Study on asymptotic analytical solutions using HAM for strongly nonlinear vibrations of a restrained cantilever beam with an intermediate lumped mass

Presented herein is to establish the asymptotic analytical solutions for the fifth-order Duffing type temporal problem having strongly inertial and static nonlinearities. Such a problem corresponds to the strongly nonlinear vibrations of an elastically restrained beam with a lumped mass. Taking into consideration of the inextensibility condition and using an assumed single mode Lagrangian method, the single-degree-of-freedom ordinary differential equation can be derived from the governing equations of the beam model. Various parameters of the nonlinear unimodal temporal equation stand for different vibration modes of inextensible cantilever beam. By imposing the homotopy analysis method (HAM), we establish the asymptotic analytical approximations for solving the fifth-order nonlinear unimodal temporal problem. Within this research framework, both the frequencies and periodic solutions of the nonlinear unimodal temporal equation can be explicitly and analytically formulated. For verification, numerical comparisons are conducted between the results obtained by the homotopy analysis and numerical integration methods. Illustrative examples are selected to demonstrate the accuracy and correctness of this approach. Besides, the optimal HAM approach is introduced to accelerate the convergence of solutions.     

The global attractor of a non-local PDE model with delay for population dynamics in ℝ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

In this paper, we consider a non-local PDE model with delay for population dynamics in ℝ ⁿ . First, we prove the existence and uniqueness of weak solutions under some suitable decayed assumptions on non-local term at infinity. Then, we obtain the global attractor by proving ω-limit compactness property of the solution operator semigroup.     

镧掺杂锡酸钡/多壁碳纳米管改性隔膜的制备及其在锂硫电池中的应用

通过将共沉淀法制备的钙钛矿型氧化物镧掺杂锡酸钡(LBSO)与多壁碳纳米管(MCNT)混合均匀,制成浆料,并利用刮涂法将其涂布在商业隔膜Celgard 2500(PP)表面构筑阻挡层,获得改性隔膜(LBSO/MCNT/PP)。基于该改性隔膜的锂硫电池在0.1C下具有高达1 433 mAh·g^-1的初始放电比容量,1C时300次循环后每圈容量衰减率为0.114%;当电流密度提高到3C时,仍具有764 mAh·g^-1的放电比容量,表现出优良的倍率性能和循环稳定性,这主要是由于该阻挡层能够有效抑制多硫化物的穿梭。     

A preconditioned general two-step modulus-based matrix splitting iteration method for linear complementarity problems of H+-matrices

Numerical Algorithms - In this paper, we present a preconditioned general two-step modulus-based iteration method to solve a class of linear complementarity problems. Its convergence theory is...     

A Partial First-Order Affine-Scaling Method

We present a partial first-order affine-scaling method for solving smooth optimization with linear inequality constraints. At each iteration, the algorithm considers a subset of the constraints to reduce the complexity. We prove the global convergence of the algorithm for general smooth objective functions, and show it converges at sublinear rate when the objective function is quadratic. Numerical experiments indicate that our algorithm is efficient.     

Immediate regularization of measure-type population densities in a two-dimensional chemotaxis system with signal consumption

This paper deals with the Neumann initial-boundary value problem for a classical chemotaxis system with signal consumption in a disk.In contrast to previous studies which have established a comprehensive theory of global classical solutions for suitably regular nonnegative initial data,the focus in the present work is on the question to which extent initially prescribed singularities can be regularized despite the presence of the nonlinear cross-diffusive interaction.The main result in this paper asserts that at least in the framework of radial solutions immediate regularization occurs under an essentially optimal condition on the initial distribution of the population density.More precisely,it will turn out that for any radially symmetric initial data belonging to the space of regular signed Borel measures for the population density and to L² for the signal density,there exists a classical solution to the Neumann initial-boundary value problem,which is smooth and approaches the given initial data in an appropriate trace sense.     

广元千佛崖石窟石刻彩妆颜料的分析

四川省广元千佛崖石窟是四川境内最大的石窟寺和摩崖造像群,承载着古代社会的历史信息,对研究当时的政治、文化和社会生活意义重大。千佛崖石窟在自然环境因素的长期作用下,目前受到多种严重病害的侵蚀,亟待保护。为了获取石刻彩妆的成分与工艺信息以支撑彩妆的保护工作,应用X射线衍射分析、剖面显微分析、扫描电镜能谱分析、激光拉曼光谱分析等方法,对广元千佛崖8处洞窟的已脱落彩妆颜料层样品进行了分析。X射线衍射分析鉴定出了铁红(Fe₂O₃)、朱砂 (HgS)、铅丹(Pb₃O₄)、炭黑等颜料成分,以及铅白 (PbSO₄)、石膏(CaSO₄·2H₂O)、长石、二氧化硅等打底层和岩体的组分,验证了样品脱落的原因是岩体的劣化。剖面显微分析和扫描电镜能谱分析表明,不同洞窟的彩妆制作工艺有区别,有的颜料直接施加在岩体表面,有的则在颜料层和岩体间有一层主要为硫酸铅的打底层;样品表面蓝绿色颜料的含量很少,仅通过激光共聚焦显微拉曼光谱成功地识别出来,其鉴定结果为蓝铜矾[Cu₄SO₄(OH)₆·2H₂O]。蓝铜矾作为颜料使用的报道很少。由于其矿物含量较少但分布广泛,古代一般不将其分离出来单独使用,而人工合成的碱式硫酸铜类颜料布勒门绿（Bremen green）出现于18世纪-19世纪,如果有纯碱式硫酸铜单独使用的情况出现,就意味着有近现代重绘的可能性,将有助于彩绘类文物保存历史的判断。该研究不仅为千佛崖石刻彩妆的保护提供了依据,丰富了文化遗产中使用蓝铜矾颜料的案例,更对彩妆的保存历史研究有潜在价值。     

Nanoscale gap filling for phase change material by pulsed deposition and inductively coupled plasma etching

The gap filling of phase change material has become a critical module in the fabrication process of phase change random access memory (PCRAM) as the device continues to scale down to 45 nm and below. However, conventional physical vapor deposition process cannot meet the nanoscale gap fill requirement anymore. In this study, we found that the pulsed deposition followed by inductively coupled plasma etching process showed distinctly better gap filling capability and scalability than single-step deposition process. The gap filling mechanism of the deposit–etch–deposit (DED) process was briefly discussed. The film redeposition during etching step was the key ingredient of gap filling improvement. We achieved void free gap filling of phase change material on the 30 nm via with aspect ratio of 1:1 by two-cycle DED process. The results provided a rather comprehensive insight into the mechanism of DED process and proposed a potential gap filling solution for 45 nm and below technology nodes for PCRAM.     

二维正弦离散映射的分岔和吸引子

由一个正弦映射和一个三次方映射通过非线性耦合,构成一个新的二维正弦离散映射. 基于此二维正弦离散映射得到系统的不动点以及相应的特征值,分析了系统的稳定性,研究了系统的复杂非线性动力学行为及其吸引子的演变过程. 研究结果表明：此二维正弦离散映射中存在复杂的对称性破缺分岔、Hopf分岔、倍周期分岔和周期振荡快慢效应等非线性物理现象. 进一步根据控制变量变化时系统的分岔图、Lyapunov指数图和相轨迹图分析了系统的分岔模式共存、快慢周期振荡及其吸引子的演变过程,通过数值仿真验证了理论分析的正确性. 关键词： 正弦离散映射 对称性破缺分岔 Hopf分岔 吸引子     

色散补偿光子晶体光纤结构参数对其色散的影响

光子晶体光纤由于其灵活可调的色散特性用作色散补偿具有极大的应用潜力. 设计了一种色散补偿光子晶体光纤, 并运用频域有限差分法模拟了其色散特性,从理论上分析了其结构参数孔间距Λ和空气占空比d/Λ对该光子晶体光纤的色散系数的影响, 并且实际制备出了3种不同结构参数的光子晶体光纤. 通过对其色散曲线对比分析表明: 当光子晶体光纤孔间距在1 μm附近时, 其色散系数随着孔间距Λ和占空比d/Λ的增大而增加, 但对于孔间距Λ的变化比占空比d/Λ更为敏感, 并且随着孔间距Λ的增加,其对色散系数的影响能力逐渐减小. 设计并制备的光子晶体光纤在1550 nm处的色散系数为-241.5 ps·nm^-1·km^-1, 相对色散斜率为0.0018, 具有较好的色散补偿能力. 关键词： 色散 色散补偿 光子晶体光纤 结构参数