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Budgets of turbulent kinetic energy (TKE) and turbulent potential energy (TPE) at different scales $\ell$ in sheared, stably stratified turbulence are analysed using a filtering approach. Competing effects in the flow are considered, along with the physical mechanisms governing the energy fluxes between scales, and the budgets are used to analyse data from direct numerical simulation at buoyancy Reynolds number $Re_b=O(100)$ . The mean TKE exceeds the TPE by an order of magnitude at the large scales, with the difference reducing as $\ell$ is decreased. At larger scales, buoyancy is never observed to be positive, with buoyancy always converting TKE to TPE. As $\ell$ is decreased, the probability of locally convecting regions increases, though it remains small at scales down to the Ozmidov scale. The TKE and TPE fluxes between scales are both downscale on average, and their instantaneous values are correlated positively, but not strongly so, and this occurs due to the different physical mechanisms that govern these fluxes. Moreover, the contributions to these fluxes arising from the sub-grid fields are shown to be significant, in addition to the filtered scale contributions associated with the processes of strain self-amplification, vortex stretching and density gradient amplification. Probability density functions (PDFs) of the $Q,R$ invariants of the filtered velocity gradient are considered and show that as $\ell$ increases, the sheared-drop shape of the PDF becomes less pronounced and the PDF becomes more symmetric about $R=0$ . 

In this work, we introduce a roll-to-roll system that can continuously print three-dimensional (3D) periodic nanostructures over large areas. This approach is based on Langmuir-Blodgett assembly of colloidal nanospheres, which diffract normal incident light to create a complex intensity pattern for near-field nanolithography. The geometry of the 3D nanostructure is defined by the Talbot effect and can be precisely designed by tuning the ratio of the nanosphere diameter to the exposure wavelength. Using this system, we have demonstrated patterning of 3D photonic crystals with a 500 nm period on a 50 × 200 mm²flexible substrate, with a system throughput of 3 mm/s. The patterning yield is quantitatively analyzed by an automated electron beam inspection method, demonstrating long-term repeatability of an up to 88% yield over a 4-month period. The inspection method can also be employed to examine pattern uniformity, achieving an average yield of up to 78.6% over full substrate areas. The proposed patterning method is highly versatile and scalable as a nanomanufacturing platform and can find application in nanophotonics, nanoarchitected materials, and multifunctional nanostructures.

 

Dearomative cycloaddition reactions represent an ideal means of converting flat arenes into three-dimensional architectures of increasing interest in medicinal chemistry. Quinolines, isoquinolines, and quinazolines, despite containing latent diene and alkene subunits, are scarcely applied in cycloaddition reactions because of the inherent low reactivity of aromatic systems and selectivity challenges. Here, we disclose an energy transfer–mediated, highly regio- and diastereoselective intermolecular [4 + 2] dearomative cycloaddition reaction of these bicyclic azaarenes with a plethora of electronically diverse alkenes. This approach bypasses the general reactivity and selectivity issues, thereby providing various bridged polycycles that previously have been inaccessible or required elaborate synthetic efforts. Computational studies with density functional theory elucidate the mechanism and origins of the observed regio- and diastereoselectivities.