This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: Laplacian coordinates of the boundary curve and local area of the shape interior, which are together represented in a non-quadric energy function. An iterative Gauss-Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are hard to achieve with previous linear least squares methods. Besides preserving local shape properties, we also introduce a scheme to preserve the global area of the shape which is useful for deforming incompressible objects.

A simple and practical manganese(iii)-promoted tandem phosphinoylation/cyclization of 2-arylindoles/2-arylbenzimidazoles with disubstituted phosphine oxides was developed.

Monomer design plays an important role in the development of polymers with desired thermal properties and chemical recyclability. Here we prepared a class of sevenmembered ring carbonates containing trans-cyclohexyl fused rings. These monomers showed excellent activity for ring-opening polymerization (ROP) with turnover frequency (TOF) up to 6 × 10 5 h −1 and catalyst loading down to 50 ppm, which yielded highmolecular-weight polycarbonates (M n up to 673 kg/mol) with great thermostability (T d > 300 °C). Ultimately, the resulting polycarbonates can completely depolymerize into their corresponding cyclic dimers that can repolymerize to synthesize the starting polymers in moderate yields, demonstrating a potential route to achieve chemical recycling. Postfunctionalization of the unsaturated polycarbonate was conducted through cross-linking reaction and "click" reaction under UV irradiation.

We systematically investigate the equilibrium shapes of droplets deposited on a set of chemically striped patterned surfaces by using an Allen–Cahn-type phase-field model. Varying the widths of the stripes d, the volume V, as well as the initial positions of the droplets, we release the droplets on the top of the surfaces and observe the final droplet shapes. It is found that there are either one or two equilibrium shapes for a fixed ratio of d/V 1/3 and each equilibrium shape corresponds to an energy minimum state. The aspect ratio of the droplets ξ shows a periodic oscillation behavior with a decreasing amplitude as d/V 1/3 decreases, similar to the stick–slip–jump movement of a slowly condensing droplet on a chemically striped patterned surface. Additionally, by comparing the movements of slowly evaporating and condensing droplets, we have observed a hysteresis phenomenon, which reveals that the final shapes of droplets also rely on the moving paths. Through modifying the dynamic contact angle boundary condition, the contact line movements of droplets under condensation and evaporation, which are far from equilibrium, are addressed.