Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Excited-state dynamics of (SO2)m clusters

A study of the excited-state dynamics of (SO2)m clusters following excitation by ultrafast laser pulses in the range of 4.5 eV (coupled 1A2, 1B1 states) and 9 eV (F band) is presented. The findings for the coupled 1A2 and 1B1 states are in good agreement with published computational work on the properties of these coupled states. A mechanism involving charge transfer to solvent is put forward as the source of the excited-state dynamics that follow the excitation of the SO2 F band within (SO2)m+1 clusters with m > 1. The proposed CTTS mechanism is supported by calculations of the energetics of the process and the observed trends in the excited-state lifetimes that correlate very well with the calculated energies.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

Photoinduced ion-pair formation in the (HI)m(H2O)n cluster system

The temporal behavior of the photoinduced ion-pair formation process in the (HI)m(H2O)n (n=1-6 for m=1 and n=1-4 for m=2) cluster system has been studied via the coupling between the g 3Sigma- Rydberg and V 1Sigma+ valence states. Comparison of the time constants obtained to those measured in previous experiments for the analogous process in HBr-water clusters, along with a detailed analysis of the signal intensity as a function of laser-pulse power, provides new insight into and confirmation of the previously proposed ion-pair formation mechanism.     

Ultrafast dynamics of the SO2(H2O)n cluster system

An investigation of the excited-state dynamics of SO2(H2O)n (n = 1-5) clusters following excitation by ultrafast laser pulses to 4.7 eV (coupled 1A2 and 1B1 states) and 9.3 eV (F band) is presented. The findings for the coupled 1A2 and 1B1 states are in good agreement with published computational work and indicate the division of the initial excited-state population into the double well produced by the coupled states. A photoinduced ion-pair formation process is proposed as a likely source of the observed dynamic behavior following the 9.3 eV excitation. Energetics calculations are also presented that support the ion-pair mechanism. A lack of cluster size dependence in the measured time constants indicate surface solvation of SO2 rather than a cluster structure with the SO2 molecule fully encompassed by water molecules.     

The electron energy loss spectrum of LiF in the band gap region

The eels of LiF has been measured in the range 0–18 eV with primary beam energies 50 eV and 1.5 keV. Four peaks are clearly resolved in the band gap region at room temperature. The amplitude of the three lower energy loss peaks was found to depend on beam exposure and temperature. It is concluded that the lowest energy peak arises at a beam induced defect, that the next two peaks arise in lithium metal liberated by the electron beam and that the peak nearest to the band edge is due to an intrinsic surface excitation.