Interval parameter perturbation method for evaluating the bounds on natural frequencies of structures with interval parameters

For structural parameters with uncertainties, interval mathematics can, in the case where the probabilistic distribution density of uncertain variables is unavailable, deal with the influence of uncertainties in structural parameters on the response of structures. In order to evaluate the region containing natural frequencies of structures with interval parameters, the interval parameter perturbation method is presented in this paper. The advantage of the present method is its computational efficiency in evaluating the region containing natural frequencies. A numerical example is used to illustrate the efficiency of the method proposed. The project is supported by National Youth Natural Science Foundation of China and National Outstanding Youth Science Foundation of China.     

用奇异摄动法设计线性二次型准最优直流控制系统

利用线性最优调节器理论可以设计出具有良好性能指标的晶闸管直流电机控制系统。这种设计方法优于传统的“双环系统”设计。然而,求解Riccati方程的计算量相当大。为寻求最佳加权Q阵,可能耗费许多时间。采用奇异摄动法设计准最优线性系统时,可以化高阶为低阶,从而简化计算工作量。本文利用奇异摄动理论设计了一个晶闸管直流电动机系统。已肯定本法适应于此类设计。本文还比较了不同设计方法所达到的动态性能。     

On the spectrum of the Heisenberg Hamiltonian

The quantum, antiferromagnetic, spin-1/2 Heisenberg Hamiltonian on thed-dimensional cubic lattice ^d is considered for any dimensiond. First the anisotropic case is considered for small transversal coupling and a convergent expansion is given for a family of eigenprojections which is complete in all finite-volume truncations. Then the general case is considered, for which an upper bound to the ground-state energy is given which is optimal for strong enough anisotropy. This bound is expressed through a functional involving the statistical expectation value at finite temperature of a certain correlation function of an Ising model defined on the lattice ^d itself.     

Dynamic Interfacial Tension Behavior of Water/Oil Systems Containing In situ-Formed Surfactants

Time-dependent interfacial tension (IFT) has been investigated for an interfacially reactive immiscible system composed of model-acidified oil and alkaline water. The acidified oil was composed of either lauric acid or linoleic acid dissolved in n-dodecane. Drop volume tensiometry was employed to measure the interfacial tension between the two phases. In the case of lauric acid, the IFT value was found to decrease sharply with increasing alkali concentration, even at low drop formation times. In the case of linoleic acid, the IFT decrease with the drop formation time was more gradual, especially at low alkali concentration. The rate of formation of the interfacial area was also found to be dependent on alkali concentration.     

Relativistic atomic natural orbital type basis sets for the alkaline and alkaline-earth atoms applied to the ground-state potentials for the corresponding dimers

New basis sets of the atomic natural orbital (ANO) type have been developed for the atoms Li–Fr and Be–Ra. The ANOs have been obtained from the average density matrix of the ground states and the lowest excited states of the atom, the positive ion, and the dimer at its equilibirium geometry. Scalar realtivisitc effects are included through the use of a Douglas–Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of the ground-state potentials for the dimers. Computed bond energies are accurate to within 0.05 eV for the alkaline dimers and 0.02 eV for the alkaline-earth dimers (except for Be₂).Acknowledgments.ensp;B.O.R. would like to express his gratitude to Prof. Jacopo Tomasi for all the inspiration that his scientific work has given him through the years and continues to do in particular through the work on solvent effects on molecular properties. This work has been supported by a grant from the Swedish Science Research Council, VR.Contribution to the Jacopo Tomasi Honorary Issue     

Free energy perturbation approach to the critical assessment of selective cyclooxygenase-2 inhibitors

The discovery of selective cyclooxygenase-2 (COX-2) inhibitors represents a major achievement of the efforts over the past few decades to develop therapeutic treatments for inflammation. To gain insights into designing new COX-2-selective inhibitors, we address the energetic and structural basis for the selective inhibition of COX isozymes by means of a combined computational protocol involving docking experiment, force field design for the heme prothetic group, and free energy perturbation (FEP) simulation. We consider both COX-2- and COX-1-selective inhibitors taking the V523I mutant of COX-2 to be a relevant structural model for COX-1 as confirmed by a variety of experimental and theoretical evidences. For all COX-2-selective inhibitors under consideration, we find that free energies of binding become less favorable as the receptor changes from COX-2 to COX-1, due to the weakening and/or loss of hydrogen bond and hydrophobic interactions that stabilize the inhibitors in the COX-2 active site. On the other hand, COX-1-selective oxicam inhibitors gain extra stabilization energy with the change of residue 523 from valine to isoleucine because of the formations of new hydrogen bonds in the enzyme-inhibitor complexes. The utility of the combined computational approach, as a valuable tool for in silico screening of COX-2-selective inhibitors, is further exemplified by identifying the physicochemical origins of the enantiospecific selective inhibition of COX-2 by -substituted indomethacin ethanolamide inhibitors.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

On the initial layer solution of the Boltzmann equation with small Knudsen number

We extend our method of systematic removal of secular terms in a singular perturbation treatment of the Boltzmann equation with small Knudsen numbers to the initial layer. The requirement that the solution through the initial layer should connect smoothly to the normal solution removes an ambiguity noted in our previous paper. We show that removal of secular terms improves Grad's solution for the initial layer and reintroduces soundlike modes associated with higher moments, first found by Wang Chang and Uhlenbeck.     

Theoretical prediction on vibrational spectra of [Ar…Ar-H]~+

As a special substance between isolated molecules and condensed phase, clusters have drawn more and more attention by theoreticians and experimentalists. The protonated rare gas cluster is one kind of simplest clusters, which can be looked on as the simplest solution composed of the simplest solute, proton, and the simplest solvent, rare gas. The study on such a system can help us to know more about the complex condensed matter. However, the information for the molecular properties of protonat…     

<Emphasis Type="Italic">Ab initio</Emphasis> study of small coinage metal telluride clusters Au<Subscript>n</Subscript>Te<Subscript>m</Subscript> (<Emphasis Type="Italic">n,m</Emphasis> = 1, 2)

The geometries of the most stable isomers of gold telluride systems AuTe, Au₂Te, and AuTe₂ are determined using the MP2 method. The aspect of gold—telluride interaction, the electron correlation, and relativistic effects on geometry and stability are investigated at the MP2 and CCSD(T) theoretical levels. The results show that the electron correlation and relativistic effects are responsible not only for gold—gold attraction but also for additional gold—telluride interaction. The gold—telluride interaction is strong enough to modify the known pattern of bare gold clusters. Both effects are essential for determining the geometry and relative stability of this type of systems.