影响无网格方法求解精度的因素分析

基于移动最小二乘法的无网格方法的计算精度除受到节点的分布密度和基底函数的阶次影响外，还受到其它因素的影响，其中权函数的选取、权函数影响域的大小及位移边界条件的引入对计算精度影响较大。本文分析了几种常用权函数在数值计算时的特点，包括计算精度、收敛情况、计算效率等，同时分析了影响域大小及边界条件的引入对计算精度的影响。通过分析给出了确定权函数及其影响域大小的方法。当受约束的自由度较多时，通过配点法引入位移边界条件会引起计算结果的振荡，通过施加稳定项可以消除振荡现象，通过对带孔方板的受力分析证明了其可行性。应用以上结论对J23—10曲柄压力机机身进行了受力分析，应力集中部位的计算结果得到了较高的精度。     

Structural and magnetic study of swift heavy ion irradiated W/Fe multilayer structure

The present study reports the effect of swift heavy ion irradiation on structural and magnetic properties of sputtered W/Fe multilayer structure (MLS) having bilayer compositions of [W(10 Å)/Fe(20 Å)]_10BL. The MLS is irradiated by 120 MeV Au⁹⁺ ions of fluences 1×10¹³ and 4×10¹³ ions/cm². Techniques like X-ray reflectivity (XRR), cross-sectional transmission electron microscopy (X-TEM) and DC magnetization with a vibrating sample magnetometer (VSM) are used for structural and magnetic characterization of pristine and irradiated MLS. Analysis of XRR data using Parratt’s formalism shows a significant increase in W/Fe layer roughness. X-TEM studies reveal that intra-layer microstructure of Fe layers in MLS becomes nano-crystalline on irradiation. DC magnetization study shows that with spacer layer thickness interlayer coupling changes between ferromagnetic to antiferromagnetic.     

Modeling study of non-line-narrowed hole-burned spectra in weakly coupled dimers and multi-chromophoric molecular assemblies

Several different models have been proposed to explain the origin of the complex anti-hole features observed in hole-burned (HB) spectra of excitonically coupled systems such as photosynthetic complexes. This lack of consensus presents a serious constraint on the interpretation of HB spectra and the underlying electronic structures of these systems. To resolve this problem we present results of modeling studies of non-resonant HB spectra taking uncorrelated excitation energy transfer and excitonic interactions into account. Simplified analytical results are compared with Monte Carlo simulations in which excitonic interactions are explicitly taken into account in order to disentangle a number of distinct effects. It is shown that these effects can accurately account for both hole shapes and the broad anti-hole structure observed in excitonically coupled systems. We argue that these models will provide a necessary framework for probing the electronic structure of these systems via HB spectroscopy.     

弹性静力问题的无网格弱-强形式结合法

基于改进的移动最小二乘(MLS)二阶导数近似,建立了一种求解弹性静力问题的无网格弱-强形式结合法(MLS-MWS)。该方法采用节点离散求解域,通过MLS构造形函数,将求解域划分为边界域和内部域,并分别使用控制方程的局部弱形式和强形式来建立离散系统方程。对强形式中涉及的近似函数二阶导数计算,提出了一种将其转化为求两次一阶导数的方法,与传统方法相比,该方法计算简单、精度高。MLS-MWS法结合了弱、强形式无网格法的优点,Neumann边界条件容易满足,并且只需在边界区域进行积分。文中应用该方法分析了两个弹性力学平面问题,分析结果表明本文方法具有良好的精度和收敛性。     

A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.     

An enhanced treatment of boundary conditions in implicit smoothed particle hydrodynamics简

In this work, an enhanced treatment of the solid boundaries is proposed for smoothed particle hydrodynamics with implicit time integration scheme （Implicit SPH）. Three types of virtual particles, i.e., boundary particles, image particles and mirror particles, are used to impose boundary conditions. Boundary particles are fixed on the solid boundary, and each boundary particle is associated with two fixed image particles inside the fluid domain and two fixed mirror particles outside the fluid domain. The image particles take the flow properties through fluid particles with moving least squares （MLS） interpolation and the properties of mirror particles can be obtained by the corresponding image particles. A repulsive force is also applied for boundary particles to prevent fluid particles from unphysical penetra- tion through solid boundaries. The new boundary treatment method has been validated with five numerical examples. All the numerical results show that Implicit SPH with this new boundary-treatment method can obtain accurate results for non-Newtonian fluids as well as Newtonian fluids, and this method is suitable for complex solid boundaries and can be easily extended to 3D problems.     

The fast measurement of head related impulse responses for all azimuthal directions using the continuous measurement method with a servo-swiveled chair

This paper proposes a method for the fast measurement of head related impulse responses (HRIRs) for all azimuthal directions using the continuous measurement method with a subject sitting on a servo-swiveled chair (SSC). The subject faces all azimuthal directions with a constant angular speed as the SSC rotates and hears corresponding spatial sounds. In our continuous measurement method, we use a maximum length sequence (MLS) as the excitation signal, record binaural signals using tiny microphones placed in the subject’s ear canal around 5 mm from the entrance, and feed them, along with the MLS signal, into a PC so that HRIRs can be extracted for all azimuthal directions and discrete elevations. In this paper, the underlying principles behind the method are described and conditions for successful implementation are examined through numerical simulations. Further, the validity of the proposed method is verified using a physical realization and empirical measurements.     

An accurate, stable and efficient domain-type meshless method for the solution of MHD flow problems

The aim of the present paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics flow problems for regular and irregular geometries subject to Dirichlet, Neumann and Robin boundary conditions. Toward this, the meshless point collocation method (MPCM) is used for MHD flow problems in channels with fully insulating or partially insulating and partially conducting walls, having rectangular, circular, elliptical or even arbitrary cross sections. MPC is a truly meshless and computationally efficient method. The maximum principle for the discrete harmonic operator in the meshfree point collocation method has been proven very recently, and the convergence proof for the numerical solution of the Poisson problem with Dirichlet boundary conditions have been attained also. Additionally, in the present work convergence is attained for Neumann and Robin boundary conditions, accordingly. The shape functions are constructed using the Moving Least Squares (MLS) approximation. The refinement procedure with meshless methods is obtained with an easily handled and fully automated manner. We present results for Hartmann number up to 10⁵${10}^5$. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the exact solution and the conventional FEM and BEM, for the Dirichlet, Neumann and Robin boundary conditions of interior problems with simple or complex boundaries.     

Quadratic stochastic intensity and prospective mortality tables

We consider a quadratic stochastic intensity model with a Gaussian autoregressive factor, derive explicit formulas for predictive mortality tables and recursive updating formulas are also provided. We also explain how to use appropriately the Kalman filter to estimate the parameters of the model and to approximate the values of the underlying factor. This methodology is applied to French human mortality tables.     

Stability-indicating liquid chromatography method development and validation for impurity profiling of montelukast sodium in bulk drug and tablet dosage form

Montelukast sodium (MLS) is a leukotriene receptor antagonist drug used in the treatment of asthma, bronchospasm, allergic rhinitis and urticaria. A reversed-phase high performance liquid chromatography method was developed to separate, identify and quantitative determination of MLS and its eight known organic impurities in tablet dosage form using a C₁₈ column and mobile phases consisting of a gradient mixture of pH 2.5 phosphate buffer and acetonitrile. The stability-indicating character of the developed method was proven using stress testing (1 m HCl at 80°C/30 min, 1 m NaOH at 80°C/30 min, H₂O at 80°C/30 min, 3% H₂O₂ at 25°C/1 min, dry heat at 105°C/10 h and UV–vis light/4 days) and was validated for specificity, quantitation limit, linearity, precision, accuracy and robustness. For MLS and its eight known impurities, the quantitation limits, linearity and recoveries were 0.015–0.03 μg/ml, correlation coefficient > 0.997 (R² > 0.995) and 85.5–107.0%, respectively. The developed chromatographic method is suitable for impurity profiling and also for assay determination of MLS in bulk drugs and pharmaceutical formulations. The mass values (m/z) of newly formed degradation products (DP1 and DP2) of montelukast sodium were identified using liquid chromatography–mass spectrometry.