耦合热弹性动力学的统一变分原理族

对耦合热弹性动力学问题,迄今文献中只建立了Ｇｕｒｔｉｎ型合卷积的统一变分原理,其缺点是只适用于常系数的线性问题,且因含卷积而使实际数值离散和求解复杂化．文中首次成功地建立了耦合热弹性动力学问题经典型（不含卷积）统一变分原理族,其关键是建议了动态差分变换和初终值条件的新处理法．该方法可以推广到各向异性材料以及非线性问题上去,同时在应用有限元法离散和求解上都比较简便．     

Sb、Ce掺杂Mg2Ge的第一性原理研究

此文用基于密度泛函理论(DFT)的第一性原理赝势平面波方法系统的计算了Sb、Ce掺杂Mg₂Ge的能带结构、态密度以及光学性质,获得了Mg₂Ge掺杂Sb后,费米面进入导带,呈现n型导电;Mg₂Ge掺杂Ce后,上自旋电子在费米能级附近处的价带和导带有一部分重叠,呈现半金属特性,进入导带电子数目增多,导电性增强. Sb、Ce掺杂Mg₂Ge后,其主要吸收峰都小于未掺杂Mg₂Ge,在可见光区域的透过率增大;Sb掺入后,在能量低于2.6 eV反射谱出现红移,Ce掺入后Mg₂Ge的吸收范围明显宽于本征Mg₂Ge;掺杂改善了Mg₂Ge对红外光子的吸收等有益结果.     

Optimal Control of Nonlinear Transport-Flow Mixed Variational Problems

Optimal control of nonlinear transport-flow mixed variational problems are studied qualitatively, and the solvability analysis of the transport and flow mixed state systems is performed on the basis of primal and dual evolution duality principles. Corresponding primal and dual mixed optimality conditions are established by the application of some fundamental perturbation conjugate duality results recently proposed [8 G. Alduncin (2013). Optimal control of evolution mixed variational inclusions. Applied Mathematics and Optimization 68:445–473.[Crossref], [Web of Science ®] , [Google Scholar]]. Further, for computational purposes, two- and three-field proximation penalty-duality algorithms in the resolution of the mixed optimality conditions are finally presented and discussed.     

On stochastic and chaotic motion

In this paper we prove results regarding certain precise relationships between random motion and chaotic motion. In particular we prove a strong invariance principle for smooth functions of certain chaotic dynamical systems, and show that solutions of dynamical systems which are coupled to such chaotic systems may be approximated by solutions of stochastic differential equations     

5d过渡金属原子吸附氮化硼纳米管的第一性原理计算

采用基于密度泛函理论的第一性原理计算方法, 研究了氮化硼纳米管六元环中心吸附5d过渡金属原子后体系的几何结构, 电子结构和磁性性质. 研究发现, 吸附原子向一个氮原子或硼原子偏移; 吸附体系在费米能级附近出现明显的杂质能级; 各个体系的总磁矩随原子序数出现规律性变化, 局域磁矩主要分布在吸附原子上.     

How universal are hydrogen bond correlations? A density functional study of intramolecular hydrogen bonding in low-energy conformers of α-amino acids

Hydrogen bonding is one of the most important and ubiquitous interactions present in Nature. Several studies have attempted to characterise and understand the nature of this very basic interaction. These include both experimental and theoretical investigations of different types of chemical compounds, as well as systems subjected to high pressure. The O–H..O bond is of course the best studied hydrogen bond, and most studies have concentrated on intermolecular hydrogen bonding in solids and liquids. In this paper, we analyse and characterise normal hydrogen bonding of the general type, D–H...A, in intramolecular hydrogen bonding interactions. Using a first-principles density functional theory approach, we investigate low energy conformers of the twenty α-amino acids. Within these conformers, several different types of intramolecular hydrogen bonds are identified. The hydrogen bond within a given conformer occurs between two molecular groups, either both within the backbone itself, or one in the backbone and one in the side chain. In a few conformers, more than one (type of) hydrogen bond is seen to occur.

Interestingly, the strength of the hydrogen bonds in the amino acids spans quite a large range, from weak to strong. The signature of hydrogen bonding in these molecules, as reflected in their theoretical vibrational spectra, is analysed. With the new first-principles data from 51 hydrogen bonds, various parameters relating to the hydrogen bond, such as hydrogen bond length, hydrogen bond angle, bond length and vibrational frequencies are studied. Interestingly, the correlation between these parameters in these bonds is found to be in consonance with those obtained in earlier experimental studies of normal hydrogen bonds on vastly different systems. Our study provides some of the most detailed first-principles support, and the first involving vibrational frequencies, for the universality of hydrogen bond correlations in materials.