量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

基于红外吸收光谱的瓦斯气体浓度检测技术

针对现有矿井瓦斯传感器的缺点,基于红外光谱吸收原理,采用差分吸收技术设计了红外瓦斯气体浓度探测系统。该系统采用单光路吸收气室和单光路双波长探测技术,利用差动放大电路为核心的微弱信号处理电路实现瓦斯浓度输出信号的检测,并采用线性关系式拟合瓦斯浓度和输出电压的关系曲线,实现了对瓦斯浓度的全量程精确探测。实验表明,该系统的测量误差小于2%,具有很高的测量精度,具备了煤矿应用的基础。     

用光学干涉法测量材料的高温线膨胀系数

采用石英传递杆将高温区材料的线膨胀量传递到室温区,并利用标准件进行标定的方法消除由传递带来的附加线膨胀量的影响,利用迈克耳孙干涉仪测量微小位移的原理,测量材料的线膨胀系数;测量相对误差仅为1.0％,而且测量过程非常直观简单.     

推导粒子数态波函数的厄米多项式算符法

引入厄米多项式算符并用其正规乘积展开式推导出了粒子数态|n〉在坐标表象和动量表象下的波函数,并由此得出了坐标和动量本征态的福克(Fock)表示形式,这是一个简洁而全新的推导方法.     

sine-Gordon型方程的无穷序列新精确解

为了获得sine-Gordon型方程的无穷序列精确解,给出三角函数型辅助方程和双曲函数型辅助方程及其Bäcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,构造了sine-Gordon方程、mKdV-sine-Gordon方程、(n+1)维双sine-Gordon方程和sinh-Gordon方程的无穷序列新精确解.其中包括无穷序列三角函数解、无穷序列双曲函数解、无穷序列Jacobi椭圆函数解和无穷序列复合型解. 关键词： sine-Gordon型方程 解的非线性叠加公式 辅助方程 无穷序列精确解     

Analysis of thermodynamic identities for materials under extreme compression

Some basic relationships for materials under extreme compression are analyzed with the help of the calculus of indeterminates. The analysis presented here provides an understanding of the origin of identities and constraints at infinite pressure which are satisfied by all physically acceptable equations of state. These identities involve the bulk modulus and its pressure derivatives, the Grüneisen parameter and its volume derivatives, the thermal expansivity, and the Anderson-Grüneisen parameter. The identity for the third-order Grüneisen parameter in terms of the pressure derivatives of the bulk modulus at extreme compression is valid even if the free-volume parameter changes with pressure.     

Apatite type lanthanum silicate and composite anode half cells

Apatite type rare earth silicates are being extensively studied as electrolyte material for intermediate temperature solid oxide fuel cells (SOFC). In this paper we presents results on synthesis of Al and/or Fe-doped ATLS, the design of compatible anode materials, thermal expansion properties and co-sintering of half-cells from expansion matched materials using the advanced pulsed electric current sintering (PECS) technique. The issues related to the co-sintering of half cells have been addressed successfully by the combined use of nano powders and PECS.     

High-temperature electrical properties of magnesiowustite Mg1 − xFexO and spinel Fe3 − x − yMgxCryO4 ceramics

Phase relationships, thermal expansion and electrical properties of Mg_1 − xFe_xO (x = 0.1-0.45) cubic solid solutions and Fe_{3 − x − y}Mg_xCr_yO_4 ± δ (x = 0.7-0.95; y = 0 or 0.5) spinels were studied at 300-1770 K in the oxygen partial pressure range from 10 Pa to 21 kPa. Increasing iron content enlarges the spinel phase stability domain at reduced oxygen pressures and elevated temperatures. The total conductivity of the spinel ceramics is predominantly n-type electronic and is essentially p(O₂)-independent within the stability domain. The computer simulations using molecular dynamics technique confirmed that overall level of ion diffusion remains low even at high temperatures close to the melting point. Temperature dependencies of the total conductivity in air exhibit a complex behavior associated with changing the dominant defect-chemistry mechanism from prevailing formation of the interstitial cations above 1370-1470 K to the generation of cation vacancies at lower temperatures, and with kinetically frozen cation redistribution in spinel lattice below 700-800 K. The average thermal expansion coefficients of the spinel ceramics calculated from dilatometric data in air vary in the range (9.6-10.0) × 10^− 6 K^− 1 at 300-500 K and (13.2-16.1) × 10^− 6 K^− 1 at 1050-1370 K. Mg_1 − xFe_xO solid solutions undergo partial decomposition on heating under oxidizing and mildly reducing conditions, resulting in the segregation of spinel phase and conductivity decrease.     

Obtaining certificates for complete synchronisation of coupled oscillators

In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators.     

随机对流扩散方程的数值仿真

本文针对对流一扩散随机过程在随机输入（即随机输运和源项）,作用下进行数值仿真。我们先将对流扩散随机微分方程中的随机函数采用有限项截断的多项式浑沌展开（Polynomial Chaos Expansion）展开,再由Galerkin映射法得到求解浑沌展开系数的确定性方程组。这是一个在物理空间包含多尺度解的大方程组。为此我...