Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded ...

This paper presents a collaborative control strategy designed to enable a team of robots to track attracting Lagrangian coherent structures (LCS) and unstable manifolds in two-dimensional flows. Tracking LCS in dynamical systems is important for many applications such as planning energy optimal paths in the ocean and predicting various physical and biological processes in the ocean. Similar to ...

Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lag...

The radiance structure inside the glass sphere (Figure 1) results from total internal reflection that allows light to reach points that are otherwise in shadow due to refraction perturbing light paths towards the center. The hard boundaries of these structures mark the narrow stripes where light travels around the sphere several times by total internal reflection, after it just managed to enter...

Exact coherent structures are three-dimensional, nonlinear traveling wave solutions of the Navier-Stokes equations. These solutions are typically unstable from onset, yet they capture the basic statistical and structural features of low Reynolds number turbulent shear flows remarkably well. These exact coherent structures have now been found in all canonical shear flows: plane Couette, Poiseuil...

The dynamics of coherent structures present in real-world environmental data is analyzed. The method developed in this Paper combines the power of the Proper Orthogonal Decomposition (POD) technique to identify these coherent structures in experimental data sets, and its optimality in providing Galerkin basis for projecting and reducing complex dynamical models. The POD basis used is the one ob...

We present a novel approach for modeling the reflectance, transmittance and absorption depth profile of thin-film multilayer structures such as solar cells. Our model is based on the net-radiation method adapted for coherent calculations and is highly flexible while using a simple algorithm. We demonstrate that as a result arbitrary multilayer structures with coherent, partly coherent and incoh...

We analyze the coherent-structure interaction and the formation of bound states in active dispersive-dissipative nonlinear media using a viscous film coating a vertical fiber as a prototype. The coherent structures in this case are droplike pulses that dominate the evolution of the film. We study experimentally the interaction dynamics and show evidence for formation of bound states. A theoreti...

We analyze vorticity fields obtained from direct numerical simulations (DNS) of statistically stationary two-dimensional turbulence where the forcing is done in wavelet space. We introduce a new eduction method for extracting coherent structures from two-dimensional turbulent flows. Using a nonlinear wavelet technique based on an objective universal threshold we separate the vorticity field int...