Calculating the evolution of a passive scalar in turbulent flow requires resolving intricate stretching and folding field. Traditionally, this that computational mesh is much smaller than smallest scale concentration Here we demonstrate use machine learning to learn discretizations governing equation give accurate computations with coarser mesh. The model learns universal small structures field...

Given a sheet of paper and a prescribed folding of its boundary, is there a way to fold the paper’s interior without stretching so that the boundary lines up with the prescribed boundary folding? For polygonal boundaries nonexpansively folded at finitely many points, we prove that a consistent isometric mapping of the polygon interior always exists and is computable in polynomial time.

Thermal unfolding of proteins is compared to folding and mechanical stretching in a simple topology-based dynamical model. We define the unfolding time and demonstrate its low-temperature divergence. Below a characteristic temperature, contacts break at separate time scales and unfolding proceeds approximately in a way reverse to folding. Features in these scenarios agree with experiments and a...

The short wave instability on corotating vortex filaments is investigated. It is shown that the short wave instability always occurs on corotating vortex filaments of fixed core structure. Moreover, when the interfilament distance is smaller than or comparable to the core size, vortex filaments produce short wave unstable modes which lead to wild stretching and folding; when vortex filaments ar...

Fascinating and elegant shapes may be folded from a single planar sheet of material without stretching, tearing or cutting, if one incorporates curved folds into the design. We present an optimizationbased computational framework for design and digital reconstruction of surfaces which can be produced by curved folding. Our work not only contributes to applications in architecture and industrial...

When fluids flow through straight channels sustained turbulence occurs only at high Reynolds numbers [typically [Formula: see text]]. It is difficult to mix multiple flowing a channel in the low number laminar regime [[Formula: text]] because absence of turbulence, mixing between component primarily via slow molecular diffusion process. This Letter reports simple way significantly enhance (in o...