Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix

This paper presents the generalized nonlinear delay differential equations of fractional variable-order. In this article, a novel shifted Jacobi operational matrix technique is introduced for solving a class of multi-terms variable-order fractional delay differential equations via reducing the main problem to an algebraic system of equations that can be solved numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical experiments are presented to demonstrate the efficiency, generality, accuracy of proposed scheme and the flexibility of this method. The numerical results compared it with other existing methods such as fractional Adams method (FAM), new predictor–corrector method (NPCM), a new approach, Adams–Bashforth–Moulton algorithm and L1 predictor–corrector method (L1-PCM). Comparing the results of these methods as well as comparing the current method (NSJOM) with the exact solution, indicating the efficiency and validity of this method. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated.

     

Effect of Doping of Zn and Ca into ErBa2Cu3O7?δ Superconductor Prepared via Co-precipitation Method

Zn- and Ca-doped ErBa₂Cu₃O_7−δ were successfully prepared via coprecipitation method using metal acetates as the starting salts. The precipitated samples were calcined for 20 h at 900 °C and sintered at 920 °C for 24 h. All heat treatments were carried out under oxygen environment. Results show that there is a selectivity of the doping site depending on the ionic radius of the dopant. Furthermore, increase in the critical temperature, T _c , was observed in 0.05 mole of calcium and zinc doped samples. The difference in ionic radius of the dopant led to the increase in porosity as the ionic radius decreases. On the other hand, structural distortion increased as the difference of ionic radius became larger.     

Optimal Linear Control of Modular Multi-Level Converters with a Prescribed Degree of Stability

Abstract

In this paper, a new control approach using an optimal linear control with prescribed degree of stability for modular multi-level converters (MMC) is presented and analyzed. The proposed controller relies on a linear quadratic regulator with integral action which brings the ability of state variable reference tracking for modular multi-level converters. Since MMC is a complex system with several state variables, a unified control system design for this system is vital. The proposed controller of this study is designed to obtain wider stability margin thanks to the implementation of prescribed degree of stability concept to minimize the quadratic performance index of the control structure. By means of this method, the poles of the closed-loop system will be shifted to the desired places in the left half side of the S-plane. The main advantages of this control strategy compared to previous methods are that it will be possible to control the state of energy for each phase separately, while there will be superior tolerance to nonlinearities and the enhanced stability margin with less sensitivity to plant-parameter variations. The performance of the designed controller is verified through MATLAB^TM simulations (The MathWorks, Natick, MA, USA) with the nonlinear model of MMC.     

4D Printing of Polyvinyl Chloride (PVC): A Detailed Analysis of Microstructure,Programming, and Shape Memory Performance

In this research, polyvinyl chloride (PVC) with excellent shape-memory effects is 4D printed via fused deposition modeling (FDM) technology. An experimental procedure for successful 3D printing of lab-made filament from PVC granules is introduced. Macro- and microstructural features of 3D printed PVC are investigated by means of wide-angle X-ray scattering (WAXS), differential scanning calorimetry (DSC), and dynamic mechanical thermal analysis (DMTA) techniques. A promising shape-memory feature of PVC is hypothesized from the presence of small close imperfect thermodynamically stable crystallites as physical crosslinks, which are further reinforced by mesomorphs and possibly molecular entanglement. A detailed analysis of shape fixity and shape recovery performance of 3D printed PVC is carried out considering three programming scenarios of cold (T_g −45 °C), warm (T_g −15 °C), and hot (T_g +15 °C) and two load holding times of 0 s, and 600 s under three-point bending and compression modes. Extensive insightful discussions are presented, and in conclusion, shape-memory effects are promising,ranging from 83.24% to 100%. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state-of-the-art shape-memory materials library for 4D printing, and provide pertinent results that are instrumental in the 3D printing of shape-memory PVC-based structures.     

Cascaded Multilevel Inverters Using Proposed Series Sub-multilevel Basic Blocks with Reduced Switching Devices

In this paper, a novel configuration of the cascaded multilevel inverters using series connection of new sub-multilevel basic blocks is presented. The basic structure of the proposed sub-multilevel inverter is made of three isolated batteries and eight unidirectional power switches. Hereby, by changing the polarity of one of such batteries and two power switches, two different modules of sub-multilevel inverters can be extracted that each of them is able to be incorporated into two different cascaded structures as the series basic blocks. Contemporary, to determine the suitable magnitudes of the integrated batteries, two different algorithms for each topology along with their relevant mathematical analysis have been also given. In this study, a complete comparison between the proposed topologies and several recently presented structures has been conducted. The compiled comparisons can prove the fact that both the proposed cascaded inverters are capable of generating a higher number of output voltage levels with less number of switching counts. Other advantages of these structures are reduction of voltage sources numbers, DC sources variety, value of total blocking voltage, and also conducting losses. In order to demonstrate the correct operation of the proposed structures and presented algorithms, some experimental results will be also shown.     

Energy minimization in the STT-RAM-based high-capacity last-level caches

The Journal of Supercomputing - Spin-transfer torque random access memory (STT-RAM) is a suitable alternative to DRAM in the large last-level caches (L3Cs) on account of low leakage, the absence of...     

Exact,analytic temperature distributions of pin fins with constant thermal conductivity and power‐law type heat transfer coefficient

In this Technical Note, the problem of determining the temperature distribution in a pin fin with power‐law heat transfer coefficients is addressed. It is demonstrated that the governing fin equation, a nonlinear second‐order differential equation, is exactly solvable for the entire range of the exponent n in the power‐law heat transfer coefficients. The exact, closed‐form analytical solutions in implicit form are convenient for physical interpretation and optimization for maximum heat transfer. Furthermore, it is proved that the exact solutions have three different structures: (1) dual in the range of , (2) unique or dual in the range of , and (3) unique in the range of . Additionally, exact analytical expressions for the fin efficiency and the fin effectiveness are provided, both as a function of the dimensionless fin parameter for the gamma of n under study.     

Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics

In this paper the meshless local radial point interpolation (MLRPI) method is applied to simulate a nonlinear partial integro-differential equation arising in population dynamics. This PDE is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. In MLRPI method, it does not require any background integration cells so that all integrations are carried out locally over small quadrature domains of regular shapes, such as circles or squares in two dimensions and spheres or cubes in three dimensions. The point interpolation method is proposed to construct shape functions using the radial basis functions. A one-step time discretization method is employed to approximate the time derivative. To treat the nonlinearity, a simple predictor–corrector scheme is performed. Also the integral term, which is a kind of convolution, is treated by the cubic spline interpolation. The numerical studies on sensitivity analysis and convergence analysis show that our approach is stable. Finally, two numerical examples are presented showing the behavior of the solution and the efficiency of the proposed method.     

Frontal polymerization accelerated by continuous conductive elements

Frontal polymerization (FP), a propagating reaction wave driven by exothermic polymerization, is increasingly considered for the rapid fabrication of fiber-reinforced composites. However, the effect of the fibers on the FP reaction has not yet been explored. In this contribution, we demonstrate that thermally conductive continuous elements accelerate FP using an experimental model system and finite-element-based numerical simulations. Furthermore, the degree of acceleration is shown to be affected by the amount of available monomer in the system. These results suggest that thermally conductive carbon fiber reinforcement may facilitate FP for composite manufacturing. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2019 , 136, 47418.     

An improved pseudospectral meshless radial point interpolation (PSMRPI) method for 3D wave equation with variable coefficients

In this paper, a pseudospectral meshless radial point interpolation (PSMRPI) technique is applied to the three-dimensional wave equation with variable coefficients subject to given appropriate initial and Dirichlet boundary conditions. The present method is a kind of combination of meshless methods and spectral collocation techniques. The point interpolation method along with the radial basis functions is used to construct the shape functions as the basis functions in the frame of the spectral collocation methods. These basis functions will have Kronecker delta function property, as well as unitary possession. In the proposed method, operational matrices of higher order derivatives are constructed and then applied. The merit of this innovative method is that, it does not require any kind of integration locally or globally over sub-domains, as it is essential in meshless methods based on Galerkin weak forms, such as element-free Galerkin and meshless local Petrov–Galerkin methods. Therefore, computational cost of PSMRPI method is low. Further, it is proved that the procedure is stable with respect to the time variable over some conditions on the 3D wave model, and the convergence of the technique is revealed. These latest claims are also shown in the numerical examples, which demonstrate that PSMRPI provides excellent rate of convergence.