into step with the bridge's vibrations, inadvertently amplifying them. Here we model this unexpected and now notorious phenomenon--which was not due to the bridge's innovative design as was(More)
Synchronization and wave formation in one-dimensional ciliary arrays are studied analytically and numerically. We develop a simple model for ciliary motion that is complex enough to describe well the behavior of beating cilia but simple enough to study collective effects analytically. Beating cilia are described as phase oscillators moving on circular(More)
Biological membranes have been proposed to contain microdomains of a specific lipid composition, in which distinct groups of proteins are clustered. Flotillin-like proteins are conserved between pro-and eukaryotes, play an important function in several eukaryotic and bacterial cells, and define in vertebrates a type of so-called detergent-resistant(More)
Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the(More)
Generally, the motion of fluids is smooth and laminar at low speeds but becomes highly disordered and turbulent as the velocity increases. The transition from laminar to turbulent flow can involve a sequence of instabilities in which the system realizes progressively more complicated states, or it can occur suddenly. Once the transition has taken place, it(More)
Discrete symmetries of dynamical ows give rise to relations between periodic orbits, reduce the dynamics to a fundamental domain, and lead to fac-torizations of zeta functions. These factorizations in turn reduce the labor and improve the convergence of cycle expansions for classical and quantum spectra associated with the ow. In this paper the general(More)
We provide an overview of current techniques and typical applications of numerical bifurcation analysis in fluid dynamical problems. Many of these problems are characterized by high-dimensional dynamical systems which undergo transitions as parameters are changed. The computation of the critical conditions associated with these transitions, popularly(More)
We consider the dynamics of a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which fluid between two free-slip walls experiences a sinusoidal body force. The model contains nine modes, most of which have a direct hydrodynamical interpretation. We analyze the stationary states and(More)
On its opening day the London Millennium footbridge experienced unexpected large amplitude wobbling subsequent to the migration of pedestrians onto the bridge. Modeling the stepping of the pedestrians on the bridge as phase oscillators, we obtain a model for the combined dynamics of people and the bridge that is analytically tractable. It provides(More)