Sensitivity improvement of aluminum-based far-ultraviolet nearly guided-wave surface plasmon resonance sensor

An aluminum (Al) based nearly guided-wave surface plasmon resonance (NGWSPR) sensor is investigated in the far-ultraviolet (FUV) region. By simultaneously optimizing the thickness of Al and dielectric films, the sensitivity of the optimized Al-based FUV-NGWSPR sensor increases from 183°/RIU to 309°/RIU, and its figure of merit rises from 26.47 RIU^-1 to 32.59 RIU^-1 when the refractive index of dielectric increases from 2 to 5. Compared with a traditional FUV-SPR sensor without dielectric, the optimized FUV-NGWSPR sensor can realize simultaneous improvement of sensitivity and figure of merit. In addition, the FUV-NGWSPR sensor with realistic materials (diamond, Ta₂O₅, and GaN) is also investigated, and 137.84%, 52.70%, and 41.89% sensitivity improvements are achieved respectively. This work proposes a method for performance improvement of FUV-SPR sensors by exciting nearly guided-wave, and could be helpful for the high-performance SPR sensor in the short-wavelength region.     

The improvement of numerical modeling in the solution of incompressible viscous flow problems using finite element method based on spherical Hankel shape functions

In this paper, the finite element method with new spherical Hankel shape functions is developed for simulating 2‐dimensional incompressible viscous fluid problems. In order to approximate the hydrodynamic variables, the finite element method based on new shape functions is reformulated. The governing equations are the Navier‐Stokes equations solved by the finite element method with the classic Lagrange and spherical Hankel shape functions. The new shape functions are derived using the first and second kinds of Bessel functions. In addition, these functions have properties such as piecewise continuity. For the enrichment of Hankel radial basis functions, polynomial terms are added to the functional expansion that only employs spherical Hankel radial basis functions in the approximation. In addition, the participation of spherical Bessel function fields has enhanced the robustness and efficiency of the interpolation. To demonstrate the efficiency and accuracy of these shape functions, 4 benchmark tests in fluid mechanics are considered. Then, the present model results are compared with the classic finite element results and available analytical and numerical solutions. The results show that the proposed method, even with less number of elements, is more accurate than the classic finite element method.     

A proper orthogonal decomposition variational multiscale meshless interpolating element-free Galerkin method for incompressible magnetohydrodynamics flow

In the recent decade, the meshless methods have been handled for solving most of PDEs due to easiness of the meshless methods. One of the popular meshless methods is the element-free Galerkin (EFG) method that was first proposed for solving some problems in the solid mechanics. The test and trial functions of the EFG are based on the special basis. Recently, some modifications have been developed to improve the EFG method. One of these improvements is the variational multiscale EFG procedure. In the current article, the shape functions of interpolation moving least squares approximation have been applied to the variational multiscale EFG technique for solving the incompressible magnetohydrodynamics flow. In order to reduce the elapsed CPU time of simulation, we employ a reduced-order model based on the proper orthogonal decomposition technique. The current combination can be referred to as the reduced-order variational multiscale EFG technique. To illustrate the reduction in CPU time used as well as the efficiency of the proposed method, we applied it for the two-dimensional cases.     

Incompressible fluid flow simulations with flow rate as the sole information at synthetic inflow and outflow boundaries

In numerically simulating heat and mass transport processes in an unconfined domain involving synthetic open (inflow and/or outflow) boundaries, how to properly specify flow conditions at these boundaries can become a challenging issue. In this work, within the context of a pressure‐based finite volume method under an unstructured grid, a solution procedure without the need for explicit specification of flow profiles at any of these boundaries when simulating incompressible fluid flow is proposed and numerically examined. Within this methodology, the flow at any open boundary is not necessarily assumed to be unidirectional or fully developed; indeed, the sole information required is the mass flow rate crossing the boundary. As a result, one can select the specific region of interest to perform simulations, rather than having to artificially increase the flow domain so as to invoke fully developed flow at all open boundaries. This not only greatly reduces computational costs (both in terms of memory requirements and simulation run‐time) but provides the means to engage with flow problems, which otherwise cannot be solved with currently available methods for handling the flow conditions at open boundaries. The proposed methodology is demonstrated by simulating laminar flow of an incompressible fluid in a two‐dimensional planar channel with a 90° T‐branch, a known inflow rate, and flow splits for the two outflow channels. The results obtained by placing the entrance and the two exits at different locations show that the flow behavior predicted is completely unaffected by using a highly truncated domain. Copyright © 2015 John Wiley & Sons, Ltd.     

一类正交空间填充设计的构造

空间填充设计在计算机试验中应用十分广泛,当拟合回归模型时,正交的空间填充设计保证了因子效应估计的独立性.基于广义正交设计,文章给出了构造二阶正交拉丁超立方体设计和列正交设计的方法,新构造的设计不仅满足任意两列之间相互正交,还能保证每一列与任一列元素平方组成的列以及任两列元素相乘组成的列都正交.当某些正交的空间填充设计不存在时,具有较小相关系数的近似正交设计可作为替代设计使用.设计构造的灵活性为计算机试验在实践中的广泛应用提供了必要的支持.     

Development of LBGK and incompressible LBGK‐based lattice Boltzmann flux solvers for simulation of incompressible flows

This paper presents lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model and incompressible LBGK model‐based lattice Boltzmann flux solvers (LBFS) for simulation of incompressible flows. LBFS applies the finite volume method to directly discretize the governing differential equations recovered by lattice Boltzmann equations. The fluxes of LBFS at each cell interface are evaluated by local reconstruction of lattice Boltzmann solution. Because LBFS is applied locally at each cell interface independently, it removes the major drawbacks of conventional lattice Boltzmann method such as lattice uniformity, coupling between mesh spacing, and time interval. With LBGK and incompressible LBGK models, LBFS are examined by simulating decaying vortex flow, polar cavity flow, plane Poiseuille flow, Womersley flow, and double shear flows. The obtained numerical results show that both the LBGK and incompressible LBGK‐based LBFS have the second order of accuracy and high computational efficiency on nonuniform grids. Furthermore, LBFS with both LBGK models are also stable for the double shear flows at a high Reynolds number of 10⁵. However, for the pressure‐driven plane Poiseuille flow, when the pressure gradient is increased, the relative error associated with LBGK model grows faster than that associated with incompressible LBGK model. It seems that the incompressible LBGK‐based LBFS is more suitable for simulating incompressible flows with large pressure gradients. Copyright © 2014 John Wiley & Sons, Ltd.     

Local and parallel finite element algorithm for stationary incompressible magnetohydrodynamics

This article presents a local and parallel finite element method for the stationary incompressible magnetohydrodynamics problem. The key idea of this algorithm comes from the two‐grid discretization technique. Specifically, we solve the nonlinear system on a global coarse mesh, and then solve a series of linear problems on several subdomains in parallel. Furthermore, local a priori estimates are obtained on a general shape regular grid. The efficiency of the algorithm is also illustrated by some numerical experiments.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1513–1539, 2017     

Nearly m-embedded subgroups and solvability of finite groups

A subgroup A of a finite group G is called {1≤G}-embedded in G if for each two subgroups K≤H of G, where K is a maximal subgroup of H, A either covers the pair (K,H) or avoids it. Moreover, a subgroup H of G is called nearly m-embedded in G if G has a subgroup T and a {1≤G}-embedded subgroup C such that G?=?HT and H∩T≤C≤H. In this paper, we mainly prove that G is solvable if and only if its Sylow 3-subgroups, Sylow 5-subgroups and Sylow 7-subgroups are nearly m-embedded in G.     

Vanishing viscosity limit of Navier–Stokes Equations in Gevrey class

In this paper, we consider the inviscid limit for the periodic solutions to Navier–Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier–Stokes equation is independent of viscosity, and that the solutions of the Navier–Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover, the convergence rate in Gevrey class is presented. Copyright © 2017 John Wiley & Sons, Ltd.     

集值映射多目标半定规划问题的epsilon-弱有效性

对于集值映射多目标半定规划问题, 在近似锥-次类凸的框架下, 建立了含矩阵和向量的择一性定理, 给出了问题的epsilon-弱有效解的epsilon-Lagrange乘子定理及标量化定理和epsilon-弱鞍点定理．