He-HCl体系各向异性势及分波散射截面的理论研究

首先用BFW势函数形式拟合了在CCSD(T)/aug-cc-pVQZ理论水平下计算的He-HCl相互作用能数据，获得了He原子与HCl分子相互作用的各向异性势；然后采用CC近似方法计算了He-HCl碰撞体系的微分散射截面和分波散射截面，并总结了分波散射截面的变化规律.结果表明，拟合势不但表达形式简洁，而且较好地描述了He-HCl系统相互作用的各向异性特征；利用碰撞体系分子间势的量子化学从头计算结果，可解决势能参数难以确定的问题.对进一步研究原子与分子碰撞机理有一定参考价值. 关键词： 各向异性势 势能参数 密耦近似 分波散射截面     

一类非线性方程解的存在和唯一性及在图像中的应用

本文我们给出一个修正的非线性扩散方程模型，与Cotte Lions和Morel的模型相比该模型有许多实质上的优点。主要的想法是把原来去噪声部分：卷积Gauss过程替代为解一个有界区域上的线性抛物方程问题，因此避开了对初始数值如何全平面延拓的问题。我们从数学上的证明该问题解的存在性和适定性，同时给出对矩形域情况的解的级数形式。最后我们给基于本模型的数值计算差分模型，并且给出几个具体图像在该模型下处理结果。     

用各向异性介质构造的一维光子晶体的特性分析

本文根据单轴晶体的传输矩阵，研究了一种由各向异性介质周期排列构成的一维光子晶体，分析了在不同入射角度和折射率条件下，该周期结构的反射和偏振的光学特性。分析结果表明，各向异性介质在折射率比值较大或与高折射率同性介绍结合使用，可获得较宽的禁带，并可实现在可见光范围内的全偏振全角度反射。     

Atomistic packing models for experimentally investigated swelling states induced by CO2 in glassy polysulfone and poly(ether sulfone)

Atomistic packing models have been created, which help to better understand the experimentally observed swelling behavior of glassy polysulfone and poly (ether sulfone), under CO₂ gas pressures up to 50 bar at 308 K. The experimental characterization includes the measurement of the time‐dependent volume dilation of the polymer samples after a pressure step and the determination of the corresponding gas concentrations by gravimetric gas‐sorption measurements. The models obtained by force‐field‐based molecular mechanics and molecular dynamics methods allow a detailed atomistic analysis of representative swelling states of polymer/gas systems, with respect to the dilation of the matrix. Also, changes of free volume distribution and backbone mobility are accessible. The behavior of gas molecules in unswollen and swollen polymer matrices is characterized in terms of sorption, diffusion, and plasticization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1874–1897, 2006     

一类非经典扩散方程整体解的存在唯一性及长时间行为

本文讨论非经典扩散方程第一初边值问题整体解的存在唯一性及长时间行为，建立了一系列新的结果，较好地改进许多已有的结论．     

Very high coercivities of top-layer diffusion Au/FePt thin films

The Au/FePt samples were prepared by depositing a gold cap layer at room temperature onto a fully ordered FePt layer, followed by an annealing at 800 °C for the purpose of interlayer diffusion. After the deposition of the gold layer and the high-temperature annealing, the gold atoms do not dissolve into the FePt Ll₀ lattice. Compared with the continuous FePt film, the TEM photos of the bilayer Au(60 nm)/FePt(60 nm) show a granular structure with FePt particles embedded in Au matrix. The coercivity of Au(60 nm)/FePt(60 nm) sample is 23.5 kOe, which is 85% larger than that of the FePt film without Au top layer. The enhancement in coercivity can be attributed to the formation of isolated structure of FePt ordered phase.     

Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.     

Application of the finite Hankel transform to a diffusion problem without azimuthal symmetry

The problem treated in this paper concerns calculating the evolution of the pressure in a single-phase, slightly compressible fluid in a porous medium consisting of communicating layers. The fluid is produced through a point sink located on the side of an otherwise sealed cylindrical wellbore. This location of the sink causes the flow around the wellbore to be azimuthally asymmetric.The problem is solved through successive application of Laplace, finite Fourier and finite Hankel transforms. Although apparently straightforward, this approach leads to serious numerical difficulties. The published form of the inversion formula for the finite Hankel transform leads to inaccurate computation for the higher azimuthal modes even with 128 bit arithmetic. An alternative form is developed which enables accurate evaluation of the solution with the more practical 64 bit arithmetic. The technique for two-layer solution presented here can be directly extended to a problem with a larger number of communicating layers. This is the first instance of successful application of the finite Hankel transform to an azimuthally asymmetric diffusion problem.     

一种新的高次边缘元方法

讨论了一种新的高次边缘元方法，它不仅消除了伪解，并具有简单高效的特点．着重研究了二次边缘元的空间构造；给出了有关计算公式．对具有精确解的条形介质填充波导主模和高次模本征值的计算表明：二次边缘元方法的计算精度比一次边缘元提高约一个数量级．块状介质填充和衬底各向异性的微带线主模色散曲线的计算证实了该方法的精确性和广泛的适用性．