薄层流中的一类三阶奇摄动边值问题的渐近分析

本文研究薄层流中出现的一类三阶奇摄动数学模型．本文不采用研究其渐近等价的二阶奇摄动微分方程的方法,而利用边界层函数法,直接讨论该数学模型的渐近解,并严格地证明了解的存在唯一性和其渐近解的一致有效性．本文的结果不仅去掉了以往方法所必须的位势条件,纠正了某个不适定的假设,而且推广了以往的结果．     

FS and FS(OH) defect centers at the MgO(1 0 0) surface: cluster and periodic calculations

We present a model of a new paramagnetic defect center which results from the interaction of atomic hydrogen with the MgO(1 0 0) surface. DFT calculations have been performed using periodic supercells and embedded cluster models where long-range polarization effects are included explicitly. The H atom promotes the creation of an oxygen vacancy (F center) by formation of the F_S⁺(OH⁻) defect where an hydroxyl group is adsorbed near an electron trapped in an oxygen vacancy. This new center has some characteristics similar to those of the classical F_S⁺ centers but a smaller formation energy; furthermore, being globally neutral, it can be treated also with supercell methods.     

Direct evidence of the dependence of surface state density on the size of SnO2 nanoparticles observed by scanning tunnelling spectroscopy

In this work, we report a scanning tunnelling spectroscopy (STS) study of 30 and 10 nm tin dioxide nanoparticles. The STS spectra give a surface band gap of 2.5 eV for both samples and show that the density of surface states in the band gap is around 6 times higher for the 30 nm particles than for the 10 nm particles. This provides direct experimental evidence for our theoretical model, which predicts a decrease in the surface state density as the particle size decreases, and partly accounts for the improved sensitivity of gas sensing devices fabricated with nanoparticles.     

Synthesis,structural analysis,and self-assembly of phenylene ethynylene oligomers and their ?F, ?CF3, and ?CH3 substituted derivatives

Oligomers consisting of aromatic building blocks separated by alkynyl units were synthesized by Sonogashira cross-coupling of aryl halides with terminal acetylenes. Strong electron acceptors such as  F and  CF₃ and weak electron donors like  CH₃ were placed as substituents on one of the benzene rings. Acetyl-protected sulfhydryl groups were attached to one end of these molecules to promote their self-organization on gold surfaces. The electron-transport properties of such self-assembled monolayers (SAMs) are highly sensitive to the local order of the molecules in the solid state. Single crystals were analyzed by X-ray diffraction experiments that revealed structural details that could lead to a better understanding of the electron-transport properties. The unsymmetrical substitution of the aromatic rings by electron-active groups in the ortho-, meta-, or para positions resulted in changes of such molecular parameters as bonding and torsion angles and planarity. These parameters, in turn, can affect the angle of the molecular attachment to a gold substrate and the density of the resulting SAMs. Patterned SAMs of some of these molecules and comparison alkane thiols were obtained on gold by microcontact printing or flooding. The SAM thickness was determined by spectroscopic ellipsometry. Surface potential differences between adjacent SAMs or between SAMs and the gold substrate were measured by scanning surface potential microscopy under ambient conditions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 541–550, 2004     

Exact analytical expressions for diatomic rotational and centrifugal distortion constants for a Kratzer-Fues oscillator

The exact closed-form expression for the vibrational-rotational eigenvalues of the Kratzer-Fues oscillator served as the starting point for a derivation of exact analytical expressions for the rotational constant B_υ, and the set D_υ to S_υ of centrifugal distortion constants up to 11th-order. The derivations employed the MAPLE symbolic algebra coprocessor. The expressions for B_υ to S_υ were then employed in the calculation of a set of constants for a Kratzer-Fues potential with specified dissociation energy and equilibrium internuclear separation for a hypothetical diatomic molecule with a reduced mass of unity. The tabulated constants serve as a benchmark against which the reliability of various existing or future numerical methods for the determination of rotational and centrifugal distortion constants may be assessed. The near-dissociation behaviour of the calculated constants was also examined and is useful in predicting the behaviour of such constants for real electronic states having pure ionic long-range form.     

The ground state well depth position Rm of Van der Waals molecules and the spectral line shapes

As the ground state potential curve is strongly related to spectral line shapes, the minumum position of the ground state potential is obtained from the experiemental absorption profile k(Δν, T) at high density of the radiating atoms. The temperature dependence of the absorption processes of Hg and Cd lines 253.65 and 326.1 nm, respectively perturbed by inert gases (Xe, Kr, Ar and Ne) had been carefully studied over a wide spectral range. Using the point of the maximum temperature dependence Δν_m in each case, we are able to calculate the position of the ground state potential R_m using a simple formula.     

Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329–4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios. AMS Subject Classifications: 60G60, 60G15, 62M15, 60H15     

On the existence of a variational principle for an operator equation with second derivative with respect to “ time”

Using methods of nonlinear functional analysis, we define the structure of an evolution operator equation of second order that can be formulated in direct variational terms.     

Electrokinetic Response of Double Layers

Based on electrokinetic equations, we calculate the dynamic response of the thin double layer of a charged surface. The double layer response acts as effective boundary conditions for the ion concentrations, flow field, and potential outside the double layer. The results can be used to further calculate the electrophoresis or the dielectric spectrum of the deformable charged suspensions.