Classical solution for a nonlinear hybrid system modeling combustion in a multilayer porous medium

Combustion processes in porous media have been used by the petroleum engineering industry to extract heavy oil from reservoirs. This study focuses on a one-dimensional nonlinear hybrid system consisting of $n$ reaction–diffusion–convection equations coupled with $n$ ordinary differential equations, which models a combustion front moving through a porous medium with $n$ parallel layers. The state variables are the temperature and fuel concentration in each layer. Coupling occurs in both the reaction function and differential operator coefficients. We prove the existence of a classical solution, first locally and then globally over time, to an initial and boundary value problem for the corresponding system. The proof uses a new approach for combustion problems in porous media. The local solution is obtained by defining an operator in a set of Hölder continuous functions and using Schauder’s fixed-point theorem to find a fixed point as the desired solution. Using Zorn’s lemma, we extend the local solution to a global solution, proving that the first-order spatial derivative of the temperature in each layer is a bounded function.     

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.     

Multilayer Porous Vanadium Nitride Microsheets Anodes for Highly Stable Na-ion Batteries

Sodiumion batteries(SIBs)have attracted intensive attention as promising alternative to lithium-ionbatteries(LIBs)for large scale energy storage systems because of low cost of sodium,similar energy storage mechanism and the reasonable performance.However,it is still a great challenge to search and design a robust structure of anode materials with excellent cycling stability and high rate capability for SIBs.Herein,multilayer porous vanadium nitride(VN)microsheets are synthesized through a facile and scalable hydrothermal synthesis-nitrogenization strategy as an effective anode material for SIBs.The multilayer porous VN microsheets not only offer more active sites for fast Na+insertion/extraction process and short diffusion pathway,but also effectively buffer the volume change of anode due to more space in the multilayer porous structure.The large proportions of capacitive behavior imply that the Na+charge storage depends on the intercalation pseudocapacitive mechanism.The multilayer porous VN microsheets electrodes manifest excellent cycling stability and rate capability,delivering a discharge capacity of 156.1 mA·h/g at 200 mA/g after 100 cycles,and a discharge capacity of 111.9 mA·h/g at 1.0 A/g even after 2300 cycles with the Coulombic efficiency of nearly 100%.     

Foam/Film Alternating Multilayer Structure with High Toughness and Low Thermal Conductivity Prepared via Microlayer Coextrusion

Multilayer membranes prepared via microlayer coextrusion have attracted wide attention due to their unique properties and broad applications. In present study, the foam/film alternating multilayer sheets based on ethylene-vinyl acetate copolymer(EVA) and high-density polyethylene are successfully prepared via microlayer coextrusion. The cells in the sheets are single-cell-array along the foamed EVA layers with uniform cell size. In addition, the effects of layer number and foam relative thickness on morphology, mechanical properties, damping and heat insulation properties are investigated. The cell size decreases significantly with increasing layer number due to the enhanced confine effects. The tensile strength, elongation at break, and heat insulation also increase significantly. However, the mechanical damping properties change little in the observed frequency. Meanwhile, with higher relative thickness of EVA foam, the sheets have lower tensile strength and lower thermal conductivity, while the damping properties are enhanced in a specific frequency scope. The elongation at break of the optimized sample comes to 800% and the thermal conductivity decreases to 61 mW·m~(-1)·K~(-1), which shows high toughness and low thermal conductivity, indicating a possible method for preparing materials with high toughness and heat-insulating properties.     

An unfeasibility view of neural network learning

We define the notion of a continuously differentiable perfect learning algorithm for multilayer neural network architectures and show that such algorithms do not exist provided that the length of the data set exceeds the number of involved parameters and the activation functions are logistic, tanh or sin.     

Effect of surface hydrogenation on the topological properties of multilayer graphene

We have investigated effects of surface hydrogenation on the topological properties of multilayer graphene by using density functional theory calculations and a tight-binding model. Hydrogen adsorption on a dimer site of a surface layer decouples the surface layer from the rest of the layers. Hydrogen adsorption on a nondimer site introduces a band mixing between the hydrogenated graphene and the rest of the graphene layers. The valley Hall effects and spin-valley-resolved Chern numbers of multilayer graphene, calculated as a function of the sublattice potential and the potential perpendicular to the layers, was found to be sensitive to details of inversion symmetry-breaking potentials. While the topological invariant depends on the adsorption site and spin polarization, surface-hydrogenated M-layer graphene was found to be topologically equivalent to (M-1)-layer graphene under inversion symmetry-breaking potentials regardless of the adsorption site.     

Dependence of electronic and optical properties of multilayer SiC and GeC on stacking sequence and external electric field

The electronic and optical properties of different stacked multilayer SiC and GeC are investigated with and without external electric field (EEF). The band gaps of multilayer SiC and GeC are found smaller than that of monolayer SiC and GeC due to the interlayer coupling effect. When EEF is applied, the direct band gaps (ΔK–M) of multilayer SiC and direct band gaps (ΔK–K) of multilayer GeC all turn to indirect band gaps (ΔK–G) as the band at the G point drops dramatically toward zero. The imaginary part ε₂(ω)s of multilayer SiC and GeC show that new absorption peaks between 2–5 eV appear when the polarized direction is perpendicular to the layer plane, and new absorption peaks in infrared region appear as the EEF is higher than a certain point when the polarized direction is parallel to the layer plane. Our calculations reveal that different stacking sequences and EEF can provide a wide tunable band structures and optical properties for multilayer SiC and GeC.     

The LS1 model for delamination propagation in multilayered materials at 0°/θ° interfaces: A comparison between experimental and finite elements strain energy release rates

The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only depends on the stacking sequence and the position of delamination is presented.