The regularity of the multiple higher-order poles solitons of the NLS equation

Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.     

颗粒毛细效应影响因素的离散元分析

颗粒毛细效应是指将一根细管插入填充有颗粒物质的容器中并对管施加竖直振动时颗粒在管内上升并最终达到一个稳定的高度的现象, 该现象为颗粒物料的逆重力输运提供了一种潜在的技术途径. 为探究颗粒毛细效应的影响因素, 采用离散元方法, 模拟再现了颗粒毛细效应过程,展示了不同管径下颗粒竖直方向速度演变特性, 考察了不同容器宽度和振动条件下颗粒最终毛细上升高度随管径的演变规律. 结果表明, 在容器宽度与粒径比为40、管振幅与粒径比为14.33、管振动频率为12 Hz情况下, 管径与粒径比$D/d = 3.33$时, 管内颗粒堵塞严重, 使得颗粒上升缓慢,并造成颗粒柱中断; $D/d = 8.33$时, 起初毛细上升高度增加迅速, 随后毛细上升高度的增大逐渐减缓, 管内颗粒在管径方向几乎不存在速度梯度; $D/d =15$时, 随着颗粒毛细上升高度的增大, 管内颗粒柱分离为速度截然不同的两层, 上层颗粒在管径方向几乎不存在速度梯度, 而下层颗粒存在明显的速度梯度.研究还发现, 在毛细效应能够发生的管径范围内, 存在一个对应于颗粒最终毛细上升高度最大值的临界管径, 当管径小于临界管径时, 颗粒最终毛细上升高度随管径的增大而增大, 当管径大于临界管径时, 颗粒最终毛细上升高度随管径的增大而趋于减小; 增大容器宽度,临界管径有所增大; 增大振幅、适当提高频率能够有效促进临界管径的增大.      

The effect of behavior of wearing masks on epidemic dynamics

Nonlinear Dynamics - Recently, COVID-19 has attracted a lot of attention of researchers from different fields. Wearing masks is a frequently adopted precautionary measure. In this paper, we...     

Magnetic properties of a triangle double-layer graphene nanoisland: a Monte Carlo study

The European Physical Journal Plus - We analyze the solution of the Schrödinger equation with a quark–antiquark potential obtained in a paper published recently in this journal. The...     

X-ray diffraction and Raman spectra of merrillite at high pressures

ABSTRACT

The compressibility and effect of pressure on the vibrations of merrillite, Ca₉NaMg(PO₄)₇, were studied by using diamond anvil cell at room temperature combined with in-situ synchrotron X-ray diffraction and Raman spectroscopy up to about 18 and 15?GPa, respectively. The pressure-volume data was fitted by a third-order Birch–Murnaghan equation of state to determine the isothermal bulk modulus as K₀ ?=?87.2(32) GPa with pressure derivative K₀′?=?3.2(4). If K₀′?=?4, the isothermal bulk modulus was obtained as 81.6(10) GPa. The axial compressibility was estimated and an axial elastic anisotropy exists since a-axis is less compressible than the c-axis. The Raman frequencies of all observed modes for merrillite continuously increase with pressure, and the pressure dependences of stretching modes (v ₃ and v ₁) are larger than those of the bending modes (v ₄ and v ₂) and external modes. The isothermal mode Grüneisen parameters and intrinsic anharmonicity of merrillite were also calculated.     

双子佯谬与星际航行

计算了在两个假想的星际航行方案中,与"双子佯谬"相关的时间差别.这种差别体现了惯性与非惯性参考系经历的时间有绝对差异,而不再是"相对"效应.     

干式变压器有限元仿真模型的电磁和振动分析

随着电力需求的逐年增长,干式变压器的数量也在不断增加。干式变压器在运行时存在着振动和噪声的问题,为了对干式变压器振动的规律与特点进行研究,本文建立了干式变压器本体振动的有限元仿真模型,通过电磁分析获得相应的磁场分布,然后利用结构动力学分析得到其本体振动的相关规律。通过对处于运行状态的变压器振动数据进行实测分析,得到变压器振动的特征频率,然后对仿真结果进行对比分析,可以发现振动幅度与频率之间存在的关系。本文的研究结果可对干式变压器的减振降噪研究提供参考。     

Effect of polyethylene glycol on corrosion of fresh macroporous silicon in 1.0 M NaOH and application in determination of porosity and thickness by gravimetric measurement

Abstract

This work presents on improvement in gravimetric measurement for determining the porosity and thickness of microporous silicon. Herein, the corrosion of fresh macroporous silicon (f-MPSi) in 1.0?M NaOH with different concentrations of polyethylene glycol (PEG 200/400/600) was studied by weight loss measurement and scanning electron microscopy (SEM). The results showed that the corrosion rate decreased with increasing polyethylene glycol concentration, and increased with an increase in temperature. Polyethylene glycol can inhibit the corrosion of f-MPSi in NaOH solution. Moreover, 1.0?M NaOH/PEG 600 (10%) can be used as the optimized solution to remove f-MPSi for measuring its porosity and thickness by gravimetric measurement.     

Synthesis of a Novel Phosphorus-Containing Curing Agent and Its Effects on the Flame Retardancy,and Thermal Stability of Epoxy Resins

Russian Journal of Applied Chemistry - A novel curing agent containing phosphorus and carboxyl group compound diphenyl(2,3-dicarboxylpropyl)phosphine oxide (DPDCPPO) was synthesized and used as a...     

Functional Zwitterionic Polymers on Surface: Structures and Applications

Zwitterionic polymers are important in a wide range of industrial, biological and medical fields. Their chemical structures include an equal amount of anion and cation groups, and such structures give rise to many unique functionalities, such as temperature response, anti‐polyelectrolyte effect, and strong hydration properties. In this review, we focus on the structures and applications of functional zwitterionic polymers on surfaces. We review three areas of applications according to the architecture of the polymeric systems: surface coating, complex solutions, and hydrogel. We review the simulation and theory work and highlight some outlooks for further development.