Multilevel a posteriori error analysis for reaction–convection–diffusion problems

We present a new approach to the a posteriori error analysis of stable Galerkin approximations of reaction–convection–diffusion problems. It relies upon a non-standard variational formulation of the exact problem, based on the anisotropic wavelet decomposition of the equation residual into convection-dominated scales and diffusion-dominated scales. The associated norm, which is stronger than the standard energy norm, provides a robust (i.e., uniform in the convection limit) control over the streamline derivative of the solution. We propose an upper estimator and a lower estimator of the error, in this norm, between the exact solution and any finite dimensional approximation of it. We investigate the behaviour of such estimators, both theoretically and through numerical experiments. As an output of our analysis, we find that the lower estimator is quantitatively accurate and robust.     

Applications of density functional theory methods in millimeter‐wave spectroscopy

Density functional theory (DFT), using the most common functionals, and ab initio quantum chemistry methods are used to calculate the rotational constants and dipole moments of the astrophysically important molecules HCN, CH₃CN, CH₃CNH⁺, HCCCN, and HCCNC. As far as millimeter‐wave spectroscopy is of interest the DFT methods performed well with most functionals, giving results within ±1% of experiments for rotational constants and ±3% for dipole moments. Analyzing the results obtained with all theoretical models, it may be concluded that the Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Paar (B3LYP) and Becke's three‐parameter functional with Perdew–Wang correlational functional [B3PW91/6‐31G(d, p)] give the best performances. A detailed analysis of the electron correlation effects shows that HCCCN is more stable than is HCCNC, by 1.16 eV, with important contribution arising from triple excitations. This result is also compared with those obtained with DFT methods. Despite occasional difficulties, DFT with the currently available functionals are of great utility in quickly assessing spectroscopic parameters of astrophysical interest. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

A fictitious domain approach to the numerical solution of PDEs in stochastic domains

We present an efficient method for the numerical realization of elliptic PDEs in domains depending on random variables. Domains are bounded, and have finite fluctuations. The key feature is the combination of a fictitious domain approach and a polynomial chaos expansion. The PDE is solved in a larger, fixed domain (the fictitious domain), with the original boundary condition enforced via a Lagrange multiplier acting on a random manifold inside the new domain. A (generalized) Wiener expansion is invoked to convert such a stochastic problem into a deterministic one, depending on an extra set of real variables (the stochastic variables). Discretization is accomplished by standard mixed finite elements in the physical variables and a Galerkin projection method with numerical integration (which coincides with a collocation scheme) in the stochastic variables. A stability and convergence analysis of the method, as well as numerical results, are provided. The convergence is “spectral” in the polynomial chaos order, in any subdomain which does not contain the random boundaries.     

Theoretical studies of photodissociation and rydbergization in the first triplet state (3s3A″2) of ammonia

Ab initio investigations at the RHF and CI levels have been carried out on a section of the potential energy surface of the Rydberg 3s³A″₂ state of NH₃ leading to dissociation into NH₂(²B₁) and H(²S). It was found that the barrier towards dissociation is due to a Rydberg-valence transformation. The barrier height calculated with the CI wavefunction is significantly smaller than at the RHF level The results may explain the difficulties associated with experimental observation of the 3s³A″₂ state.     

种植沙生植物--沙棘改善内蒙古地区生态环境

结合内蒙古地区现状，对沙棘的生物学和生态学特性、沙棘属植物化学成分和微量元素及种植沙生植物——沙棘的重要性和必要性进行了详细的研究和探讨。研究表明，沙棘属植物具有极强的生态适应性并富含多种营养成分和生物活性物质，并以耐干旱、耐瘠薄、萌蘖及固氮能力强等特点被称为治理非宜林地水土流失、改善生态环境的先锋树种。种植沙棘是治理内蒙古脆弱生态环境最经济、最有效的措施，是贫瘠的不毛之地发展经济、增加收入的经济树种。另外．种植沙棘的技术简便，容易掌握，投资少，见效快。