On finite difference approximation of a matrix-vector product in the Jacobian-free Newton-Krylov method

The Jacobian-free Newton-Krylov (JFNK) method is a special kind of Newton-Krylov algorithm, in which the matrix-vector product is approximated by a finite difference scheme. Consequently, it is not necessary to form and store the Jacobian matrix. This can greatly improve the efficiency and enlarge the application area of the Newton-Krylov method. The finite difference scheme has a strong influence on the accuracy and robustness of the JFNK method. In this paper, several methods for approximating the Jacobian-vector product, including the finite difference scheme and the finite difference step size, are analyzed and compared. Numerical results are given to verify the effectiveness of different finite difference methods.     

三维泊松方程基于Richardson外推法的高阶紧致差分方法

基于Richardson外推法提出了数值求解三维泊松方程的高阶紧致差分方法.方法通过利用四阶和六阶紧致差分格式,分别在细网格和粗网格上求解,然后利用Richardson外推技术和算子插值方法,得到三维泊松方程在细网格上的六阶和八阶精度的数值解.数值实验结果验证了该方法的精确性和有效性.     

一类推广的干摩擦问题周期解的存在性

为了得到干摩擦问题存在周期解的判断方法,利用微分包含理论对系统+k~2x+μSngp(t)+T(t)a.e.进行了讨论.在周期外力p(t)周期等于固有周期2π/R的情形下得到了周期解存在的充要条件,在周期外力p(t)周期不等于固有周期整数倍2nπ/R的情形下得到了周期解存在的充分条件.     

含广布腐蚀坑结构寿命评估方法

为了定量评估含广布腐蚀损伤老龄化飞机结构的剩余强度, 采用等效裂纹方法将腐蚀坑沿垂 直于外界最大主应力方向进行投影处理, 使其转化为具有相同寿命的等效初始表面裂纹, 然 后采用参数化有限元方法,求解等效裂纹前沿的应力强度因子、裂纹扩展方向和裂纹扩展增量, 建立并应用应力强度因子变化历程, 采用循环接循环的损伤累积方法对含广布等效表面裂纹 在疲劳载荷作用下的寿命进行了预测. 预测结果为复杂环境中含广布腐蚀坑的飞机结构寿命 预测提供了参考.     

Electrocatalytic oxidation of quinine sulfate at a multiwall carbon nanotubes-ionic liquid modified glassy carbon electrode and its electrochemical determination

The electrocatalytic oxidation of quinine sulfate (QS) was investigated at a glassy carbon electrode, modified by a gel containing multiwall carbon nanotubes (MWCNTs) and room-temperature ionic liquid of 1-Butyl-3-methylimidazolium hexafluorophate (BMIMPF₆) in 0.10 M of phosphate buffer solution (PBS, pH 6.8). It was found that an irreversible anodic oxidation peak of QS with E _pa as 0.99 V appeared at MWCNTs-RTIL/glassy carbon electrode (GCE). The electrode reaction process was a diffusion-controlled one and the electrochemical oxidation involved two electrons transferring and two protons participation. Furthermore, the charge-transfer coefficient (α), diffusion coefficient (D), and electrode reaction rate constant (k _f) of QS were found to be 0.87, 7.89 × 10⁻³ cm²⋅s⁻¹ and 3.43 × 10⁻² s⁻¹, respectively. Under optimized conditions, linear calibration curves were obtained over the QS concentration range 3.0 × 10⁻⁶ to 1.0 × 10⁻⁴ M by square wave voltammetry, and the detection limit was found to be 0.44 μM based on the signal-to-noise ratio of 3. In addition, the novel MWCNTs-RTIL/GCE was characterized by the electrochemical impedance spectroscopy and the proposed method has been successfully applied in the electrochemical quantitative determination of quinine content in commercial injection samples and the determination results could meet the requirement.     

煎炸胡麻油分子光谱分析研究

为保证煎炸食品的安全,探索煎炸食用油变化的规律,该实验利用三维荧光结合紫外-可见吸收光谱研究了胡麻油不同煎炸时间的物理化学性质的变化.结果表明,胡麻油在煎炸的前2 h内,其物理化学性质没有明显的变化,但是当连续使用超过6 h以后,其荧光光谱与紫外吸收光谱都有较大变化,说明胡麻油在连续煎炸6 h后,其物理化学性质变化最为...     

Coniferous canopy BRF simulation based on 3-D realistic scene

It is difficulties for the computer simulation method to study radiation regime at large-scale.Simplified coniferous model was investigated in the present study.It makes the computer simulation methods such as L-systems and radiosity-graphics combined method(RGM) more powerful in remote sensing of heterogeneous coniferous forests over a large-scale region.L-systems is applied to render 3-D coniferous forest scenarios,and RGM model was used to calculate BRF(bidirectional reflectance factor) in visible and ne...     

Determination of the radiation dose scattered outside the target volume treated with IMRT technique

Intensity Modulated Radiation Therapy (IMRT) is an advanced mode of high precision radiation therapy that uses computer controlled linear accelerators to deliver precise radiation doses to a malignant tumor or specific areas within the tumor. This is achieved using a more precise adjustment of the beam to the three dimensional shape of the tumor by modulating or controlling the intensity of the radiation beam in multiple small volumes. IMRT also allows higher radiation doses to be focused to regions within the tumor while minimizing the dose to surrounding normal critical structures. This work aims at determining the radiation dose in two target volumes (tumors) treated at same time and the scattered dose distribution in organs at risk using thermoluminescent dosimeters of LiF:Mg,Ti for IMRT treatment technique and a polymethylmethacrylate (PMMA) phantom. The shortest distance between the cavities 1 and 2 that simulate tumors is 1.5 cm and the shortest distances from the cavity 1 to the cavities 3, 4 and 5 are, respectively, 1.9 cm, 2.2 cm and 2.65 cm. The shortest distance from the cavity 2 to cavities 3, 4 and 5 are, respectively, 5.4 cm; 5.7 cm and 1.5 cm. The relative difference for the doses measured by TLD-100 and provided by the TPS were +3.7% and −1.38%. The out-of-target doses received by cavities 3, 4 and 5 corresponded on average to 19.36, 17.84% and 6.72% of the highest dose received by the cavity 1 and the doses received by cavities 3, 4 and 5 corresponded on average to 29.51%, 27.20% and 10.24% of the dose received by cavity 2.     

群体迁移行为的理论与实证研究

人类行为往往取决于经济社会的某种趋势性影响, 对其动力学的定量描述和准确理解是当前复杂系统研究的热点. 本文提出由迁移距离, 迁移人口年龄和迁出地经济人口密度所描述的群体迁移欲望函数, 及广义势. 借助于朗之万方程, 将其转变为Hamilton-Jacobi方程, 从而对群体决策行为进行统计理论分析. 采用高维最陡降线的方式求解Hamilton-Jacobi方程. 其解的形式揭示了群体迁移过程中信息熵随着迁移群体年龄的变化呈现一个单峰; 信息熵对迁移距离的二阶导随迁移距离而穿零变化(对应一种相变); 信息熵随着经济人口密度也呈现单峰. 进一步分析信息熵的这些变化规律所蕴含的意义及其机理, 从而获得对人类群体迁移行为的新理解, 为政府管理提供参考和启示.     

广义不确定性原理下费米气体低温热力学性质

在考虑到广义不确定性原理时, 统计物理中的态密度必须做出修正, 这导致对传统统计物理的所有结果都有不同程度的修正. 在高能、高温条件下, 此修正是颠覆传统观念的, 在低温条件下, 也有一定的修正. 研究了低温条件下考虑到广义不确定性原理时, 理想费米气体和具有弱相互作用费米气体的热力学性质, 分别给出理想费米气体和弱相互作用费米气体的化学势、内能和定容热容的解析表达式, 并以铜电子气体为例进行了具体数值计算, 将计算结果与不考虑广义不确定性原理时的费米气体的热力学性质进行了比较, 探讨了广义不确定性原理对系统热力学性质的影响. 考虑到广义不确定性原理后费米气体的化学势、费米能和基态能增大, 热容减少, 内能随温度的增加先增大, 到某一温度(对于铜电子气体, T/T_F0～0.3)时, 增值为零, 温度再增加内能减少. 这些修正的具体数值主要由粒子数密度决定, 粒子数密度越大, 修正越大.