Wavelet multiresolution interpolation Galerkin method for nonlinear boundary value problems with localized steep gradients

The wavelet multiresolution interpolation for continuous functions defined on a finite interval is developed in this study by using a simple alternative of transformation matrix. The wavelet multiresolution interpolation Galerkin method that applies this interpolation to represent the unknown function and nonlinear terms independently is proposed to solve the boundary value problems with the mixed Dirichlet-Robin boundary conditions and various nonlinearities, including transcendental ones, in which the discretization process is as simple as that in solving linear problems, and only common two-term connection coefficients are needed. All matrices are independent of unknown node values and lead to high efficiency in the calculation of the residual and Jacobian matrices needed in Newton’s method, which does not require numerical integration in the resulting nonlinear discrete system. The validity of the proposed method is examined through several nonlinear problems with interior or boundary layers. The results demonstrate that the proposed wavelet method shows excellent accuracy and stability against nonuniform grids, and high resolution of localized steep gradients can be achieved by using local refined multiresolution grids. In addition, Newton’s method converges rapidly in solving the nonlinear discrete system created by the proposed wavelet method, including the initial guess far from real solutions.

     

Rate-dependent asymmetric hysteresis modeling and robust adaptive trajectory tracking for piezoelectric micropositioning stages

Nonlinear Dynamics - Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis...     

Dynamic and wear characteristics of self-lubricating bearing cage: effects of cage pocket shape

34,354,966 active cases and 460,787 deaths because of COVID-19 pandemic were recorded on November 06, 2021, in India. To end this ongoing global COVID-19 pandemic, there is an urgent need to implement multiple population-wide policies like social distancing, testing more people and contact tracing. To predict the course of the pandemic and come up with a strategy to control it effectively, a compartmental model has been established. The following six stages of infection are taken into consideration: susceptible (S), asymptomatic infected (A), clinically ill or symptomatic infected (I), quarantine (Q), isolation (J) and recovered (R), collectively termed as SAIQJR. The qualitative behavior of the model and the stability of biologically realistic equilibrium points are investigated in terms of the basic reproduction number. We performed sensitivity analysis with respect to the basic reproduction number and obtained that the disease transmission rate has an impact in mitigating the spread of diseases. Moreover, considering the non-pharmaceutical and pharmaceutical intervention strategies as control functions, an optimal control problem is implemented to mitigate the disease fatality. To reduce the infected individuals and to minimize the cost of the controls, an objective functional has been constructed and solved with the aid of Pontryagin’s maximum principle. The implementation of optimal control strategy at the start of a pandemic tends to decrease the intensity of epidemic peaks, spreading the maximal impact of an epidemic over an extended time period. Extensive numerical simulations show that the implementation of intervention strategy has an impact in controlling the transmission dynamics of COVID-19 epidemic. Further, our numerical solutions exhibit that the combination of three controls are more influential when compared with the combination of two controls as well as single control. Therefore, the implementation of all the three control strategies may help to mitigate novel coronavirus disease transmission at this present epidemic scenario.

     

阻尼对空爆荷载等效静载动力系数的影响

为考查阻尼参数对空爆荷载等效静载动力系数的影响,理论推导了空爆荷载下结构等效单自由体系弹塑性位移解及延性比解,设计并计算了阻尼比0.000 1～0.1、延性比1～4的20种典型工况的动力系数,并与现行抗爆设计规范动力系数公式结果进行了对比。结果表明:阻尼比小于0.000 1时可基本代表无阻尼状态,阻尼比0.01的动力系数比无阻尼的最大降低幅度为2.08%,数值差异很小,因此阻尼比为0.01以内时,可忽略阻尼对动力系数的影响;阻尼比0.05的动力系数比无阻尼的降低幅度约9.92%,数值差异较大,认为阻尼比0.05以上时将具有明显的经济效益;现行设计规范动力系数更适用于柔性结构体系,运用于刚性结构抗爆设计时,计算误差较大,对阻尼比较小的结构设计更不利。     

Novel filled polymer composites prepared from in situ polymerization via a colloidal approach: II. Blends of kaolin/Nylon-6 in situ composites with conventional Nylon-6 and -66

A novel in situ composite comprised of kaolin clay fillers and polyamide 6 (Nylon-6) was synthesized via a colloidal approach by suspending kaolin particles in aqueous caprolactam and then polymerizing the caprolactam under elevated temperature and pressure. This in situ polymerization technique enables the deposition of nylon molecules directly onto the filler surface. It offers a much larger contact surface area for the nylon molecules to interact with the filler particles and enhances filler/matrix interaction through polymer miscibility. The kaolin particles were shown to be uniformly dispersed in Nylon-6 matrix without appreciable agglomeration. In the highly clay-loaded composites such as the 50/50 kaolin/Nylon-6 in situ composite, the deposited nylon molecules probably form a coated layer on the filler particles. This kind of nylon coated fillers may be applied as a reinforcing entity to commercial Nylon-6 or −;66 by improving particle dispersion and melt processability. The 50/50 kaolin/Nylon-6 in situ composites have been used as a masterbatch for blending with commercial Nylon-6 and Nylon-66 to take advantage of their good properties and to reduce cost. Rheology and mechanical properties of the masterbatch/nylon composites have been investigated in comparison with those of the conventional melt-mixed composites. The improvement of rheological and mechanical properties of the in situ composites has been discussed in relation to the composite structure. © 1996 John Wiley & Sons, Inc.     

Novel filled polymer composites prepared from in situ polymerization via a colloidal approach: I. Kaolin/Nylon-6 in situ composites

A mineral-filled in situ composite was prepared by a colloidal approach by first suspending kaolin filler particles in aqueous caprolactam, and then polymerizing caprolactam in situ at high pressure and temperature. The purpose of this colloidal in situ polymerization is to improve particle dispersion and to enhance interaction of the filler to the polymer matrix. X-ray diffraction studies of the in situ kaolin/Nylon-6 composites revealed that the x-ray peak corresponding to the α-crystal form of Nylon-6 diminished with increasing kaolin loading, while the γ-crystal structure became more pronounced. The degree of crystallinity of Nylon-6 remained fairly unchanged with the kaolin loading level in the in situ composites. Calorimetric and dynamic mechanical studies exhibited that the glass transition temperature of the resulting composite increased significantly with increase in kaolin concentration, suggesting strong filler-matrix interaction at the kaolin/Nylon-6 interface. Scanning electron microscopic (SEM) results showed uniform filler dispersion in the in situ composites relative to the conventional melt-mixed composites. Modulus and tensile strength of these in situ composites were found to be distinctively higher than that of the conventional melt-mixed kaolin/Nylon-6 composites. However, as typical for composite materials, drawability and fracture toughness decreased with increasing kaolin loading. © 1996 John Wiley & Sons, Inc.     

Interpenetrating networks of conjugated ionic polyacetylenes

An interpenetrating polymer network (IPN) based on poly(N-butyl 2-ethynylpyridinum bromide) (PB2EPB) and polycarbonate-urethane (PCU) has been prepared and characterized. The simultaneous full IPNs of PCU and PB2EPB have two glass transition temperatures corresponding to those of the linear chain blends measured by DSC. This suggests immiscibility of the two networks in the IPNs. The IPNs display a multiphase morphology which is confirmed by SEM observation. The full IPNs exhibit excellent solvent resistance, good thermal stability and good mechanical properties. High UV absorption of these materials extending to the visible range and beyond indicates that the polyacetylene network is extensively conjugated. The electrical conductivity of the IPNs increases linearly with increasing polyacetylene content reaching 10^-4 S/cm. © 1996 John Wiley & Sons, Inc.     

The Toda rarefaction problem

In the Toda shock problem (see [7], [11], [8], and also [3]) one considers a driving particle moving with a fixed velocity 2a and impinging on a one-dimensional semi-infinite lattice of particles, initially equally spaced and at rest, and interacting with exponential forces. In this paper we consider the related Toda rarefaction problem in which the driving particle now moves away from the lattice at fixed speed, in analogy with a piston being withdrawn, as it were, from a container filled with gas. We make use of the Riemann-Hilbert factorization formulation of the related inverse scattering problem. In the case where the speed 2 |a| of the driving particle is sufficiently large (|a| > 1), we show that the particle escapes from the lattice, which then executes a free motion of the type studied, for example, in [5]. In other words, in analogy with a piston being withdrawn too rapidly from a container filled with gas, cavitation develops. © 1996 John Wiley & Sons, Inc.     

高温超导体磁通跳跃数值模拟

文中基于超导磁通动力学理论,考虑电磁力与热激活对磁通运动的影响,基本物理模型由等效电阻率随超导体温度和磁场变化的磁通扩散方程,以及比热随超导体温度变化的热传导方程组成。在此基础上,用差分法数值求解了这一复杂非线性系统的磁热耦合控制方程,得到了与实验观测结果基本一致的数值模拟结果。结果还表明：外加磁场变化速度、超导体初始温度以及超导尺寸对于磁通跳跃均产生明显的影响。