Discrete Fourier Transform Analysis of Chronoamperometric Currents Obtained Under Ultrasound

A discrete Fourier transform (DFT) technique was used to analyze chronoamperometric currents at a Pt microdisk electrode (Ø=15 μm) in an electrolyte containing [Fe(CN)₆]^3?/[Fe(CN)₆]^4? under ultrasound at a frequency of 26.3 kHz and the powers of 0–50 W. The currents were measured by a high‐speed data acquisition card. Considering the effects of acoustic vibrations and cavitations on the limiting currents, a microdisk electrode and a high frequency sampling (10 MHz) were used to collect the current signals to restrain the deviation of average from sampling period in other methods. The results show that the amplitudes at 0 Hz and 26.3 kHz are related to the decay of ultrasound at constant power output when the separation between sono‐horn and electrode increases, and also related to the reactant concentration at the same ultrasonic conditions. The frequency signals are always shown in frequency spectrum despite different ultrasonic conditions. The amplitudes reflect the intensity of ultrasound and the concentration of reactant in solution, so they can be called specific frequencies. This method can be used to analyze quantitatively the effects of ultrasound on electrochemical reaction, determine the reactant concentration and measure the distribution of ultrasonic intensity in a solution.     

Multi-scale magnetic resonance measurements and validation of Discrete Element Model simulations

This short review describes the capabilities of magnetic resonance (MR) to image opaque single- and two-phase granular systems, such as rotating cylinders and gas-fluidized beds operated in different fluidization regimes. The unique capability of MR to not only image the solids’ distribution (voidage) but also the velocity of the particulate phase is clearly shown. It is demonstrated that MR can provide measurements over different length and time scales. With the MR equipment used for the studies summarized here, temporal and spatial scales range from sub-millisecond to hours and from a few hundred micrometres to a few centimetres, respectively. Besides providing crucial data required for an improved understanding of the underlying physics of granular flows, multi-scale MR measurements were also used to validate numerical simulations of granular systems. It is shown that predictions of time-averaged properties, such as voidage and velocity of the particulate phase, made using the Discrete Element Model agree very well with MR measurements.     

从诺贝尔经济学奖看数学对经济学的作用

本文在分析2003年诺贝尔经济学奖学术贡献的基础上，阐述了数学思维方式和数学方法对经济问题的解决、经济理论的发展等方面的作用．     

常微分方程通解、特解、所有解的区别与联系

通过具体实例分析、讨论了高等数学中常微分方程的通解、特解和微分方程的所有解之间的区别与联系,并对高等数学教材中二阶线性微分方程的降阶法与二阶常系数非齐次线性微分方程特解求解过程中的作法进行了说明.     

The Influence of Visual and Spatial Reasoning in Interpreting Simulated 3D Worlds

This paper explores the way in which young children (6 year olds) made sense of screen-based images on the computer. The participants were required to interpret 3D-like representations and relate these images to objects in their environment. Both static and relatively dynamic software programs were used in the investigation. Some of the children could not make links between the screen representation and the intended three-dimensional (3D) objects. It is argued that young children should be exposed to activities that establish explicit links between 2D and 3D objects ``away' from the computer before attempting the more difficult links required to interpret and represent 3D objects in ICT contexts. This revised version was published online in July 2006 with corrections to the Cover Date.     

数学建模融入经济数学教学中的案例及分析

经济数学是财经类专业的重要基础课程,在经济数学教学中讲授数学的基本概念和定理的同时,怎样引入数学模型进行教学,培养和激发学生学习数学的兴趣,是我们从事经济数学教学的教师都应该探讨的问题.本文结合经济数学教学的实践,介绍了经济数学教学中的几个经典经济模型案例,将数学与经济学有机地联系起来,让数学变得既生动又符合实际,取得了很好的教学效果.     

光纤法珀应变传感器串并联混合复用的离散腔长变换解调研究

光纤法珀传感器复用的输出信号复杂,解调相当困难.为实现其串并联混合结构复用,根据光纤法珀应变传感器的双光干涉原理,阐述了传感器串并联混合复用的输出信号特征,分析了信号中各项成分对离散腔长变换方法解调结果的影响,并进行了计算机仿真.最后搭建实验平台,进行了四个传感器串并联混合复用的实验研究,证明该方案可行,解调准确度1 μm.     

高等数学教学改革研究进展

通过分析国内外高等数学教学改革研究历史与现状,阐明21世纪高等数学课程地位、作用和价值,及与21世纪相适应的高等数学教学改革意义、方向与方法.并结合个人教学实践分析、总结了具有代表性的高等数学教学理念、教学内容与课程体系、实践教学、计算机技术应用等方面改革成果与经验.最后对高等数学教学改革的继续深入和目前存在问题提出一些观点.     

GPU accelerated simulations of 3D deterministic particle transport using discrete ordinates method

Graphics Processing Unit (GPU), originally developed for real-time, high-definition 3D graphics in computer games, now provides great faculty in solving scientific applications. The basis of particle transport simulation is the time-dependent, multi-group, inhomogeneous Boltzmann transport equation. The numerical solution to the Boltzmann equation involves the discrete ordinates (S_n) method and the procedure of source iteration. In this paper, we present a GPU accelerated simulation of one energy group time-independent deterministic discrete ordinates particle transport in 3D Cartesian geometry (Sweep3D). The performance of the GPU simulations are reported with the simulations of vacuum boundary condition. The discussion of the relative advantages and disadvantages of the GPU implementation, the simulation on multi GPUs, the programming effort and code portability are also reported. The results show that the overall performance speedup of one NVIDIA Tesla M2050 GPU ranges from 2.56 compared with one Intel Xeon X5670 chip to 8.14 compared with one Intel Core Q6600 chip for no flux fixup. The simulation with flux fixup on one M2050 is 1.23 times faster than on one X5670.     

Discrete solitons in nonlinear Schrödinger lattices with a power-law nonlinearity

We study the discrete nonlinear Schrödinger lattice model with the onsite nonlinearity of the general form, |u|^2σu. We systematically verify the conditions for the existence and stability of discrete solitons in the one-dimensional version of the model predicted by means of the variational approximation (VA), and demonstrate the following: monostability of fundamental solitons (FSs) in the case of the weak nonlinearity, 2σ+1<3.68; bistability, in a finite range of values of the soliton’s power, for 3.68<2σ+1<5; and the presence of a threshold (minimum norm of the FS), for 2σ+1≥5. We also perform systematic numerical simulations to study higher-order solitons in the same general model, i.e., bound states of the FSs. While all in-phase bound states are unstable, stability regions are identified for antisymmetric double solitons and their triple counterparts. These numerical findings are supplemented by an analytical treatment of the stability problem, which allows quantitively accurate predictions for the stability features of such multipulses. When these waveforms are found to be unstable, we show, by means of direct simulations, that they self-trap into a persistent lattice breather, or relax into a stable FS, or sometimes decay completely.