Uncertainty quantification in a chemical system using error estimate-based mesh adaption

This paper describes a rigorous a posteriori error analysis for the stochastic solution of non-linear uncertain chemical models. The dual-based a posteriori stochastic error analysis extends the methodology developed in the deterministic finite elements context to stochastic discretization frameworks. It requires the resolution of two additional (dual) problems to yield the local error estimate. The stochastic error estimate can then be used to adapt the stochastic discretization. Different anisotropic refinement strategies are proposed, leading to a cost-efficient tool suitable for multi-dimensional problems of moderate stochastic dimension. The adaptive strategies allow both for refinement and coarsening of the stochastic discretization, as needed to satisfy a prescribed error tolerance. The adaptive strategies were successfully tested on a model for the hydrogen oxidation in supercritical conditions having 8 random parameters. The proposed methodologies are however general enough to be also applicable for a wide class of models such as uncertain fluid flows.     

On Suboptimal LCS-alignments for Independent Bernoulli Sequences with Asymmetric Distributions

Let X = X ₁ ... X _n and Y = Y ₁ ... Y _n be two binary sequences with length n. A common subsequence of X and Y is any subsequence of X that at the same time is a subsequence of Y; The common subsequence with maximal length is called the longest common subsequence (LCS) of X and Y. LCS is a common tool for measuring the closeness of X and Y. In this note, we consider the case when X and Y are both i.i.d. Bernoulli sequences with the parameters ϵ and 1 − ϵ, respectively. Hence, typically the sequences consist of large and short blocks of different colors. This gives an idea to the so-called block-by-block alignment, where the short blocks in one sequence are matched to the long blocks of the same color in another sequence. Such and alignment is not necessarily a LCS, but it is computationally easy to obtain and, therefore, of practical interest. We investigate the asymptotical properties of several block-by-block type of alignments. The paper ends with the simulation study, where the of block-by-block type of alignments are compared with the LCS.     

Eu3+-site occupation in CaTiO3 perovskite material at low temperature

In order to clarify the site occupancy of rare-earth ions in rare-earth doped perovskite materials, the un-doped pure CaTiO₃ and Eu³⁺-doped CaTiO₃ samples with a series of Ca/Ti ratio were synthesized via high-temperature solid-state reaction method. X-ray diffraction (XRD) powder patterns confirm that the crystal structure keeps invariant at various Ca/Ti ratios. Measurement results of unit-cell parameters and X-ray photoelectron spectroscopy (XPS) indicate that Eu³⁺ ions enter into the Ca²⁺ site. The high-resolution photoluminescence spectra of Eu³⁺ ions at 20 K in all samples did not witness a significant change under the excitation at different wavelength, implying that Eu³⁺ ions occupy only one type of site. Considering the small spectral splitting range of ⁵D₀ → ⁷F₂ transition and the large intensity ratio of ⁵D₀ → ⁷F₂/⁵D₀ → ⁷F₁, it can be concluded that Eu³⁺ occupies Ca²⁺ site with larger coordinate numbers rather than Ti⁴⁺ site.     

Local defect structures and EPR studies on (FeO6)9− and (FeO4)5− clusters in YGG: Fe3+ system

The octahedral (FeO₆)^9? and tetrahedral (FeO₄)^5? clusters in yttrium gallium garnet (YGG): Fe³⁺ system are investigated based on the 252 × 252 complete energy matrices for d⁵ configuration ions in trigonal and tetragonal ligand fields, moreover, the EPR and optical spectra are made unified calculation. The results indicate that the defect structures around Fe³⁺ centres display expansion effects at different temperatures 4.2 and 295 K, and which are close to those in YIG garnet, respectively. Simultaneously, the defect structure parameters for Fe³⁺ centres in YGG are determined, and the relationship between the defect structure and the temperature has been discussed.     

Analytic approximation of the blow‐up time for nonlinear differential equations by the ADM–Padé technique

We present a new approach to calculate analytic approximations of blow‐up solutions and their critical blow‐up times. Our approach applies the Adomian decomposition–Padé method to quickly and easily compute the critical blow‐up times, which comprises the Adomian decomposition method combined with the Padé approximants technique. We validate our new approach with a variety of numerical examples, including nonlinear ODEs, systems of nonlinear ODEs, and nonlinear PDEs. Furthermore, our new method is shown to be more convenient than prior art that relies on compound discretized algorithms. Copyright © 2013 John Wiley & Sons, Ltd.