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1.
We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This a posteriori estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. Here, we present a new, carefully designed modification of this error estimate which not only results in less computational work but also appears to perform satisfactorily for singular problems. We give a full analytical justification for the asymptotical correctness of the error estimate when it is applied to a general nonlinear regular problem. For the singular case, we are presently only able to provide computational evidence for the full convergence order, the related analysis is still work in progress. This global estimate is the basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution. Most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.  相似文献   
2.
The exciton-exciton interaction is investigated for spatially indirect excitons in coupled quantum wells. The Hartree-Fock and Heitler-London approaches are improved by a full two-exciton calculation including the van der Waals effect. Using these potentials for the singlet and triplet channel, the two-body scattering matrix is calculated and employed to derive a modified relation between exciton density and blue shift. Such a relation is of central importance for gauging exciton densities on the way toward Bose condensation.  相似文献   
3.
High-accuracy film thickness measurements in the range below 100 nm can be made by various complex methods like spectral ellipsometry (SE), scanning force microscopy (SFM), grazing incidence X-ray reflectometry (GIXR), or X-ray fluorescence analysis (XRF). The measurement results achieved with these methods are based on different interactions between the film and the probe. A key question in nanotechnology is how to achieve consistent results on a level of uncertainty below one nanometre with different techniques.Two different types of thickness standards are realised. Metal film standards for X-ray techniques in the thickness range 10 to 50 nm are calibrated by GIXR with monochromatised synchrotron radiation of 8048 eV. The results obtained at four different facilities show excellent agreement. SiO2 on Si standards for SE and SFM in the thickness range 6 to 1000 nm are calibrated by GIXR with monochromatised synchrotron radiation of 1841 eV and with a metrological SFM. Consistent results within the combined uncertainties are obtained with the two methods. Surfaces and interfaces of both types of standards are additionally investigated by transmission electron microscopy (TEM). PACS 61.10.Kw; 68.55.Jk; 06.20.Fn; 06.60.Mr; 07.79.Lh  相似文献   
4.
Stochastic simulations on manifolds usually are traced back to n via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry.  相似文献   
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A systematic extension of Ruedenberg's expansion formula is applied to evaluate two-electron integrals occurring in calculations on molecular structure. Minimum STO basis sets are used for all SCF-calculations within the framework of the MEDO-method (Multipole Expansion of Diatomic Overlap). The errors due to this approximation scheme are almost negligible compared to those introduced by the truncated basis set: LiH, Li2 and N2 are chosen as examples.  相似文献   
9.
The intrinsic acidity constant Kint. of surface silanol groups has been determined by coulometric titration of silicagel at 25° in solutions of the constant ionic strength 0,1M consisting primarily of sodium perchlorate. The experimental data are consistent with   相似文献   
10.
The e.m.f. of the cell Ag, AgCl/NaCl solution/sodium sensitive glass electrode was measured at 25°C. In pure water as a solvent, measured activity coefficients agree with tabulated osmotically determined values; hence, the ideality of the sodium response of the glass electrode is confirmed. Choosing a Tris – Tris. HCl buffer of the constant ionic strength 0,5M as a solvent, the applicability of HARNED'S rule was demonstrated. Conditions for measuring sodium ion concentrations with sodium sensitive glass electrodes are discussed.  相似文献   
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