Polymer 4D printing: Advanced shape-change and beyond

4D printing is an exciting branch of additive manufacturing. It relies on established 3D printing techniques to fabricate objects in much the same way. However, structures which fall into the 4D printed category have the ability to change with time, hence the “extra dimension.” The common perception of 4D printed objects is that of macroscopic single-material structures limited to point-to-point shape change only, in response to either heat or water. However, in the area of polymer 4D printing, recent advancements challenge this understanding. A host of new polymeric materials have been designed which display a variety of wonderful effects brought about by unconventional stimuli, and advanced additive manufacturing techniques have been developed to accommodate them. As a result, the horizons of polymer 4D printing have been broadened beyond what was initially thought possible. In this review, we showcase the many studies which evolve the very definition of polymer 4D printing, and reveal emerging areas of research integral to its advancement.     

Electro-assisted Molecular Assembly Giving Atomic-Scale Catalytic Active-Site Detection

The artificially accurate design of nonmetal electrocatalysts’ active site has been a huge challenge because no pure active species with the specific structure could be strictly controlled by traditional synthetic methods. Species with a multiconfiguration in the catalyst hinder identification of the active site and the subsequent comprehension of the reaction mechanism. We have developed a novel electro-assisted molecular assembly strategy to obtain a pure pentagon ring on perfect graphene avoiding other reconstructed structures. More importantly, the active atom was confirmed by the subtle passivation process as the topmost carbon atom. Recognition of the carbon-defect electrocatalysis reaction mechanism was first downsized to the single-atom scale from the experimental perspective. It is expected that this innovative electro-assisted molecular assembly strategy could be extensively applied in the active structure-controlled synthesis of nonmetal electrocatalysts and verification of the exact active atom.     

A microfluidics-dispensing-printing strategy for Janus photonic crystal microspheres towards smart patterned displays

From the implementation point of view, the printable magnetic Janus colloidal photonic crystals (CPCs) microspheres are highly desirable. Herein, we developed a dispensing-printing strategy for magnetic Janus CPCs display via a microfluidics-automatic printing system. Monodisperse core/shell colloidal particles and magnetic Fe₃O₄ nanoparticles precursor serve as inks. Based on the equilibrium of three-phase interfacial tensions, Janus structure is successfully formed, followed by UV irradiation and self-assembly of colloid particle to generate magnetic Janus CPCs microspheres. Notably, this method shows distinct superiority with highly uniform Janus CPCs structure, where the TMPTA/Fe₃O₄ hemisphere is in the bottom side while CPCs hemisphere is in the top side. Thus, by using Janus CPCs microspheres with two different structural colors as pixel points, a pattern with red flower and green leaf is achieved. Moreover, 1D linear Janus CPCs pattern encapsulated by hydrogel is also fabricated. Both the color and the shape can be changed under the traction of magnets, showing great potentials in flexible smart displays. We believe this work not only offers a new feasible pathway to construct magnetic Janus CPCs patterns by a dispensing-printable fashion, but also provides new opportunities for flexible and smart displays.     

Interface and defects engineering for multilayer laser coatings

High-reflective multilayer laser coatings are widely used in advanced optical systems from high power laser facilities to high precision metrology systems. However, the real interface quality and defects will significantly affect absorption/scattering losses and laser induced damage thresholds of multilayer coatings. With the recent advances in the control of coating design and deposition processes, these coating properties can be significantly improved when properly engineered the interface and defects. This paper reviews the recent progress in the physics of laser damage, optical losses and environmental stability involved in multilayer reflective coatings for high power nanosecond near-infrared lasers. We first provide an overview of the layer growth mechanisms, ways to control the microstructures and reduce layer roughness, as well as the nature of defects which are critical to the optical loss and laser induced damage. Then an overview of interface engineering based on the design of coating structure and the regulation of deposition materials reveals their ability to improve the laser induced damage threshold, reduce the backscattering, and realize the desirable properties of environmental stability and exceptional multifunctionality. Moreover, we describe the recent progress in the laser damage and scattering mechanism of nodule defects and give the approaches to suppress the defect-induced damage and scattering of the multilayer laser coatings. Finally, the present challenges and limitations of high-performance multilayer laser coatings are highlighted, along with the comments on likely trends in future.     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Well-posedness of two pseudo-parabolic problems for electrical conduction in heterogeneous media

We prove a well-posedness result for two pseudo-parabolic problems, which can be seen as two models for the same electrical conduction phenomenon in heterogeneous media, neglecting the magnetic field. One of the problems is the concentration limit of the other one, when the thickness of the dielectric inclusions goes to zero. The concentrated problem involves a transmission condition through interfaces, which is mediated by a suitable Laplace-Beltrami type equation.     

Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.