Convergence and stability of the finite difference scheme for nonlinear parabolic systems with time delay

In this article, a class of nonlinear evolution equations – reaction–diffusion equations with time delay – is studied. By combining the domain decomposition technique and the finite difference method, the results for the existence, convergence and the stability of the numerical solution are obtained in the case of subdomain overlap and when the time-space is completely discretized. This revised version was published online in June 2006 with corrections to the Cover Date.     

Use of Cu dopant and it's doping effects on polyaniline conducting system in water and tetrahydrofuran

The structural modification and properties of polymeric materials are of utmost importance in deciding their applications. In the present study, the synthesis of polyaniline (PANI) has been carried out via chemical oxidation in acidic medium by potassium-dichromate and the yield of synthesized polyaniline was found to be 75-80%. The copper per chlorate tetrabenzonitrile salt (CuClO₄·4BN) used for chemical doping in synthesized polyaniline is stable in organic solvent like acetonitrile (AN) and benzonitrile (BN). The effect of Cu⁺¹ oxidation state (dopant) in polyaniline has been characterized by FTIR. Electrical and dielectric measurements show the decrease in the intensity of the Cu⁺¹ salt signal and the appearance of a radical signal due to the formation of oxidative coupled in polymeric species. Electrical and dielectric properties of doped polyaniline samples show significant changes due to the effect of dopant (CuClO₄·4BN). It is observed that the conductivity is contributing both by formation of ionic complex and particularly dominated by electronic due to the mobility of charge carriers along the polyaniline chain.     

弱噪声极限下二维布朗运动的随机共振现象

在弱噪声极限下，应用多维Fokker-Planck方程的与时间有关问题方面的理论，推导了对称双稳势阱中二维布朗粒子的概率跃迁速率，并基于绝热近似理论研究了弱噪声极限下受小幅低频周期力驱动的二维布朗运动的随机共振现象.与以前的结果相比，所得到的信噪比与阻尼系数的大小无关.精确的数值模拟结果进一步说明了所得的信噪比的适用性. 关键词： 二维布朗运动 弱噪声极限 随机共振 信噪比     

Reactor modeling of magnetically enhanced capacitive RF discharge

Magnetic and collisional effects on capacitive radio frequency (RF) discharges for magnetically enhanced reactive ion etching (MERIE) are investigated. Using simplified plasma and sheath models, a collisional magnetic-sheath equation that governs the sheath dynamics under a de magnetic field crossed with a sinusoidal RF electric field is obtained. The sheath equation includes global effects of the bulk plasma. Together with the power-balance equation and the particle-conservation equation, the sheath equation is used to extract a circuit model and predict the electrical behavior of MERIE reactors. Numerical results on the plasma density and the power in MERIE reactors agree well with reported experimental results and the circuit model describes the repeated discharge properties well     

Impedance model of helical resonator discharge

Modeling and measurement results of the RF input impedance of a helical resonator discharge are given. A simple microstrip transmission line model is used to extract an equivalent circuit of a helical resonator discharge. The transmission line model consists of a grounded cylinder for RF shielding, a helical copper coil for RF heating, and a high density plasma. Transmission line parameters for an experimental helical resonator discharge chamber are extracted, and the results are compared with the measured results. The measured transmission line parameters for the experimental reactor are the characteristic impedance of 200 Ω, the attenuation constant of 6×10^-3 Np/m, and the wave number of 0.36 rad/m, which have good agreement with the calculated values     

RTT关系与长程自旋链模型

证明了具有Yangian对称性的长程互作用可积链模型族必定可以由RTT关系导出 ,从而将这类模型完全纳入Yang-Baxter系统 .讨论具有一般性 ,同时也给出了满足RTT关系的转移矩阵T(u)的量子行列式产生Hamilton量的一般方案     

An asymptotic formula for the voltage potential in the case of a near-surface conductivity inclusion

We rigorously derive an asymptotic expansion of the steady-state voltage potentials in the presence of a conductivity inclusion of small volume that is close to a planar surface. This new formula is motivated by the practically important inverse problem of imaging a conductivity inclusion near a planar interface. Partly supported by ACI Jeunes Chercheurs (0693) from the Ministry of Education and Scientific Research, France. Partially supported by grant R02-2003-000-10012-0 from the Korea Science and Engineering Foundation. Received: December 2, 2003; revised: January 18, 2004     

Effect of magnetic field on the TC and magnetic properties for the aligned MnBi compound

In the compound MnBi, a first-order transition from the paramagnetic to the ferromagnetic state can be triggered by an applied magnetic field and the Curie temperature increases nearly linearly with an increase in magnetic field by ∼2 K/T. Under a field of 10 T, T_C increases by 20 and 22 K during heating and cooling, respectively. Under certain conditions a reversible magnetic field or temperature induced transition between the paramagnetic and ferromagnetic states can occur. A magnetic and crystallographic H-T phase diagram for MnBi is given. Magnetic properties of MnBi compound aligned in a Bi matrix have been investigated. In the low temperature phase MnBi, a spin-reorientation takes place during which the magnetic moments rotate from being parallel to the c-axis towards the basal plane at ∼90 K. A measuring Dc magnetic field applied parallel to the c-axis of MnBi suppresses partly the spin-reorientation transition. Interestingly, the fabricated magnetic field increases the temperature of spin-reorientation transition T_s and the change in magnetization for MnBi. For the sample solidified under 0.5 T, the change in magnetization is ∼70% and T_s is ∼91 K.     

一类新Hardy空间AH~p的小波特征

本文通过引进与Ｂｅｕｒｌｉｎｇ代数Ａ￣ｐ有关的“帐蓬空间”ＴＡ￣ｐ，构造了由Ａ￣ｐ所确定的新Ｈａｒｄｙ空间ＨＡ￣ｐ的小波特征。     

有理Bezier三角曲面片的快速算法

改进了有理Ｂｅｚｉｅｒ三角曲面片及方向导数表示式，并给出点及一阶方向导数的快速算法。该算法比ｄｅ Ｃａｓｔｅｌｊａｎ算法快而且稳定。