On a Lemma Arising in the Solution of Waring’s Problem

Siberian Mathematical Journal - We give a simple proof of one assertion used in solving Waring’s problem.     

基于有限元的区域分解方法在永磁聚焦系统仿真中的应用

随着计算机技术以及并行求解技术的发展,区域分解方法越来越多地应用于计算电磁学的各个领域.针对微波管中的永磁聚焦系统仿真,该文提出一种基于有限元的非重叠区域分解方法,其引入一种新型传输条件,并采用内罚的方式推导出有限元弱形式.该区域分解法的最大优势是不需要引入多余的未知量,并且最终集成的有限元矩阵满足对称正定性,适合采用预处理共轭梯度法进行矩阵方程的求解.该文仿真了多个微波管永磁聚焦系统,并与商业软件Maxwell进行了详细的对比,结果表明所提出的区域分解方法和Maxwell精度相当,却拥有着更加优越的计算性能.     

Spatiotemporal Magnetocaloric Microenvironment for Guiding the Fate of Biodegradable Polymer Implants

The degradation behavior of implants is significantly important for bone repair. However, it is still unprocurable to spatiotemporally regulate the degradation of the implants to match bone ingrowth. In this paper, a magneto-controlled biodegradation model is established to explore the degradation behavior of magnetic scaffolds in a magnetothermal microenvironment generated by an alternating magnetic field (AMF). The results demonstrate that the scaffolds can be heated by magnetic nanoparticles (NPs) under AMF, which dramatically accelerated scaffold degradation. Especially, magnetic NPs modified by oleic acid with a better interface compatibility exhibit a greater heating efficiency to further facilitate the degradation. Furthermore, the molecular dynamics simulations reveal that the enhanced motion correlation between magnetic NPs and polymer matrix can accelerate the energy transfer. As a proof-of-concept, the feasibility of magneto-controlled degradation for implants is demonstrated, and an optimizing strategy for better heating efficiency of nanomaterials is provided, which may have great instructive significance for clinical medicine.     

Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision

Journal of Fourier Analysis and Applications - We develop a theory of Sobolev orthogonal polynomials on the Sierpiński gasket ( $$SG$$ ), which is a fractal set that can be viewed as a limit...     

Nacre-Inspired,Liquid Metal-Based Ultrasensitive Electronic Skin by Spatially Regulated Cracking Strategy

The realization of liquid metal-based wearable systems will be a milestone toward high-performance, integrated electronic skin. However, despite the revolutionary progress achieved in many other components of electronic skin, liquid metal-based flexible sensors still suffer from poor sensitivity due to the insufficient resistance change of liquid metal to deformation. Herein, a nacre-inspired architecture composed of a biphasic pattern (liquid metal with Cr/Cu underlayer) as “bricks” and strain-sensitive Ag film as “mortar” is developed, which breaks the long-standing sensitivity bottleneck of liquid metal-based electronic skin. With 2 orders of magnitude of sensitivity amplification while maintaining wide (>85%) working range, for the first time, liquid metal-based strain sensors rival the state-of-art counterparts. This liquid metal composite features spatially regulated cracking behavior. On the one hand, hard Cr cells locally modulate the strain distribution, which avoids premature cut-through cracks and prolongs the defect propagation in the adjacent Ag film. On the other hand, the separated liquid metal cells prevent unfavorable continuous liquid-metal paths and create crack-free regions during strain. Demonstrated in diverse scenarios, the proposed design concept may spark more applications of ultrasensitive liquid metal-based electronic skins, and reveals a pathway for sensor development via crack engineering.     

Optimization of the Ambulance Fleet Location and Relocation

Journal of Applied and Industrial Mathematics - We study the problem of optimal location of the ambulance fleet at the base stations. The objective is to minimize the average waiting time for...     

Dynamic mechanism of epileptic seizures generation and propagation after ischemic stroke

Nonlinear Dynamics - Epilepsy is the second largest neurological disease which seriously threatens human life and health. The one important reason of inducing epileptic seizures is ischemic stroke...     

Space-Confined Atomic Clusters Catalyze Superassembly of Silicon Nanodots within Carbon Frameworks for Use in Lithium-Ion Batteries

Incorporating nanoscale Si into a carbon matrix with high dispersity is desirable for the preparation of lithium-ion batteries (LIBs) but remains challenging. A space-confined catalytic strategy is proposed for direct superassembly of Si nanodots within a carbon (Si NDs⊂C) framework by copyrolysis of triphenyltin hydride (TPT) and diphenylsilane (DPS), where Sn atomic clusters created from TPT pyrolysis serve as the catalyst for DPS pyrolysis and Si catalytic growth. The use of Sn atomic cluster catalysts alters the reaction pathway to avoid SiC generation and enable formation of Si NDs with reduced dimensions. A typical Si NDs⊂C framework demonstrates a remarkable comprehensive performance comparable to other Si-based high-performance half LIBs, and higher energy densities compared to commercial full LIBs, as a consequence of the high dispersity of Si NDs with low lithiation stress. Supported by mechanic simulations, this study paves the way for construction of Si/C composites suitable for applications in future energy technologies.     

Sandwich-like Catalyst–Carbon–Catalyst Trilayer Structure as a Compact 2D Host for Highly Stable Lithium–Sulfur Batteries

Herein, we propose the construction of a sandwich-structured host filled with continuous 2D catalysis–conduction interfaces. This MoN-C-MoN trilayer architecture causes the strong conformal adsorption of S/Li₂S_x and its high-efficiency conversion on the two-sided nitride polar surfaces, which are supplied with high-flux electron transfer from the buried carbon interlayer. The 3D self-assembly of these 2D sandwich structures further reinforces the interconnection of conductive and catalytic networks. The maximized exposure of adsorptive/catalytic planes endows the MoN-C@S electrode with excellent cycling stability and high rate performance even under high S loading and low host surface area. The high conductivity of this trilayer texture does not compromise the capacity retention after the S content is increased. Such a job-synergistic mode between catalytic and conductive functions guarantees the homogeneous deposition of S/Li₂S_x, and avoids thick and devitalized accumulation (electrode passivation) even after high-rate and long-term cycling.