Sparsity-based single-shot subwavelength coherent diffractive imaging.

Coherent Diffractive Imaging (CDI) is an algorithmic imaging technique where intricate features are reconstructed from measurements of the freely diffracting intensity pattern. An important goal of such lensless imaging methods is to study the structure of molecules that cannot be crystallized. Ideally, one would want to perform CDI at the highest achievable spatial resolution and in a single-shot measurement such that it could be applied to imaging of ultrafast events. However, the resolution of current CDI techniques is limited by the diffraction limit, hence they cannot resolve features smaller than one half the wavelength of the illuminating light. Here, we present sparsity-based single-shot subwavelength resolution CDI: algorithmic reconstruction of subwavelength features from far-field intensity patterns, at a resolution several times better than the diffraction limit. This work paves the way for subwavelength CDI at ultrafast rates, and it can considerably improve the CDI resolution with X-ray free-electron lasers and high harmonics.

Instability and equilibration of centrifugally stable stratified Taylor-Couette flow.

The flow between two concentric cylinders, V(r), is studied analytically and computationally for a fluid with stable axial density stratification. A sufficient condition for linear, inviscid instability is d(V/r)(2)/dr<0 (i.e., all anticyclonically sheared flows) rather than the Rayleigh condition for centrifugal instability, d(Vr)(2)/dr<0. This implies a far wider range of instability than previously identified. The instability persists with finite viscosity and nonlinearity, leading to chaos and fully developed turbulence through a sequence of bifurcations. Laboratory tests are feasible and desirable.

Anisotropy and coherent vortex structures in planetary turbulence.

High-resolution numerical simulations were made of unforced, planetary-scale fluid dynamics. In particular, the simulation was based on the quasi-geostrophic equations for a Boussinesq fluid in a uniformly rotating and stably stratified environment, which is an idealization for large regions of either the atmosphere or ocean. The solutions show significant discrepancies from the long-standing theoretical prediction of isotropy. The discrepancies are associated with the self-organization of the flow into a large population of coherent vortices. Their chaotic interactions govern the subsequent evolution of the flow toward a final configuration that is nonturbulent.