加热模型及其最优控制

本文应用Pontryagin最大值原理研究加热过程,提出一个在加热过程中节能的最优控制方案。     

Ab initio方法研究~(40)Ca~(35)Cl分子的自旋轨道耦合效应和跃迁性质

本文研究了~(40)Ca~(35)Cl分子低态的自旋轨道耦合分裂以及获得更精确的光谱常数和更高的激发态.以从头算理论为基础,使用多参考组态相互作用方法获得了该分子的势能曲线和自旋轨道分裂,之后求解径向一维薛定谔方程获得光谱常数.得到了~(40)Ca~(35)Cl分子7个Λ-S低电子态的势能曲线和永久偶极矩,以及A~2Π→~2Σ~+,1~2Δ和C~2Π→~2Σ~+,1~2Δ跃迁的跃迁偶极矩,得到的光谱常数(不管是考虑了自旋轨道耦合(SOC)还是没有考虑SOC)与实验值非常符合,且要好于之前的理论计算结果 .值得注意的是,目前的计算还首次得到了C~2Π→~2Σ+,1~2Δ跃迁的跃迁性质,为之后实验观察~(40)Ca~(35)Cl分子的高激发态光谱和跃迁性质提供有益的理论参考.     

团簇Aun+1-1、AunCr-1 (n=1-10)吸附CO的密度泛函理论研究

采用密度泛函理论对CO在阴离子团簇Aun+1-1、AunCr-1(n=1-10))表面的吸附做了系统研究.结果表明,团簇Aun+1CO-1、AunCrCO-1的基态结构是在团簇Aun+1-1、AunCr-1最低能量结构的基础上吸附CO形成; 吸附后的CO键长变长,振动频率减小,表明CO分子被活化;取值相同时,AunCrCO-1的平均结合能高,表明团簇Aun+1CO-1掺杂Cr后稳定性升高.HOMO-LOMO能隙结果表明Aun+1CO-1替代掺杂Cr原子后团簇的化学活性得到了提升,AunCrCO-1、Aun+1CO-1团簇能隙具有奇偶振荡的现象;轨道电荷分析表明CO与团簇相互作用实质是C原子与成键Au原子或Cr原子间转移电荷,CO在与团簇相互作用过程中O原子轨道电荷分布几乎没有发生变化.     

Efimov's Effect in a Model of Perturbation Theory of the Essential Spectrum

A model operator similar to the energy operator of a system with a nonconserved number of particles is studied. The essential spectrum of the operator is described, and under some natural conditions on the parameters it is shown that there are infinitely many eigenvalues lying below the bottom of the essential spectrum.     

Nonlinear Boundary Stabilization of Nonuniform Timoshenko Beam

In this paper, the stabilization problem of nonuniform Timoshenko beam by some nonlinear boundary feedback controls is considered. By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, it is shown that the vibration of the beam under the proposed control actiondecays exponentially or in negative power of time t as t→∞.     

Global smooth solutions to the multi-dimensional hydrodynamic model for two-carrier plasmas

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.     

Some noncoercive parabolic equations with lower order terms in divergence form

This paper deals with existence and regularity results for the problem $ \cases{u_t-\mathrm{div}(a(x,t,u )\nabla u)=-\mathrm{div}(u\,E) \qquad in \Omega\times (0,T),\cr u=0 \qquad on \partial \Omega\times (0,T), \cr u (0)= u_0 \qquad in \Omega ,\cr} $ under various assumptions on E and $ u_0 $. The main difculty in studying this problem is due to the presence of the term div(uE), which makes the differential operator non coercive on the "energy space" $ L^2 (0, T; H_0^1 (\Omega)) $.AMS Subject Classification: 35K10, 35K15, 35K65.     

低密度氢气的分子间平均相互作用势理论和计算

本文提出了分子单中心模型,并通过对构型的平均,两个定理的提出与证明,色散能修正的证明,从数学上论证了这个模型的合理性。由此模型可以直接求出两个氢分子间的平均相互作用势,从而改变了长期以来,总是先算有限几种构型然后再作平均的传统作法。通过数字计算,得到了迄今为止最好的全程平均相互作用势曲线。势阱深度及平衡分子间距分别为-2.91meV和3.44(实验值:-2.85～-3.00meV,3.43～3.49)。     

二维变系数扩散方程交替分组显格式的稳定性分析

1.引言 由于高性能并行计算机的出现和并行计算的推动,十多年来,抛物型方程有限差分并行算法设计与分析一直受到关注. D.J.Evalns和A.R.B.Abdullah(1983,[1,2]利用Saul’yev非对称格式对常系数抛物方程设计了AGE(交替分组显格式)算法,并用矩阵分析的方法证明了该算法的无条件稳定性.该算法有明显的并行性,倍受推崇,且计算的实践([8],[9])表明它对变系数的抛物方程也是可行的,但稳定性的分析成为一个难点.张宝琳([3])在一维情     

变系数波动方程所决定的控制系统的最小能量控制和快速控制问题

本文研究变系数波动方程所决定的控制系统的最小能量控制和快速控制问题 .在所讨论的系统精确可控的前提下 ,得到了系统的最小能量控制和快速控制的解析表达式